Redshift FAQ article development

[PAllen]

I think that should be a sufficient coverage on Cosmic distance ladder. Article looks good now,

Very nice! I hope a few more people proof read it for polishing, but it looks good enough to me.

 

[Mordred]

EXPANSION AND REDSHIFT
1) Why are all the galaxies accelerating from us ?
2) Is Redshift the same as Dopplershift ?
3) What is causing the expansion of the Universe ?
4) Is Expansion, faster than light in parts of the Universe, and How does this not violate the faster than light speed limit ?
5) What is a Cepheid or standard candle ?
6) What do we mean when we say Homogeneous and Isotropic ?
7) How do we measure the distance to Galaxies ?
8) What is outside the Universe?
9) What do we mean when an object leaves our universe ?
10) Why is the CMB, so vital in cosmology ?

These are some of the common questions I will attempt to address in the following article

First we must define some terms and symbols used.

Planck constant: h\ =\ 6.62606876(52)\ \times\ 10^{-34}\ J\ s
Gravitational constant: G\ =\ 6.673(10)\ \times\ 10^{-11}\ m^{3} kg^{-1} s^{-2}
Speed of light in a vacuum:c\ =\ 2.99792458\ \times\ 10^{8}\ m\ s^{-1}

The parsec (symbol: pc) is a unit of length used in astronomy, equal to about 30.9 trillion kilometres(19.2 trillion miles). In astronomical terms, it is equal to 3.26 light-years, and in scientific terms it is equal to 3.09×10¹³ kilometres
Mpc=1 million Parsecs

Universe: The Universe in cosmology is defined as the Observable Universe The Observable universe from Earth is 46 Billion light years, or 4.3×10²⁶ meters with an age as of 2013, is 13.772 ± 0.059 billion years. So how do we see farther than 13.772 billion years, the answer lies in expansion. As light is traveling towards us, spacetime has expanded.
One common Question posters often ask is " What is outside our Universe, this question has no meaning as without space or time you have nonexistence. Also their is no clear consensus on, if the Universe is Finite or Infinite. " When an object is said to leave our universe" we mean that the object has crossed the observable universe or rather that it is redshifted to the point of non detectable.


The CMB, (Cosmic Microwave Background) The CMB is thermal radiation filling the Observable universe almost uniformaly, This provides strong evidence of the Homogeneous and Isotropic measurements and of distances. As the universe expanded, both the plasma and the radiation filling it grew cooler. When the universe cooled enough, protons and electrons combined to form neutral atoms. These atoms could no longer absorb the thermal radiation, and so the universe became transparent instead of being an opaque fog. Precise measurements of cosmic background radiation are critical to cosmology, since any proposed model of the universe must explain this radiation. . CMB photons were emitted at about 3000 Kelvin and are now 2.73 Kelvin blackbody radiation. CMB photons were emitted at about 3000 Kelvin and are now 2.73 Kelvin blackbody radiation. Their currently observed energy is 1/1000th of their energy as emitted

Doppler shift and redshift are the same phenomenon in general relativity. Often, however, you will see Doppler factored into components with different names used, as will be explained below. In all cases of Doppler, the light emitted by one body and received by the other will be Red/Blue shifted ie its wavelength will be stretched. So the color of the light is more towards the red/blue end of the spectrum. As shown by the formula below.

\frac{\Delta_f}{f} = \frac{\lambda}{\lambda_o} = \frac{v}{c}=\frac{E_o}{E}=\frac{hc}{\lambda_o} \frac{\lambda}{hc}


The Doppler Redshift results from the relative motion of the light emitting object and the observer. If the source of light is moving away from you then the wavelength of the light is stretched out, i.e., the light is shifted towards the red. When the wavelength is compressed from an object moving towards you then it moved towards the blue end of the spectrum. These effects, individually called the blueshift, and the redshift are together known as doppler shifts. The shift in the wavelength is given by a simple formula

(Observed wavelength - Rest wavelength)/(Rest wavelength) = (v/c)

f=\frac{c+v_r}{c+v_s}f_o



c=velocity of waves in medium
v_r is the velocity measured by the source using the source’s own proper-time clock(positive if moving toward the source
v_s is the velocity measured by the reciever using the source’s own proper-time clock(positive if moving away from the reciever)

The above are for velocities where the source is directly away or towards the observer and for low velocities less than relativistic velocities. A relativistic doppler formula is required when velocity is comparable to the speed of light. There are different variations of the above formula for Tansverse Doppler shift or other angles.
Doppler shift is used to describe Redshift due to inertial velocity one example is a car moving away from you the light will be Red Shifted, as it approaches you the light and sound will be blueshifted. In general relativity and cosmology, there is a fundamental complication in this simple picture - relative velocity cannot be defined uniquely over large distances. However, it does become unique when compared along the path of light. With relative velocity compared along the path of the light, the special relativity Doppler formula describes redshift for all situations in general relativity and cosmology. It is important to realize that gravity and expansion of the universe affect light paths, and how emitter velocity information is carried along a light path; thus gravity and expansion contribute to Doppler redshift.


The Cosmological Redshift is a redshift attributed to the expansion of space. The expansion causes a Recession Velocity for galaxies (on average) that is proportional to DISTANCE. This recession velocity then produces a Doppler (red) shift proportional to distance (please note that this recession velocity must be converted to a relative velocity along the light path before it can be used in the Doppler formula). The further away an object is the greater the amount of RedShift. This is given in accordance with Hubbles Law. In order to quantify the velocity of this galactic movement, Hubble proposed Hubble's Law of Cosmic Expansion, aka Hubble's law, an equation that states:

Hubbles Law: The greater the distance of measurement the greater the recessive velocity

velocity = H₀ × distance.


Velocity represents the galaxy's recessive velocity; H₀ is the Hubble constant, or parameter that indicates the rate at which the universe is expanding; and distance is the galaxy's distance from the one with which it's being compared.

The Hubble Constant has been calculated at different values over time, this is essential as the rate of expansion varies over time but the current accepted value is 70 kilometers/second per megaparsec, or Mpc. The latter being a unit of distance in intergalactic space described above.
Any measurement of redshift above the Hubble distance defined as H₀ = 4300±400 Mpc will have a recessive velocity of greater than the speed of light. This does not violate GR because a recession velocity is not a relative velocity or an inertial velocity. It is precisely analogous to a separation speed. If, in one frame of reference, one object is moving East at .9c, and another West at .9c, they are separating by 1.8c. This is their recession velocity. Their relative velocity remains less than c. In cosmology, two things change from this simple picture: expansion can cause separation speeds much greater even than 2c; and relative velocity is not unique, but no matter what path it is compared along, it is always less than c, as expected.

z = (Observed wavelength - Rest wavelength)/(Rest wavelength) or more accurately

1+z= λ_observed/λ_emitted or z=(λ_observed-λ_emitted)/λ_emitted



1+Z=\frac{\lambda}{\lambda_o} or 1+Z=\frac{\lambda-\lambda_o}{\lambda_o}

λ₀= rest wavelength
Note that positive values of z correspond to increased wavelengths (redshifts).
Strictly speaking, when z < 0, this quantity is called a blueshift, rather than
a redshift. However, the vast majority of galaxies have z > 0. One notable blueshift example is the Andromeda Galaxy, which is gravitationally bound and approaching the Milky way.

WMAP nine-year results give the redshift of photon decoupling as z=1091.64 ± 0.47 So if the matter that originally emitted the oldest CMBR photons has a present distance of 46 billion light years, then at the time of decoupling when the photons were originally emitted, the distance would have been only about 42 million light-years away.


Cosmological Redshift is distance dependant as mentioned above, if you were to teleport to the other side of the galaxy where you measured that greater than light recessive velocity, you would find the same expansion rate as your original location relative to an equal distance. Indeed expansion occurs the same throughout the cosmos. However Gravity in Galaxy clusters are strong enough to prevent expansion. In other words galaxy clusters are gravitationally bound.

In regards to expansion it is important to realize that galaxies are not moving from us due to inertia, rather the space between between two coordinates are expanding. This is important in that no FORCE is acting upon the galaxies to cause expansion. That expansion is homogeneous and isotropic. In other words, there is no preferred location (Homogeneous) and no preferred direction (Isotropic). Keep in mind these terms describe the universe on large scales. Indeed below 100 Mpc we know that galaxy clusters, large scale clusters are not homogeneous or isotropic.
As expansion is homogeneous and isotropic then there is no difference in expansion at one location or another. In the LambdaCDM model expansion is attributed to the cosmological constant.

Cosmological Constant is a homogeneous energy density that causes the expansion of the universe to accelerate. Originally proposed early in the development of general relativity in order to allow a static universe solution it was subsequently abandoned when the universe was found to be expanding. Now the cosmological constant is invoked to explain the observed acceleration of the expansion of the universe. The cosmological constant is the simplest realization of dark energy, which is the more generic name given to the unknown cause of the acceleration of the universe. Indeed what we term as "Dark" energy is an unknown energy that comprises most of the energy density of our cosmos around 73%. However the amount of dark energy per M³ is quite small some estimates are around about 6 × 10^-10 joules per cubic meter. However their is a lot of space between Large scale clusters, so that small amount per M³ adds up to a significant amount of energy in total

Another term often used for the cosmological constant is vacuum energy described originally by the false vacuum inflationary Model by A.Guth. The cosmological constant uses the symbol Λ . the greek letter Lambda.
This False vacuum inflationary model is one that describes a total energy balance of zero, where gravity is the negative energy. In this model what we term as "Nothing " is really a quantum vacuum with quantum fluctuations described by the Heisenburg uncertainty principle. Virtual particles pop in and out of existence all the time, As expansion occurs those virtual particles Quantum tunnel between the false vacuum and the true vacuum, becoming real particles. The full explanation is a little more involved than this quick explanation however this model is often referred to as a "Universe from Nothing" or the "Ultimate free lunch" . Many of our current inflationary models have their roots in this model. However one fundamental problem with all inflationary models is "Runaway expansion" Once the process starts no one has found a mechanism to stop expansion.
One means of relating to expansion is with the use of the a grid of squares. Each horizontal and vertical crossing on that grid is a coordinate. In expansion the space between all coordinates not gravitationally bound expand equally. In other words the coordinates do not change, the space between coordinates change. I should also note their is no clear consensus on whether the universe is finite or infinite. If its infinite now then it was infinite in the past. Same with Finite. The Big Bang model only describes the Universe from 10-⁴³ seconds and is not considered as starting from a black hole singularity, rather its properly described as a rapid expansion of spacetime.

WMAP data confirms that the universe is flat or close to flat.


Gravitational Redshift describes Doppler between static emitter and receiver in a gravitational field. Static observers in a gravitational field are accelerating, not inertial, in general relativity. As a result (even though they are static) they have a relative velocity in the sense described under Doppler. Because they are static, so is this relative velocity along a light path. In fact, the relative velocity for Doppler turns out to depend only on the difference in gravitational potential between their positions. Typically, we dispense with discussion of the relative velocity along a light path for static observers, and directly describe the resulting red shift as a function of potential difference. When the potential increases from emitter to receiver, you have red shift; when it decreases you have blue shift. The formula below is the gravitational redshift formula or Einstein shift in an uncharged, non rotating, spherical mass.
<br /> \frac{\lambda}{\lambda_o}=\frac{1}{\sqrt{(1 - \frac{2GM}{r c^2})}}<br />


G=gravitational constant
c=speed of light
M=mass of gravitational body
r= distance from gravitational body of Mass M

Cosmic Distance ladder, also known as extragalactic distance scale. Is easily thought of as a series of different
measurement method's at different distance scales. Rather than cover a large range of those distance scales or rungs on the ladder I will cover a few of the essential steps to cosmological distance scales. The first rung on the ladder is naturally.

Direct measurements: Direct measurements form the fundamental distance scale. Units such as the distance from Earth to the sun that are used to develop a fundamental unit called astronaumical unit or AU. During the orbit around the sun we can take a variety of measurements such as Doppler shifts to use as a calibration for The AU unit. This Unit is also derived by a method called Parallax.

Parallax. Parallax is essentially trigonometric measurements of a nearby object in space. When our orbit forms a right angle triangle to us and the object to be measured
With the standardized AU unit we can take two AU to form the short leg. The Sun at right angle to us the distance to the object to be measured.

Moving Cluster Parallax is a technique where the motions of individual stars in a nearby star cluster can be used to find the distance to the cluster.

Stellar parallax is the effect of parallax on distant stars . It is parallax on an interstellar scale, and allows us to set a standard for the Parsec.

Standard Candles A common misconception of standard candles is that only type 1A supernova are used. Indeed any known fundamental distance measurement, In particular a Stellar objects Luminousity or brightness. By comparing an objects Luminousity to the observed brightness we can calculate the distance to an object using the inverse square law. Standard candles include any object of known Luminousity, such as Cepheids, Novae, Type 1A Supernova. Galaxy clusters.

My thanks to the following Contributors for their feedback and support.

PAllen
Naty1
Jonathon Scott
marcus

Article by Mordred, PAllen

 

[Mordred]

Just added the contributors list to the article.

 

[DennisN]

Very nice! I hope a few more people proof read it for polishing, but it looks good enough to me.

I heard a request for an Office Assistant. Your request has been answered... I have read the entire text and I will provide my suggestions below (mostly formal and very little science), from top to bottom:

---------------------------------------------------------------------

Redshift -> redshift
Dopplershift -> Doppler shift
Why is the CMB, so vital in cosmology ? (remove comma)

---------------------------------------------------------------------
There are many words that currently are capitalized, but should not be capitalized, unless they are at the start of a sentence.

These are:

Expansion, Homogeneous, Isotropic, Billion, Question, Finite, Infinite, Observable, Redshift, Recession Velocity, Gravity, Galaxy clusters, False vacuum, "Nothing", Quantum tunnel, "Universe from Nothing", "Ultimate free lunch", "Runaway expansion", Parallax, Moving Cluster Parallax

------------------------------------------------------------------------
Further suggestions:


The Observable universe from Earth is 46 Billion light years (ambiguous, use e.g. "The radius of the observable universe is...")

---

"So how do we see farther than 13.772 billion years, the answer lies in expansion. As light is traveling towards us, spacetime has expanded."

This is a question without a question mark, split to e.g.

"So how do we see farther than 13.772 billion years? The answer lies in expansion; as light is traveling towards us, spacetime has expanded."

---

"What is outside our Universe, this question has no meaning as without space or time you have nonexistence."

A question without question mark, split to e.g.

"What is outside our Universe? This question..."

---

concensus -> consensus
non detectable->nondetectable
uniformaly->uniformly

"CMB photons were emitted at about 3000 Kelvin and are now 2.73 Kelvin blackbody radiation."
This is repeated twice. CMB is important, but not that important .

"In all cases of Doppler" - insert "shift", I think.

"Red/Blue shifted"-> "red- or blueshifted"
"red/blue end of the spectrum. As shown by the formula below."
-> "red or blue end of the spectrum, as shown by the formula below."

"reciever"->"receiver" (twice)

"relativistic doppler formula"->"relativistic Doppler formula"

"Tansverse Doppler shift"->"transverse Doppler shift"

Insert punctuation: "Doppler shift is used to describe redshift due to inertial velocity. One example..."

"Red Shifted"->"redshifted"
"RedShift"->"redshift"
"Hubbles Law"->"Hubble's Law" (twice)
"GR"->"general relativity" (it's a newbie FAQ, remember )
"East"->"east", "West"->"west"
"Milky way"->"Milky Way"
"distance dependant"-> e.g. "depending on distance"

"Cosmological Constant"->"The cosmological constant"
"dark energy per M³"->"dark energy per m³"
"small amount per M³"->"small amount per m³"
"Heisenburg uncertainty principle"->"Heisenberg uncertainty principle"

"One means of relating to expansion is with the use of the a grid of squares."
I suggest perhaps
"One way to describe expansion is to use a square grid."

"their is no clear concensus"->"there is no consensus"
"blackhole singularity"->"black hole singularity"
"describes Doppler between static emitter"
->"describes Doppler shift between a static emitter"

"red shift"->"redshift" (multiple)
"blue shift"->"blueshift"
"non rotating"->"nonrotating"
"Cosmic Distance ladder"->"Cosmic distance ladder"
"method's"->"methods"
"the sun"->"The Sun" (twice)
"for The AU unit. This Unit"->"for the AU unit. This unit"
"The Sun at right angle"->"The Sun at a right angle"
"the Parsec"->"the parsec"
"Standard Candles"->"Standard candles"
"In particular a Stellar objects Luminousity or brightness"
->
"In particular a stellar object's luminosity or brightness"
Luminousity -> luminosity (multiple)
"Novae"->"novae", "Supernova"->"supernova", "Galaxy clusters"->"galaxy clusters".

From your friendly office assistant, over and out.

 

[Jonathan Scott]

EXPANSION AND REDSHIFT

One common Question posters often ask is " What is outside our Universe, this question has no meaning as without space or time you have nonexistence. Also their is no clear consensus on, if the Universe is Finite or Infinite. " When an object is said to leave our universe" we mean that the object has crossed the observable universe or rather that it is redshifted to the point of non detectable.

Come on, surely you can do better than this garbled mess! For a start "their is" should be "there is" and "consensus" only has one c (like "consent"), and the double quotes seem to be randomly scattered.

I appreciate your attempts, but I don't think this is anywhere near up to the appropriate quality for an FAQ item so far.

 

[Mordred]

Come on, surely you can do better than this garbled mess! For a start "their is" should be "there is" and "consensus" only has one c (like "consent"), and the double quotes seem to be randomly scattered.

I appreciate your attempts, but I don't think this is anywhere near up to the appropriate quality for an FAQ item so far.

I never claimed the article is complete. Right now were in the proofing stage. That includes better ways to express the ideas presented in the article. In an article this size its easy to miss mistakes, hence multiple eyes

 

[Mordred]

I heard a request for an Office Assistant. Your request has been answered... I have read the entire text and I will provide my suggestions below (mostly formal and very little science), from top to bottom:

---------------------------------------------------------------------

Redshift -> redshift
Dopplershift -> Doppler shift
Why is the CMB, so vital in cosmology ? (remove comma)

---------------------------------------------------------------------
There are many words that currently are capitalized, but should not be capitalized, unless they are at the start of a sentence.

These are:

Expansion, Homogeneous, Isotropic, Billion, Question, Finite, Infinite, Observable, Redshift, Recession Velocity, Gravity, Galaxy clusters, False vacuum, "Nothing", Quantum tunnel, "Universe from Nothing", "Ultimate free lunch", "Runaway expansion", Parallax, Moving Cluster Parallax

------------------------------------------------------------------------
Further suggestions:


The Observable universe from Earth is 46 Billion light years (ambiguous, use e.g. "The radius of the observable universe is...")

---

"So how do we see farther than 13.772 billion years, the answer lies in expansion. As light is traveling towards us, spacetime has expanded."

This is a question without a question mark, split to e.g.

"So how do we see farther than 13.772 billion years? The answer lies in expansion; as light is traveling towards us, spacetime has expanded."

---

"What is outside our Universe, this question has no meaning as without space or time you have nonexistence."

A question without question mark, split to e.g.

"What is outside our Universe? This question..."

---

concensus -> consensus
non detectable->nondetectable
uniformaly->uniformly

"CMB photons were emitted at about 3000 Kelvin and are now 2.73 Kelvin blackbody radiation."
This is repeated twice. CMB is important, but not that important .

"In all cases of Doppler" - insert "shift", I think.

"Red/Blue shifted"-> "red- or blueshifted"
"red/blue end of the spectrum. As shown by the formula below."
-> "red or blue end of the spectrum, as shown by the formula below."

"reciever"->"receiver" (twice)

"relativistic doppler formula"->"relativistic Doppler formula"

"Tansverse Doppler shift"->"transverse Doppler shift"

Insert punctuation: "Doppler shift is used to describe redshift due to inertial velocity. One example..."

"Red Shifted"->"redshifted"
"RedShift"->"redshift"
"Hubbles Law"->"Hubble's Law" (twice)
"GR"->"general relativity" (it's a newbie FAQ, remember )
"East"->"east", "West"->"west"
"Milky way"->"Milky Way"
"distance dependant"-> e.g. "depending on distance"

"Cosmological Constant"->"The cosmological constant"
"dark energy per M³"->"dark energy per m³"
"small amount per M³"->"small amount per m³"
"Heisenburg uncertainty principle"->"Heisenberg uncertainty principle"

"One means of relating to expansion is with the use of the a grid of squares."
I suggest perhaps
"One way to describe expansion is to use a square grid."

"their is no clear concensus"->"there is no consensus"
"blackhole singularity"->"black hole singularity"
"describes Doppler between static emitter"
->"describes Doppler shift between a static emitter"

"red shift"->"redshift" (multiple)
"blue shift"->"blueshift"
"non rotating"->"nonrotating"
"Cosmic Distance ladder"->"Cosmic distance ladder"
"method's"->"methods"
"the sun"->"The Sun" (twice)
"for The AU unit. This Unit"->"for the AU unit. This unit"
"The Sun at right angle"->"The Sun at a right angle"
"the Parsec"->"the parsec"
"Standard Candles"->"Standard candles"
"In particular a Stellar objects Luminousity or brightness"
->
"In particular a stellar object's luminosity or brightness"
Luminousity -> luminosity (multiple)
"Novae"->"novae", "Supernova"->"supernova", "Galaxy clusters"->"galaxy clusters".

From your friendly office assistant, over and out.

Many thanks I'll make those corrections.

 

[Naty1]

This is wrong in GR. ... for Doppler in curved spacetime you must specifically compare (parallel transport) along the light path. Gravity (curvature) affect the light path and how it carries the emitter motion (4 velocity). ...

oops..I did not read the original context carefully...it's clearly and properly stated as a path effect.

 

[Jonathan Scott]

I never claimed the article is complete. Right now were in the proofing stage. That includes better ways to express the ideas presented in the article. In an article this size its easy to miss mistakes, hence multiple eyes

For an FAQ you need to be really straightforward and uncontroversial. It's difficult. I hope others have time to help you sort it out.

Have you tried calculating the redshift (to first order) within a rapidly spinning system such as a space station (a) as a Special Relativity velocity effect and (b) as due to the effective "gravitational potential" experienced within the spinning system because of the centripetal acceleration? I've always felt that's particularly educational.

 

[Mordred]

EXPANSION AND REDSHIFT
1) Why are all the galaxies accelerating from us?
2) Is Redshift the same as Doppler shift?
3) What is causing the expansion of the universe?
4) Is expansion, faster than light in parts of the Universe, and How does this not violate the faster than light speed limit?
5) What is a Cepheid or standard candle?
6) What do we mean when we say homogeneous and isotropic?
7) How do we measure the distance to galaxies?
8) What is outside the universe?
9) What do we mean when anm object leaves our universe?
10) Why is the CMB so vital in cosmology?

These are some of the common questions I will attempt to address in the following article

First we must define some terms and symbols used.

Planck constant: h\ =\ 6.62606876(52)\ \times\ 10^{-34}\ J\ s
Gravitational constant: G\ =\ 6.673(10)\ \times\ 10^{-11}\ m^{3} kg^{-1} s^{-2}
Speed of light in a vacuum:c\ =\ 2.99792458\ \times\ 10^{8}\ m\ s^{-1}

The parsec (symbol: pc) is a unit of length used in astronomy, equal to about 30.9 trillion kilometers (19.2 trillion miles). In astronomical terms, it is equal to 3.26 light-years, and in scientific terms it is equal to 3.09×10¹³ kilometers
Mpc=1 million Parsecs

Universe: A generalized definition of the universe can be described as everything that is. In Cosmology the universe can be described as everything measurable in our space-time either directly or indrectly. Or the Observable universe. The observable universe is 46 Billion light years, or 4.3×10²⁶ meters with an age as of 2013, is 13.772 ± 0.059 billion years.
In the hot big bang model we do not think of the universe as starting from a singularity (infinitely, hot, dense point) instead measurements agree space-time simply expanding.
Whether or not the universe is finite or infinite is not known. However if it is infinite now so it must be in the beginning.
Common misconceptions arise when one tries to visualize a finite universe Such questions include.
"So how do we see farther than 13.772 billion years?" The answer lies in expansion; as light is traveling towards us, space-time has expanded.
" If the universe is finite what exists outside the Universe?" If you think about this question with the above definition of the universe you will realize that the question is meaningless. One accurate answer in regards to cosmology is nonexistent.
"What makes up the barrier between our universe and outside our universe?" The short answer is there is no barrier.

The CMB, (Cosmic Microwave Background) The CMB is thermal radiation filling the Observable universe almost uniformly, This provides strong evidence of the homogeneous and isotropic measurements and distances. As the universe expanded, both the plasma and the radiation filling it grew cooler. When the universe cooled enough, protons and electrons combined to form neutral atoms. These atoms could no longer absorb the thermal radiation, and so the universe became transparent instead of being an opaque fog. Precise measurements of cosmic background radiation are critical to cosmology, since any proposed model of the universe must explain this radiation. CMB photons were emitted at about 3000 Kelvin and are now 2.73 Kelvin blackbody radiation. Their currently observed energy is 1/1000th of their energy as emitted

Doppler shift and redshift are the same phenomenon in general relativity. However you will often see Doppler factored into components with different names used, as will be explained below. In all cases of Doppler, the light emitted by one body and received by the other will be red or blueshifted i.e. its wavelength will be stretched. So the color of the light is more towards the red or blue end of the spectrum. As shown by the formula below.

\frac{\Delta_f}{f} = \frac{\lambda}{\lambda_o} = \frac{v}{c}=\frac{E_o}{E}=\frac{hc}{\lambda_o} \frac{\lambda}{hc}


The Doppler Redshift results from the relative motion of the light emitting object and the observer. If the source of light is moving away from you then the wavelength of the light is stretched out, i.e., the light is shifted towards the red. When the wavelength is compressed from an object moving towards you then it moves towards the blue end of the spectrum. These effects, individually called the blueshift and the redshift are together known as Doppler shifts. The shift in the wavelength is given by a simple formula

(Observed wavelength - Rest wavelength)/(Rest wavelength) = (v/c)

f=\frac{c+v_r}{c+v_s}f_o



c=velocity of waves in a medium
v_r is the velocity measured by the source using the source’s own proper-time clock(positive if moving toward the source
v_s is the velocity measured by the receiver using the source’s own proper-time clock(positive if moving away from the receiver)

The above are for velocities where the source is directly away or towards the observer and for low velocities less than relativistic velocities. A relativistic Doppler formula is required when velocity is comparable to the speed of light. There are different variations of the above formula for transverse Doppler shift or other angles.
Doppler shift is used to describe redshift due to inertial velocity one example is a car moving away from you the light will be redshifted, as it approaches you the light and sound will be blueshifted. In general relativity and cosmology, there is a fundamental complication in this simple picture - relative velocity cannot be defined uniquely over large distances. However, it does become unique when compared along the path of light. With relative velocity compared along the path of the light, the special relativity Doppler formula describes redshift for all situations in general relativity and cosmology. It is important to realize that gravity and expansion of the universe affect light paths, and how emitter velocity information is carried along a light path; thus gravity and expansion contribute to Doppler redshift.


The Cosmological Redshift is a redshift attributed to the expansion of space. The expansion causes a Recession Velocity for galaxies (on average) that is proportional to DISTANCE. This recession velocity then produces a Doppler (red) shift proportional to distance (please note that this recession velocity must be converted to a relative velocity along the light path before it can be used in the Doppler formula). The further away an object is the greater the amount of redshift. This is given in accordance with Hubble’s Law. In order to quantify the velocity of this galactic movement, Hubble proposed Hubble's Law of Cosmic Expansion, aka Hubble's law, an equation that states:

Hubble’s Law: The greater the distance of measurement the greater the recessive velocity

Velocity = H₀ × distance.


Velocity represents the galaxy's recessive velocity; H₀ is the Hubble constant, or parameter that indicates the rate at which the universe is expanding; and distance is the galaxy's distance from the one with which it's being compared.

The Hubble Constant has been calculated at different values over time, this is essential as the rate of expansion varies over time but the current accepted value is 70 kilometers/second per mega parsec, or Mpc. The latter being a unit of distance in intergalactic space described above.
Any measurement of redshift above the Hubble distance defined as H₀ = 4300±400 Mpc will have a recessive velocity of greater than the speed of light. This does not violate GR because a recession velocity is not a relative velocity or an inertial velocity. It is precisely analogous to a separation speed. If, in one frame of reference, one object is moving east at .9c, and another west at .9c, they are separating by 1.8c. This is their recession velocity. Their relative velocity remains less than c. In cosmology, two things change from this simple picture: expansion can cause separation speeds much greater even than 2c; and relative velocity is not unique, but no matter what path it is compared along, it is always less than c, as expected.

z = (Observed wavelength - Rest wavelength)/(Rest wavelength) or more accurately

1+z= λ_observed/λ_emitted or z=(λ_observed-λ_emitted)/λ_emitted



1+Z=\frac{\lambda}{\lambda_o} or 1+Z=\frac{\lambda-\lambda_o}{\lambda_o}

λ₀= rest wavelength
Note that positive values of z correspond to increased wavelengths (redshifts).
Strictly speaking, when z < 0, this quantity is called a blueshift, rather than
a redshift. However, the vast majority of galaxies have z > 0. One notable blueshift example is the Andromeda Galaxy, which is gravitationally bound and approaching the Milky Way.

WMAP nine-year results give the redshift of photon decoupling as z=1091.64 ± 0.47 So if the matter that originally emitted the oldest CMBR photons has a present distance of 46 billion light years, then at the time of decoupling when the photons were originally emitted, the distance would have been only about 42 million light-years away.


Cosmological Redshift is distance dependant as mentioned above, if you were to teleport to the other side of the galaxy where you measured that greater than light recessive velocity, you would find the same expansion rate as your original location relative to an equal distance. Indeed expansion is the same throughout the cosmos. However gravity in galaxy clusters is strong enough to prevent expansion. In other words galaxy clusters are gravitationally bound.

In regards to expansion it is important to realize that galaxies are not moving from us due to inertia, rather the space between two coordinates are expanding. This is important in that no FORCE is acting upon the galaxies to cause expansion. That expansion is homogeneous and isotropic. In other words, there is no preferred location ( Homogeneous) and no preferred direction (Isotropic). Keep in mind these terms describe the universe on large scales. Indeed below 100 Mpc we know that galaxy clusters, large scale clusters are not homogeneous or isotropic.
As expansion is homogeneous and isotropic then there is no difference in expansion at one location or another. In the LambdaCDM model expansion is attributed to the cosmological constant.

Cosmological Constant is a homogeneous energy density that causes the expansion of the universe to accelerate. Originally proposed early in the development of general relativity in order to allow a static universe solution it was subsequently abandoned when the universe was found to be expanding. Now the cosmological constant is invoked to explain the observed acceleration of the expansion of the universe. The cosmological constant is the simplest realization of dark energy, which the more generic name is given to the unknown cause of the acceleration of the universe. Indeed what we term as "Dark" energy is an unknown energy that comprises most of the energy density of our cosmos around 73%. However the amount of dark energy per m³ is quite small. Some estimates are around about 6 × 10^-10 joules per cubic meter. However their is a lot of space between large scale clusters, so that small amount per m³ adds up to a significant amount of energy in total

Another term often used for the cosmological constant is vacuum energy described originally by the false vacuum inflationary Model by A.Guth. The cosmological constant uses the symbol Λ, the Greek letter Lambda.
This False vacuum inflationary model is one that describes a total energy balance of zero, where gravity is the negative energy. In this model what we term as "Nothing” is really a quantum vacuum with quantum fluctuations described by the Heisenberg uncertainty principle. Virtual particles pop in and out of existence all the time, as a result of expansion those virtual particles quantum tunnel between the false vacuum and the true vacuum, becoming real particles. The full explanation is a little more involved than this quick explanation however this model is often referred to as a "Universe from Nothing" or the "Ultimate free lunch" . Many of our current inflationary models have their roots in this model. However one fundamental problem with all inflationary models is "Runaway expansion" Once the process starts no one has found a mechanism to stop expansion.
One means of relating to expansion is with the use of a grid of squares. Each horizontal and vertical crossing on that grid is a coordinate. In expansion the space between all coordinates not gravitationally bound expand equally. In other words the coordinates do not change, the space between coordinates change. I should also note there is no clear consensus on whether the universe is finite or infinite. If it’s infinite now then it was infinite in the past. Same thing applies with finite. The Big Bang model only describes the Universe from 10 ^-43 seconds and is not considered as starting from a black hole singularity, rather its properly described as a rapid expansion of space-time.

WMAP data confirms that the universe is flat or close to flat.


Gravitational Redshift describes Doppler between static emitter and receiver in a gravitational field. Static observers in a gravitational field are accelerating, not inertial, in general relativity. As a result (even though they are static) they have a relative velocity in the sense described under Doppler. Because they are static, so is this relative velocity along a light path. In fact, the relative velocity for Doppler turns out to depend only on the difference in gravitational potential between their positions. Typically, we dispense with discussion of the relative velocity along a light path for static observers, and directly describe the resulting redshift as a function of potential difference. When the potential increases from emitter to receiver, you have redshift; when it decreases you have blue shift. The formula below is the gravitational redshift formula or Einstein shift in an uncharged, non rotating, spherical mass.
<br /> \frac{\lambda}{\lambda_o}=\frac{1}{\sqrt{(1 - \frac{2GM}{r c^2})}}<br />


G=gravitational constant
c=speed of light
M=mass of gravitational body
r= distance from gravitational body of Mass M

Cosmic Distance ladder, also known as Extragalactic distance scale. Is easily thought of as a series of different measurement methods for specific distance scales. Rather than cover a large range of those distance scales or rungs on the ladder I will cover a few of the essential steps to cosmological distance scales. The first rung on the ladder is naturally.

Direct measurements: Direct measurements form the fundamental distance scale. Units such as the distance from Earth to the sun that are used to develop a fundamental unit called astronomical unit or AU. During the orbit around the sun we can take a variety of measurements such as Doppler shifts to use as a calibration for the AU unit. This Unit is also derived by a method called Parallax.

Parallax. Parallax is essentially trigonometric measurements of a nearby object in space. When our orbit forms a right angle triangle to us and the object to be measured
With the standardized AU unit we can take two AU to form the short leg. With the Sun at a right angle to us the distance to the object to be measured is the long leg of the triangle.

Moving Cluster Parallax is a technique where the motions of individual stars in a nearby star cluster can be used to find the distance to the cluster.

Stellar parallax is the effect of parallax on distant stars . It is parallax on an interstellar scale, and allows us to set a standard for the parsec.

Standard candles A common misconception of standard candles is that only type 1A supernova are used. Indeed any known fundamental distance measurement or stellar object whose luminosity or brightness is known can be used as a standard candle. By comparing an objects luminosity to the observed brightness we can calculate the distance to an object using the inverse square law. Standard candles include any object of known luminosity, such as Cepheid’s, novae, Type 1A supernova and galaxy clusters.

My thanks to the following Contributors, for their feedback and support.

PAllen
Naty1
Jonathon Scott
marcus

Article by Mordred, PAllen

 

[Mordred]

For an FAQ you need to be really straightforward and uncontroversial. It's difficult. I hope others have time to help you sort it out.

Have you tried calculating the redshift (to first order) within a rapidly spinning system such as a space station (a) as a Special Relativity velocity effect and (b) as due to the effective "gravitational potential" experienced within the spinning system because of the centripetal acceleration? I've always felt that's particularly educational.

That would be educational. No I haven't tried that as of yet. Sounds like a fun challenge lol.

I agree with a FAQ being uncontroversial and straightforward, that is currently my goal in tis article and yes its challenging. I fully expected this project to take a while for those reasons.

I'm still hunting some of the problems Dennis pointed out, I know I'm missing some of the suggested corrections

 

[Mordred]

I changed the Observable unit section. Still working on that section. However so far it reads far better. Can everyone agree on the definition I used for Cosmology based definition as everything measurable in our space-time either directly or indirectly.

 

[Mordred]

EXPANSION AND REDSHIFT
1) Why are all the galaxies accelerating from us?
2) Is Redshift the same as Doppler shift?
3) What is causing the expansion of the universe?
4) Is expansion, faster than light in parts of the Universe, and How does this not violate the faster than light speed limit?
5) What is a Cepheid or standard candle?
6) What do we mean when we say homogeneous and isotropic?
7) How do we measure the distance to galaxies?
8) What is outside the universe?
9) What do we mean when an object leaves our universe?
10) Why is the CMB so vital in cosmology?

These are some of the common questions I will attempt to address in the following article

First we must define some terms and symbols used.

Planck constant: h\ =\ 6.62606876(52)\ \times\ 10^{-34}\ J\ s
Gravitational constant: G\ =\ 6.673(10)\ \times\ 10^{-11}\ m^{3} kg^{-1} s^{-2}
Speed of light in a vacuum:c\ =\ 2.99792458\ \times\ 10^{8}\ m\ s^{-1}

The parsec (symbol: pc) is a unit of length used in astronomy, equal to about 30.9 trillion kilometers (19.2 trillion miles). In astronomical terms, it is equal to 3.26 light-years, and in scientific terms it is equal to 3.09×10¹³ kilometers
Mpc=1 million Parsecs

Universe: A generalized definition of the universe can be described as everything that is. In Cosmology the universe can be described as everything measurable in our space-time either directly or indirectly. This definition forms the basis of the observable universe.

The Observable universe is 46 Billion light years, or 4.3×10²⁶ meters with an age as of 2013, is 13.772 ± 0.059 billion years.
In the hot big bang model we do not think of the universe as starting from a singularity (infinitely, hot, dense point) instead measurements agree space-time as simply expanding. That expansion is homogeneous and isotropic. If you were to take a telescope and look at the night sky, no matter where you look the universe looks the same or homogeneous meaning no preferred location. As you change directions with the telescope you will find that no matter which direction you look the universe looks the same or isotropic meaning no preferred direction. These terms in cosmology are only accurate at certain scales. Below 100Mpc it is obvious that the universe is inhomogeneous and anisotropic. As such objects as stars and galaxies reside in this scale. This also tells us that there is no center of the universe, as a center is a preferred location. These terms also describe expansion. Expansion will be covered in more detail in the Cosmological Redshift section.
Whether or not the universe is finite or infinite is not known. However if it is infinite now so it must be in the beginning.
Common misconceptions arise when one tries to visualize a finite universe such questions include.

"So how do we see farther than 13.772 billion light years?" The answer lies in expansion; as light is traveling towards us, space-time has expanded.
“If the universe is finite what exists outside the Universe?" If you think about this question with the above definition of the universe you will realize that the question is meaningless. One accurate answer in regards to cosmology is nonexistent.
"What makes up the barrier between our universe and outside our universe?" The short answer is there is no barrier.


The CMB, (Cosmic Microwave Background) The CMB is thermal radiation filling the Observable universe almost uniformly, This provides strong evidence of the homogeneous and isotropic measurements and distances. As the universe expanded, both the plasma and the radiation filling it grew cooler. When the universe cooled enough, protons and electrons combined to form neutral atoms. These atoms could no longer absorb the thermal radiation, and so the universe became transparent instead of being an opaque fog. Precise measurements of cosmic background radiation are critical to cosmology, since any proposed model of the universe must explain this radiation. CMB photons were emitted at about 3000 Kelvin and are now 2.73 Kelvin blackbody radiation. Their currently observed energy is 1/1000th of their energy as emitted.

In order to measure an objects motion and distance in cosmology it is important to properly understand redshift, Doppler shift and gravitational redshift. Incorrect usage of any of these can lead to errors in our measurements.

Doppler shift and redshift are the same phenomenon in general relativity. However you will often see Doppler factored into components with different names used, as will be explained below. In all cases of Doppler, the light emitted by one body and received by the other will be red or blueshifted i.e. its wavelength will be stretched. So the color of the light is more towards the red or blue end of the spectrum. As shown by the formula below.

\frac{\Delta_f}{f} = \frac{\lambda}{\lambda_o} = \frac{v}{c}=\frac{E_o}{E}=\frac{hc}{\lambda_o} \frac{\lambda}{hc}


The Doppler Redshift results from the relative motion of the light emitting object and the observer. If the source of light is moving away from you then the wavelength of the light is stretched out, i.e., the light is shifted towards the red. When the wavelength is compressed from an object moving towards you then it moves towards the blue end of the spectrum. These effects, individually called the blueshift and the redshift are together known as Doppler shifts. The shift in the wavelength is given by a simple formula

(Observed wavelength - Rest wavelength)/(Rest wavelength) = (v/c)

f=\frac{c+v_r}{c+v_s}f_o



c=velocity of waves in a medium
v_r is the velocity measured by the source using the source’s own proper-time clock(positive if moving toward the source
v_s is the velocity measured by the receiver using the source’s own proper-time clock(positive if moving away from the receiver)

The above are for velocities where the source is directly away or towards the observer and for low velocities less than relativistic velocities. A relativistic Doppler formula is required when velocity is comparable to the speed of light. There are different variations of the above formula for transverse Doppler shift or other angles.
Doppler shift is used to describe redshift due to inertial velocity one example is a car moving away from you the light will be redshifted, as it approaches you the light and sound will be blueshifted. In general relativity and cosmology, there is a fundamental complication in this simple picture - relative velocity cannot be defined uniquely over large distances. However, it does become unique when compared along the path of light. With relative velocity compared along the path of the light, the special relativity Doppler formula describes redshift for all situations in general relativity and cosmology. It is important to realize that gravity and expansion of the universe affect light paths, and how emitter velocity information is carried along a light path; thus gravity and expansion contribute to Doppler redshift.


The Cosmological Redshift is a redshift attributed to the expansion of space. The expansion causes a Recession Velocity for galaxies (on average) that is proportional to DISTANCE. This recession velocity then produces a Doppler (red) shift proportional to distance (please note that this recession velocity must be converted to a relative velocity along the light path before it can be used in the Doppler formula). The further away an object is the greater the amount of redshift. This is given in accordance with Hubble’s Law. In order to quantify the velocity of this galactic movement, Hubble proposed Hubble's Law of Cosmic Expansion, aka Hubble's law, an equation that states:

Hubble’s Law: The greater the distance of measurement the greater the recessive velocity

Velocity = H₀ × distance.


Velocity represents the galaxy's recessive velocity; H₀ is the Hubble constant, or parameter that indicates the rate at which the universe is expanding; and distance is the galaxy's distance from the one with which it's being compared.

The Hubble Constant The Hubble “constant” is a constant only in space, not in time,the subscript ‘0’ indicates the value of the Hubble constant today and the Hubble parameter is thought to be decreasing with time. The current accepted value is 70 kilometers/second per mega parsec, or Mpc. The latter being a unit of distance in intergalactic space described above.
Any measurement of redshift above the Hubble distance defined as H₀ = 4300±400 Mpc will have a recessive velocity of greater than the speed of light. This does not violate GR because a recession velocity is not a relative velocity or an inertial velocity. It is precisely analogous to a separation speed. If, in one frame of reference, one object is moving east at .9c, and another west at .9c, they are separating by 1.8c. This is their recession velocity. Their relative velocity remains less than c. In cosmology, two things change from this simple picture: expansion can cause separation speeds much greater even than 2c; and relative velocity is not unique, but no matter what path it is compared along, it is always less than c, as expected.

z = (Observed wavelength - Rest wavelength)/(Rest wavelength) or more accurately

1+z= λ_observed/λ_emitted or z=(λ_observed-λ_emitted)/λ_emitted



1+Z=\frac{\lambda}{\lambda_o} or 1+Z=\frac{\lambda-\lambda_o}{\lambda_o}

λ₀= rest wavelength
Note that positive values of z correspond to increased wavelengths (redshifts).
Strictly speaking, when z < 0, this quantity is called a blueshift, rather than
a redshift. However, the vast majority of galaxies have z > 0. One notable blueshift example is the Andromeda Galaxy, which is gravitationally bound and approaching the Milky Way.

WMAP nine-year results give the redshift of photon decoupling as z=1091.64 ± 0.47 So if the matter that originally emitted the oldest CMBR photons has a present distance of 46 billion light years, then at the time of decoupling when the photons were originally emitted, the distance would have been only about 42 million light-years away.


Cosmological Redshift is distance dependant as mentioned above, if you were to teleport to the other side of the galaxy where you measured that greater than light recessive velocity, you would find the same expansion rate as your original location relative to an equal distance. Indeed expansion is the same throughout the cosmos. However gravity in galaxy clusters is strong enough to prevent expansion. In other words galaxy clusters are gravitationally bound. In regards to expansion it is important to realize that galaxies are not moving from us due to inertia, rather the space between two coordinates are expanding. This is important in that no FORCE is acting upon the galaxies to cause expansion. As expansion is homogeneous and isotropic then there is no difference in expansion at one location or another. In the LambdaCDM model expansion is attributed to the cosmological constant.

Cosmological Constant is a homogeneous energy density that causes the expansion of the universe to accelerate. Originally proposed early in the development of general relativity in order to allow a static universe solution it was subsequently abandoned when the universe was found to be expanding. Now the cosmological constant is invoked to explain the observed acceleration of the expansion of the universe. The cosmological constant is the simplest realization of dark energy, which the more generic name is given to the unknown cause of the acceleration of the universe. Indeed what we term as "Dark" energy is an unknown energy that comprises most of the energy density of our cosmos around 73%. However the amount of dark energy per m³ is quite small. Some estimates are around about 6 × 10^-10 joules per cubic meter. However their is a lot of space between large scale clusters, so that small amount per m³ adds up to a significant amount of energy in total

Another term often used for the cosmological constant is vacuum energy described originally by the false vacuum inflationary Model by A.Guth. The cosmological constant uses the symbol Λ, the Greek letter Lambda.
This False vacuum inflationary model is one that describes a total energy balance of zero, where gravity is the negative energy. In this model what we term as "Nothing” is really a quantum vacuum with quantum fluctuations described by the Heisenberg uncertainty principle. Virtual particles pop in and out of existence all the time, as a result of expansion those virtual particles quantum tunnel between the false vacuum and the true vacuum, becoming real particles. The full explanation is a little more involved than this quick explanation however this model is often referred to as a "Universe from Nothing" or the "Ultimate free lunch" . Many of our current inflationary models have their roots in this model. However one fundamental problem with all inflationary models is "Runaway expansion" Once the process starts no one has found a mechanism to stop expansion.
One means of relating to expansion is with the use of a grid of squares. Each horizontal and vertical crossing on that grid is a coordinate. In expansion the space between all coordinates not gravitationally bound expand equally. In other words the coordinates do not change, the space between coordinates change. I should also note there is no clear consensus on whether the universe is finite or infinite. If it’s infinite now then it was infinite in the past. Same thing applies with finite. The Big Bang model only describes the Universe from 10 ^-43 seconds and is not considered as starting from a black hole singularity, rather its properly described as a rapid expansion of space-time.

WMAP data confirms that the universe is flat or close to flat.


Gravitational Redshift describes Doppler between static emitter and receiver in a gravitational field. Static observers in a gravitational field are accelerating, not inertial, in general relativity. As a result (even though they are static) they have a relative velocity in the sense described under Doppler. Because they are static, so is this relative velocity along a light path. In fact, the relative velocity for Doppler turns out to depend only on the difference in gravitational potential between their positions. Typically, we dispense with discussion of the relative velocity along a light path for static observers, and directly describe the resulting redshift as a function of potential difference. When the potential increases from emitter to receiver, you have redshift; when it decreases you have blue shift. The formula below is the gravitational redshift formula or Einstein shift in an uncharged, non rotating, spherical mass.
<br /> \frac{\lambda}{\lambda_o}=\frac{1}{\sqrt{(1 - \frac{2GM}{r c^2})}}<br />


G=gravitational constant
c=speed of light
M=mass of gravitational body
r= distance from gravitational body of Mass M

Cosmic Distance ladder, also known as Extragalactic distance scale. Is easily thought of as a series of different measurement methods for specific distance scales. Rather than cover a large range of those distance scales or rungs on the ladder I will cover a few of the essential steps to cosmological distance scales. The first rung on the ladder is naturally.

Direct measurements: Direct measurements form the fundamental distance scale. Units such as the distance from Earth to the sun that are used to develop a fundamental unit called astronomical unit or AU. During the orbit around the sun we can take a variety of measurements such as Doppler shifts to use as a calibration for the AU unit. This Unit is also derived by a method called Parallax.

Parallax. Parallax is essentially trigonometric measurements of a nearby object in space. When our orbit forms a right angle triangle to us and the object to be measured
With the standardized AU unit we can take two AU to form the short leg. With the Sun at a right angle to us the distance to the object to be measured is the long leg of the triangle.

Moving Cluster Parallax is a technique where the motions of individual stars in a nearby star cluster can be used to find the distance to the cluster.

Stellar parallax is the effect of parallax on distant stars . It is parallax on an interstellar scale, and allows us to set a standard for the parsec.

Standard candles A common misconception of standard candles is that only type 1A supernova are used. Indeed any known fundamental distance measurement or stellar object whose luminosity or brightness is known can be used as a standard candle. By comparing an objects luminosity to the observed brightness we can calculate the distance to an object using the inverse square law. Standard candles include any object of known luminosity, such as Cepheid’s, novae, Type 1A supernova and galaxy clusters.

My thanks to the following Contributors, for their feedback and support.

PAllen
Naty1
Jonathon Scott
marcus

Article by Mordred, PAllen

 

[Mordred]

I made a few changes in the beginning section to better cover common questions also to define honmogeneous an isotropic earlier on in the article. Hopefully this gives the article a better flow .

 

[Naty1]

A few minor comments...You may want to note:

"So how do we see farther than 13.772 billion years?"

should be 13.7 billion LIGHT years.

H₀ is the Hubble constant currently.

Something is wrong here:

One accurate answer in regards to cosmology is nonexistent.

That expansion is homogeneous and isotropic. In other words, there is no preferred location (Homogeneous) and no preferred direction (Isotropic). Keep in mind these terms describe the universe on large scales.

This seems a bit convoluted: 'homogeneous and isotropic' are assumptions of space...as you correctly described much earlier. Once such assumptions are made so that we can simplify cosmological model calculations, the uniform expansion of space follows. I am not sure if anyone knows that the actual expansion of space is actually uniform...maybe somebody will comment...

I'd suggest simply saying the uniform expansion of space follows from the assumptions that space is uniform...homogeneous and isotropic.

 

[Mordred]

A few minor comments...You may want to note:



should be 13.7 billion LIGHT years.

H₀ is the Hubble constant currently. .

.


the constant H₀ isn't going to change, The value I gave I added the date of the value.

Velocity represents the galaxy's recessive velocity; H0 is the Hubble constant, or parameter that indicates the rate at which the universe is expanding; and distance is the galaxy's distance from the one with which it's being compared.

The Hubble Constant has been calculated at different values over time, this is essential as the rate of expansion varies over time but the current accepted value is 70 kilometers/second per megaparsec, or Mpc.

Something is wrong here:

One accurate answer in regards to cosmology is nonexistent.

.

.


this statement I agree is questionable. I didn't want to use the word nothing, for obvious reasons. So the only way I could think of was nonexistent.

I'm open to suggestions on better ways to express this.

This seems a bit convoluted: 'homogeneous and isotropic' are assumptions of space...as you correctly described much earlier. Once such assumptions are made so that we can simplify cosmological model calculations, the uniform expansion of space follows. I am not sure if anyone knows that the actual expansion of space is actually uniform...maybe somebody will comment...

I'd suggest simply saying the uniform expansion of space follows from the assumptions that space is uniform...homogeneous and isotropic.

.

Its considered homogeneous and isotropic on the right scales, Out of the 5 introductory to cosmology textbooks I have the value of 100 Mpc or above is often stated. However there has been some dispute on that aspect, Does the value need to be increased ?
Both CMB and Planck confirm the homogeneous and isotropic nature of the universe. So I would think its more than just an assumption to make the maths easier. I'm open to suggestions on better descriptives for the actual homogeneous and isotropic nature of expansion in non gravitationally bound regions.

 

[Mordred]

2.2 On large scales, the universe is isotropic
and homogeneous
What does it mean to state that the universe is isotropic and homogeneous?
Saying that the universe is isotropic means that there are no preferred directions
in the universe; it looks the same no matter which way you point your
telescope. Saying that the universe is homogeneous means that there are no
preferred locations in the universe; it looks the same no matter where you set
up your telescope. Note the very important quali¯er: the universe is isotropic
and homogeneous on large scales. In this context, \large scales" means that
the universe is only isotropic and homogeneous on scales of roughly 100Mpc
or more.
The isotropy of the universe is not immediately obvious. In fact, on small
scales, the universe is blatantly anisotropic. Consider, for example, a sphere
3 meters in diameter, centered on your navel (Figure 2.2a). Within this
sphere, there is a preferred direction; it is the direction commonly referred
to as \down". It is easy to determine the vector pointing down. Just let go
of a small dense object. The object doesn't hover in midair, and it doesn't
move in a random direction; it falls down, toward the center of the Earth.
On signi¯cantly larger scales, the universe is still anisotropic. Consider,
for example, a sphere 3 AU in diameter, centered on your navel (Figure 2.2b).
Within this sphere, there is a preferred direction; it is the direction pointing
toward the Sun, which is by far the most massive and most luminous object
within the sphere. It is easy to determine the vector pointing toward the
Sun. Just step outside on a sunny day, and point to that really bright disk
of light up in the sky.
On still large scales, the universe is still anisotropic. Consider, for example,
a sphere 3 Mpc in diameter, centered on your navel (Figure 2.2c).
This sphere contains the Local Group of galaxies, a small cluster of some 40
galaxies. By far the most massive and most luminous galaxies in the Local
Group are our own Galaxy and M31, which together contribute about 86% of
the total luminosity within the 3 Mpc sphere. Thus, within this sphere, our
Galaxy and M31 de¯ne a preferred direction. It is fairly easy to determine
the vector pointing from our Galaxy to M31; just step outside on a clear

here is a quote from "Introductory to Cosmology" by Barbera Ryden. The drawings references are merely circles.
All of my textbooks describe this in a similar manner

 

[Naty1]

regarding the Hubble parameter:

The Hubble “constant” is a constant only in space, not in time,

the subscript ‘0’ indicates the value of the Hubble constant today and

the Hubble parameter is thought to be decreasing with time.

I have trouble extracting any of those concepts from the current description you posted.

I'm open to suggestions on better descriptives for the actual homogeneous and isotropic nature of expansion in non gravitationally bound regions.

It's space that is described this way, not expansion. Such a description of space leads to the uniform expansion...or uniform distance increases, if you prefer...

see what others may comment...if anything...

 

[PAllen]

It's space that is described this way, not expansion. Such a description of space leads to the uniform expansion...or uniform distance increases, if you prefer...

see what others may comment...if anything...

In principle, you could have space that is (at any cosmological time slice) neither homogenous nor isotropic, yet experiences homogenous and isotropic expansion (preserving the spatial asymmetries). Alternatively, you could homogenous, isotropic space (at some cosmological time), the experiences anisotropic and / or inhomogeneous expansion; space would then loose its symmetries due to the asymmetric expansion.

The only real connection I see is that if space retains these symmetries, then the expansion must have them. Every other implication (if ... then) statement I can think of relating spatial and expansion symmetries is false (except of course, the contrapositive of the above).

 

[Mordred]

regarding the Hubble parameter:

The Hubble “constant” is a constant only in space, not in time,

the subscript ‘0’ indicates the value of the Hubble constant today and

the Hubble parameter is thought to be decreasing with time.

I have trouble extracting any of those concepts from the current description you posted.
/QUOTE]

that descriptive is better than the one I used.

It's space that is described this way, not expansion. Such a description of space leads to the uniform expansion...or uniform distance increases, if you prefer...

see what others may comment...if anything...

This descriptive sounds good, however is it accurate ? consider the cause of expansion, as vacuum energy as described in the inflationary model. There is no evidence of variations in the vacuum energy. The vacuum energy is also homogenous and isotropic. As this energy is constant, homogenous and isotropic and the rate of expansion requires the cosmological constant. That would mean expansion is also homogenous and isotropic, the difference in expansion rates is a sum of energy densities. However the vacuum energy density in all areas in space remain the same. So in these terms, outside of gravitationally bound regions describing the 100Mpc takes that into consideration.
I'm willing to go either way on the two decriptives but it seems to me that expansion can be accurately described as homogenous and isotropic on the right scales.


Take for example the De-Sitter universe. this is a universe where matter is removed.

the rate of expansion is defined as h\propto\sqrtλ

this shows that its homogenous and isotropic.

I will use your Hubble constant descriptive its more accurate than what I have.

 

[Mordred]

I added your suggested change to he Hubble constant thanks for pointing that out Naty1

 

[Naty1]

Pallen:

In principle, you could have space that is (at any cosmological time slice) neither homogenous nor isotropic, yet experiences homogenous and isotropic expansion (preserving the spatial asymmetries).

now THAT would be an interesting cosmological model. [LOL]

If there is a mainstream model that does not assume symmetrical space and mass/energy, I have not yet come across it.

The only real connection I see is that if space retains these symmetries, then the expansion must have them.

That's one nice way to express what I was trying to describe. I do not see how you can derive the FLRW cosmological model nor any other that is practical without such an assumption up front. If you do not make such an assumption it seems you are stuck with numerical approximations as solutions...like trying to apply the FLRW model to a lumpy galaxy and finding out expansion may not even be forecast..

If you watch Leonard Susskind derive even a Newtonian model of space [Youtube Cosmology Lecture #2, and it is quite cool and simple by the way] you'll note the FIRST thing he does after drawing a variable diameter sphere of matter/energy is to ASSUME homogeneous and isotropic mass[energy] density for that sphere...and all others of any size.

 

[Mordred]

I can't think of any models where one stays homogenous and isotropic while the other doesn't either..The part about the universe retaining assymetries I have read about once but can't recall where.

 

[PAllen]

Pallen:


now THAT would be an interesting cosmological model. [LOL]

If there is a mainstream model that does not assume symmetrical space and mass/energy, I have not yet come across it.

I said "in principle" not "in a mainstream model". The point was to clarify the logical coupling of concepts. Note that both of the following are both correct ways of looking at it:

- If any spatial slice is homogenous and isotropic, and expansion is homogenous and isotropic, then all spatial slices are homogenous and isotropic.

- If all spatial slices are homogenous and isotropic, then expansion must be homogenous and isotropic.

 

[Naty1]

The part about the universe retaining assymetries I have read about once but can't recall where.

Funny you should mention that:

I just posted a link to a NY Times [newspaper] article earlier today on
new Planck Satellite data...

Universe as an Infant: Fatter Than Expected and Kind of Lumpy
https://www.physicsforums.com/showthread.php?t=680161

That title could be a description of my wife! [No,no, I did NOT say that!]

 

[Mordred]

lol even more funny is I was reading it while you posted this lol

 

[Mordred]

I've been considering if I should add critical density and space-time geometry to the article. In one camp the FAQ is already large. In the other it would encourage more ppl to use it as a reference.

 

[PAllen]

I've been considering if I should add critical density and space-time geometry to the article. In one camp the FAQ is already large. In the other it would encourage more ppl to use it as a reference.

I lean towards leaving it out. Another FAQ could be created on critical density, open/closed geometry, flat or not, etc.

Supporting this further, is that before finalizing this FAQ, another step is collecting references. Almost all FAQ in PF provide references to more detailed treatment of the issues. As this one is big, I would see a minimum of six, possibly 10 references being required.

 

[Mordred]

I lean towards leaving it out. Another FAQ could be created on critical density, open/closed geometry, flat or not, etc.

Supporting this further, is that before finalizing this FAQ, another step is collecting references. Almost all FAQ in PF provide references to more detailed treatment of the issues. As this one is big, I would see a minimum of six, possibly 10 references being required.

Yeah I agree on leaving that out, the references in regards to the FAQ on PF is something I wasn't aware of. Should be easy enough to find some decent articles for reference.
I'll look around for some decent articles, and try to find sites that will stay so that the links don't become broken or unusable.

 

[PAllen]

Yeah I agree on leaving that out, the references in regards to the FAQ on PF is something I wasn't aware of. Should be easy enough to find some decent articles for reference.
I'll look around for some decent articles, and try to find sites that will stay so that the links don't become broken or unusable.

Here is a technical reference sent to me by PM, from back when we were debating whether Doppler was distinct from other redshift's in GR.

http://arxiv.org/abs/1111.6704

It is modern, evenhanded, and I think represents modern consensus. In particular, on page 4, it endorses the view that all spectral shifts in GR are correctly regarded as Doppler effect for curved spacetime, but also clarifies (as I agree) that this does not imply they can be regarded as purely kinematic in origin.

[Interesting to me was the demonstration that over large distances in open, non-flat RW models, you cannot split the Doppler into kinematic vs non-kinematic components even for distant co-moving observers (this paper only considers co-moving observers, which they call fundamental observers).]