Cosmology questions, something that is puzzling me for days

[CarpathianLord]

Hello folks

My name is Mike. I am into Cosmology ever since I was a kid. Throughout the years I strayed away from Cosmology unfortunately but I am very very fond of Cosmology...and thus...call me an amateur Cosmologist :D

Anyway...

These days couple of questions puzzle me in the Cosmology theory.

First one is this

According to the Big Bang theory, and the research that has been carried out, we have recorded the Cosmic Background radiation, but we don't have proof what is beyond that...

Here is an image from Stephen Hawking's "Universe in a nutshell"
http://joscalesfineart.files.wordpress.com/2012/02/002.jpg

So according to this diagram, we can only "see" the background radiation and not beyond that, we have no proof of the matter density and I am sure we cannot "see" the Big Bang it self, and I am dying to know WHY we cannot "see" that. According to Einstein theory as we see further (deeper) in the Universe we see the past (millions and billions of years), but we cannot see the beginning of the Universe. Some kind of a hotspot of radiation, matter density of some sort. We only see the remains of that explosion in the form of CBR as I gather.

Second question

If the Universe is expanding, the information of this expansion is gathered by the so called redshift effect. The redshift effect is "collected" by objects that are millions and some of them billions of light years away. So actually we are seeing an early expanding Universe. That is no proof that the Universe is expanding now at this very moment. Maybe it has started collapsing by now, and yet we do say "The Universe IS EXPANDING", I think a very courageous gesture.

Maybe I am wrong, so please enlighten me on these questions.

Thank you very much

Mike

 

[skydivephil]

It depends on what you mean by the word "see".
After the big bang the universe was a plasma, this state was present until 380,000 years after the big bang. Such a plasma is opaque, you cannot see through it. Like the sun, you can't look at the sun and see into the interior. When the density declined the fog cleared and photons were set free, these photons are what we see when we see the CMB.
However there are relationships in the CMB which we can observe. Different models of what happened before the CMB make different predictions for these relationships.
Also there are two things which the CMB does not block us from seeing, these are neutrinos and gravity waves. But these are extrmely difficult to detect. At the moment no neutrino (the cosmic neutrino background) or primordial gravity waves have been detected. To detect these is not going to happen in the near future in my opinion but i sure hope I am wrong. I don't know of any plans to detect the CNB. There are plans to build a space based to detector to observe the gravity waves from the big bang. But they need 12 spacecraft flying in an array. You can bet this is not going to happen any time soon.

There is some hope that there will be an indirect sign of the gravity waves via their effect on the polarisation of the CMB. Maybe Planck which gives us polarisation data next year will find this. Its pretty unlikely though and most likely will need its own dedicated mission.

In science I don't think talking about the word "proof" is a good idea. Better to say "the evidence suggests". In this case we have a model called Lambda CDM which tells us the universe is not only expanding it is doing so at accelerating rate. That model fits the data very well. it is possible in this model that the universe was contracting before the big bang but afterwards it is expanding.

 

[h_cat]

We estimate the expansion rate by comparing the redshift to the distance of an object. The redshift alone doesn't tell us too much. It is of course true that we can not observe the "present" universe. We only observe our present light cone. So we don't know but assume that the expansion is constant anywhere. If we measure expansion in our vicinity we assume it happens all over even we can only observe it in the future.
From what we measure it appears that the expansion is slightly accelerating because nearby galaxys have a higher escape velociity/distance than the ones further away (older).
Anyway we do assume very much and know very little in general but we have to live with that uncertainty.

sw_cat

 

[Mordred]

In regards to distance measures this article written by PF members will provide a convenient short cut.

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

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 Hot Big Bang model does not describe prior to 10^-43 seconds. The LambdaCDM or $\Lambda$CDM model is a fine tuned version of the general FLRW (Freidmann Lemaitre Robertson Walker) metrics, where the six observationally based model parameters are chosen for the best fit to our 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 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.
A key note is 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. One way to visualize this is to use a grid where each vertical and horizontal joint is a coordinate. The space between the coordinates increase rather than the coordinates changing. 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 $\Lambda$CDM model expansion is attributed to the cosmological constant described later on. The rate a galaxy is moving from us is referred to as recession velocity. 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 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. In the De_Sitter FLRW metric (matter removed model)
this is described in the form.

H_o$\propto\sqrt\Lambda$

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.
The dark energy density parameter is given in the form:
$\Omega_\Lambda$ which is approximately 0.685

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

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 off the vacuum surrounding an uncharged, non rotating, spherical mass.
$$\frac{\lambda}{\lambda_o}=\frac{1}{\sqrt{(1 - \frac{2GM}{r c^2})}}$$

G=gravitational constant
c=speed of light
M=mass of gravitational body
r= the radial coordinate (measured as the circumference, divided by 2pi, of a sphere centered around the massive body)

The rate of expansion is expressed in the $\Lambda$CDM model in terms of
The scale factor, cosmic scale factor or sometimes the Robertson-Walker scale factor parameter of the Friedmann equations represents the relative expansion of the universe. It relates the proper distance which can change over time, or the comoving distance which is the distance at a given reference in time.

d(t)=a(t)d_o

where d(t) is the proper distance at epoch (t)
d₀ is the distance at the reference time (t_o)
a(t) is the comoving angular scale factor. Which is the distance coordinate for calculating proper distance between objects at the same epoch (time)
r(t) is the comoving radial scale factor. Which is distance coordinates for calculating proper distances between objects at two different epochs (time)

$$Proper distance =\frac{\stackrel{.}{a}(t)}{a}$$

The dot above a indicates change in.

the notation R(t) indicates that the scale factor is a function of time and its value changes with time. R(t)<1 is the past, R(t)=1 is the present and R(t)>1 is the future.

$$H(t)=\frac{\stackrel{.}{a}(t)}{a(t)}$$

Expansion velocity
$$v=\frac{\stackrel{.}{a}(t)}{a}$$

This shows that Hubble's constant is time dependant.



Cosmic Distance ladder, also known as Extragalactic distance scale. Is easily thought of as a series of different measurement methods for specific distance scales. Previous in the article we discussed the various forms of Redshift. These principles are used in conjunction with the following methods described below. Modern equipment now allows use spectrometry. Spectrographs of an element give off a definite spectrum of light or wavelengths. By examining changes in this spectrum and other electromagnetic frequencies with the various forms of shifts caused by relative motion, gravitational effects and expansion. We can now judge an objects luminosity where absolute luminosity is the amount of energy emitted per second.

Luminosity is often measured in flux where flux is

$$f=\frac{L}{4\pi r^2}$$

However cosmologists typically use a scale called magnitudes. The magnitude scale has been developed so that a 5 magnitude change corresponds to a differents of 100 flux.
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]

The term Big Bang is a misnomer. There was no explosion merely a rapid expansion of space from a hot dense state of unknown size
and origins.

Survival of the fittest is the answer to evolution. We can genetically trace our evolutionary history provided we have sample dna of each evolutionary form. Good luck convincing your friend on that aspect.

There is no outside the universe even though you stated solar system your beginnings reference implies universe.

 

[Spourk]

According to the Big Bang theory, and the research that has been carried out, we have recorded the Cosmic Background radiation, but we don't have proof what is beyond that...

Hi Mike,

Going to quote an explanation from Marcus from This Thread Marcus started, post #5 that answers this question pretty well:

"Notice that today our particle horizon is 46.28 which is the farthest matter is NOW which could have sent us light we'd be receiving today. It is the maximum distance from home a flash of light could have reached in the whole time since start of expansion (through its own efforts aided by expansion).
But notice that the matter that emitted CMB (the most ancient light we actually do see today) is only at 45.33. That's because light emitted earlier by more distant matter DID NOT GET THRU because the partially ionized gas was effectively opaque. That opacity caused the difference between 45.33 and 46.28.

Get familiar with the fact that the wavelengths of the ancient light are by now expanded 1090-fold, and the moment the gas became transparent was year 373,000, when distances were 1/1090 of their present-day size."

Take a look at the table he referencing also, and read over Mordred's response because it explains redshift and what we're seeing when we're observing distant galaxies moving away sometimes faster than the speed of light. (Hence the red shift).

 

[Mordred]

my signature also contains several useful links. The cosmology101 site is one I am developing. It includes the links below as well as Phind's balloon analogy page (with his permission of course).

I will be adding more material to the site just started construction today on it.

the other two links contains Jorrie's cosmocalc and lightcone calculator. the main page is the second link the first link is the calculator itself. The light cone generates the table mentioned in Marcus's post

 

[Naty1]

That is no proof that the Universe is expanding now at this very moment. Maybe it has started collapsing by now, and yet we do say "The Universe IS EXPANDING", I think a very courageous gesture.

Maybe you are correct...since the universe may be infinite nobody knows for sure what may be going on 'way out there'. But so far, hour after hour, day after day, etc, etc, we keep getting CMBR with the same characteristics...so it seems a reasonable bet things are still expanding...

Our best view so far is that billions of years in the future the universe will be very big, very empty, dark and cold...'dead'...maximum entropy...To date, from the emergence of the CMBR, the temperature has decreased from about 3,000K to about 2.7K...over about 13.7B years...and a sudden reversal is not expected especially as expansion appears to be accelerating without any braking mechanism so far known.

[and you better hope it stays that way, because if things were to start to 'collapse' at some time, and it proceeds as fast as things are likely expanding now, we'd get precious little warning...and even if we did, about all we could do is ever so briefly 'party down'.]

 

[Spourk]

[and you better hope it stays that way, because if things were to start to 'collapse' at some time, and it proceeds as fast as things are likely expanding now, we'd get precious little warning...and even if we did, about all we could do is ever so briefly 'party down'.]

That is a pretty chilling thought. What would happen if everything we see now as red-shifted, was suddenly blue-shifted and moving at us exponentially... How long would it take for us to see the effects, galactic collisions? What would the implications be?

 

[Naty1]

Spourk: relax, dude, our sun will engulf us long before in a massive fireball...and if not, crashing with Andromedia might! Just party down!

 

[Spourk]

Ha, much better. If it involves the life of our sun I know I have plenty of time, and any excuse to party down seems a good one to me, as long as it doesn't end you up in jail or the middle of the antarctic. :tongue: