Physics Forums - Cosmology

Stellar formation / Expansion / Education questions

TigerDaveJr — Sat, 18 May 2013 01:43:58 GMT

Regarding the creation of the universe and the current model:

Is it assumed that the universe, at the time of creation was finite in size (or at least more finite than it is now) prior to the rapid expansion, or was the protoexistance finite in size in an infinite universe? So, did the universe AND its contents expand, or did a collection of mass within the universe expand, creating the physicality we know today?

I have seen the expansion explained like a balloon. However, if this were true, would not most mass be on the 'outside' of the balloon? Is there content in the middle of the universe, or is there a hollow center that is getting bigger as we get further from the center? I've read that asking about the center is impossible, and that the universe has infinite shape, but if that's true can we say we're expanding? Would there not be an origin point, or is that one of the problems that a physics-uneducated person like myself would be unable to grasp (re: Plato's allegory of the cave).

Can we not use red shift in order to determine the relative center of this expansion? I understand that we observe red shift based upon where we're standing, but should we not be able to calculate from all that where the overall center is? Where are we in regards to this?

Was expansion more like bread dough? Did the pre-expansion material tear? Was that tearing uneven, that left behind general emptiness in some spots and densely clumped matter in others that led to our original star nurseries?

Are galaxies considered expanding or collapsing? I've heard that there's supposed to be black holes in the center, so is this local mass "going down the drain" or is this mass being spun off from the center? Is it both? Do we consider galaxies to be generally "on par" with each other in the creation of more complex atomic structures, or do we expect each birth/nova/collapse/rebirth cycle of stellar material to continually generate more complex material, and that individually from galaxy to galaxy?

Second to last, is it possible, in the same way that we view time against the overall amazingness of deep time, that this initial universal expansion was just one bubble in an even larger sea of expanding pockets that we have yet to get close enough to see the evidence of? Not getting into dimensions, but is our universe just one in an entire "hyper-universe" of immense activity, that we can't directly "observe" in the same way that our tiny blip of existence fits in the concepts of deep time?

Finally and most importantly, where should I be aiming myself educationally in order to learn the answers to these questions, and to ask even more?

How would you teach quantitative cosmology? What examples to use?

marcus — Fri, 17 May 2013 17:34:01 GMT

By quantitative cosmology I mean with real times, distances, expansion rates, horizons, CMB stationary observers etc , derived from the standard model fitted to data. I don't mean ideas about conditions shortly before or after the start of expansion, although that is very interesting too.

The question has been on my mind: how would you approach teaching that? Say you were tutoring some interested person. I'd like to hear other people's ideas. Probably the scale factor is the most important thing to get one's mind around.

There would be two main levels to choose from: with and without the Friedman equation. I want to focus on the WITHOUT case. To deal briefly with the other case: if the person you are tutoring were good with simple differential equations and you went WITH the Friedman then it seems fairly straightforward. The conceptual structure might be like this:
the stretch in light we can observe: S = 1+z = a_now/a_then.
the distance growth rate H = a'/a, obviously a reciprocal time or percentage growth rate.
the (energy equivalent) matter density ρ comprising ordinary matter&radiation plus dark matter
the spatial flat case of the Friedman: H² - Λ/3 = [const] ρ
where the LHS is reciprocal time and the [const] converts energy density into reciprocal time.

The without-Friedman case seems like it's a lot more challenging: how do you wean learners away from purely verbal thinking and accustom them to quantities? You have to use quantitative EXAMPLES: get the learner used to seeing numbers and imagining the growth process in real terms rather than merely verbally. What sorts of examples would it be good to work through?

quintessence and quantum cosmology

Chronos — Fri, 17 May 2013 06:35:43 GMT

I'm not a big fan of quintessence, but, this paper is interesting - Quintessence with Hybrid Potential, http://arxiv.org/abs/1305.3703.

Cosmic Horizon and Surface of Last Scattering Question

Salamon — Thu, 16 May 2013 21:22:46 GMT

I have been watching Susskind's lectures on Cosmology which are great. There is something that I can't wrap my head around.

I know that if we look far away enough into the past (about 100,000 years after the big bang I think he said) , the radiation that is being emitted comes from plasma and as a result blocks any light from getting to us from beyond. This is what I understand to be the surface of last scattering.

I also get that the Hubble law states that v = Hd and as the Hubble constant approaches a constant value, there exists a cosmic horizon defined by d =c/H such that any object that passes this distance will not be observable since it would have to send a message at faster than the speed of light in order for us to observe it.

I think Susskind said that the surface of last scattering would always be within our cosmic horizon. How can this be if the cosmic horizon remains fixed?
If the deonized gas which makes up the surface of last scattering is moving away from us at a faster and faster rate, won't it eventually move beyond the cosmic horizon?

Where am I messing up? What I am visualizing wrong?

Thanks.

Origin from Nothing - what does it mean?

StateOfTheEqn — Thu, 16 May 2013 14:06:48 GMT

I have been following Quantum Cosmology since Hawking's A Brief history of Time first appeared. That inspired me to attempt to drill down to the technical papers involved. I also made use of the book by Hawking and Penrose, The Nature of Space and Time.

Very broadly speaking there seems to be two approaches: quantum tunneling from nothing (Vilenkin and others) and the no boundary proposal (Hawking and others).

About a year ago, there appeared a paper On 'Nothing' by Brown and Dahlen where they discuss what we mean by 'nothing' in Quantum Cosmology. Link . That paper has exposed difficulties with both 'tunneling from nothing' and the 'no boundary' approach.

To quote from the abstract:

Quote:

the Hawking-Turok instanton does not mediate the quantum creation of a universe.

Form of Friedman eqn with Λ curvature constant

marcus — Sun, 12 May 2013 19:40:52 GMT

The basic equation of GR has a curvature constant Λ on the lefthand (geometric) side.
The Friedman equation is derived from the Einstein Field Equation by making a simplifying assumption of uniformity. As a spacetime curvature Λ can be written either in units of reciprocal area or reciprocal time-squared. So in the Friedman equation you might expect to see Λ ( with units of reciprocal time² or length²) again appearing on the lefthand side, and matter appearing on the right.

But that doesn't happen, so the question naturally comes up as to what the Friedman equation would look like if it were so. Well the Friedman is basically an equation governing the evolution of the expansion rate H(t). For simplicity I'll assume spatial flatness (measurements show largescale mean spatial curvature is nearly, if not precisely, zero). The Friedman actually tells us about the evolution of the SQUARE of the expansion rate, which in standard metric terms would be in units of seconds^-2. And Λ as reciprocal time² can also be expressed in that unit.

H² - Λ/3 = (8πG/3c²) ρ

where ρ is the combined average energy density (ordinary and dark matter, electromagnetic radiation).

The righthand side goes to zero in the longterm future, due to expansion. So we can solve for the longterm Hubble expansion rate. Obviously it is (Λ/3)^.5 and therefore the Hubble time is (Λ/3)^-.5

It turns out that the best-fit value of Λ, according to most recent Planck report, is
1.007 x 10^-35 s^-2

If you use that value, the longterm Hubble time (Λ/3)^-.5 comes out to 17.3 billion years.

If you then take the present-day Hubble time to be 14.4 billion years and evaluate the LHS of the Friedman equation for the present-day:
H² - Λ/3 = (8πG/3c²) ρ
at the mantissa level it is just 4.843 - 3.357 = 1.486
and you get 1.486 x 10^-36 s^-2
This can then be multiplied by 3c²/8πG to get the energy density corresponding to exact spatial flatness (energy equivalent of ordinary and dark matter etc).
It comes out to 0.2389 nanojoules per cubic meter. Google calculator gives this in the algebraically equivalent form 0.2389 nanopascal.

That is the critical density when what we are counting is just matter and energy that we actually know is energy, omitting a possibly fictitious "dark energy", which was already accounted for on the LHS by the curvature constant Lambda.

Intergalactic message exercises (for LightCone tutorial)

marcus — Sat, 11 May 2013 23:47:07 GMT

There's a tutorial wiki for Jorrie's calculator. It needs exercises that beginning learners can do to help them get used to using the calculator.
IF YOU HAVE SOME IDEAS, feel free to make up exercises and propose them. Anybody can suggest material for a textbook. He might not like what you offer, or it might duplicate existing stuff. But it might be helpful. Here's some I thought of today. They might or might not be accepted and go into the tutorial. Comments welcome.

Intergalactic Message Problems

These exercises are all based on one table. It runs from a=0.1 to a=10 in 20 steps, so when you open LightCone, set S_upper = 10, S_lower=0.1 and Steps=20. Then press calculate. The link is in my signature.

The situation is we discover that there's a laser message coming in from a distant galaxy that says "Please reply immediately!" We analyze the light and determine that the wavelength has been doubled. The peaks and valleys of the wave have been spread out by a factor of two.
We flash our reply immediately. When does it get to them? Or does it ever get to them?

Learners doing the exercises will have generated this table this table, as I just described. The Answers should go at the end of the chapter, but I will put the answer to this first one right after the table. *Spoiler alert*
[tex]{\scriptsize\begin{array}{|c|c|c|c|c|c|}\hline R_{0} (Gly) & R_{\infty} (Gly) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.92&0.693&0.307\\ \hline \end{array}}[/tex] [tex]{\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline a=1/S&S&T (Gy)&R (Gly)&D (Gly)&D_{then}(Gly)&D_{hor}(Gly)&V_{now} (c)&V_{then} (c) \\ \hline 0.100&10.00&0.545&0.8196&30.684&3.068&4.717&2.13&3.74\\ \hline 0.126&7.94&0.771&1.1568&28.684&3.611&5.687&1.99&3.12\\ \hline 0.158&6.31&1.089&1.6308&26.444&4.191&6.804&1.84&2.57\\ \hline 0.200&5.01&1.536&2.2939&23.938&4.776&8.066&1.66&2.08\\ \hline 0.251&3.98&2.165&3.2127&21.143&5.311&9.452&1.47&1.65\\ \hline 0.316&3.16&3.041&4.4626&18.045&5.706&10.920&1.25&1.28\\ \hline 0.398&2.51&4.250&6.1052&14.651&5.833&12.396&1.02&0.96\\ \hline 0.501&2.00&5.883&8.1349&11.008&5.517&13.780&0.76&0.68\\ \hline 0.631&1.58&8.015&10.4035&7.226&4.559&14.962&0.50&0.44\\ \hline 0.794&1.26&10.669&12.6018&3.483&2.767&15.863&0.24&0.22\\ \hline 1.000&1.00&13.787&14.3999&0.000&0.000&16.472&0.00&0.00\\ \hline 1.259&0.79&17.257&15.6486&3.109&3.914&16.842&0.22&0.25\\ \hline 1.585&0.63&20.956&16.4103&5.731&9.083&17.047&0.40&0.55\\ \hline 1.995&0.50&24.789&16.8364&7.890&15.743&17.153&0.55&0.94\\ \hline 2.512&0.40&28.694&17.0630&9.638&24.210&17.204&0.67&1.42\\ \hline 3.162&0.32&32.638&17.1800&11.040&34.912&17.224&0.77&2.03\\ \hline 3.981&0.25&36.601&17.2395&12.160&48.409&17.240&0.84&2.81\\ \hline 5.012&0.20&40.575&17.2696&13.051&65.411&17.270&0.91&3.79\\ \hline 6.310&0.16&44.553&17.2847&13.760&86.821&17.285&0.96&5.02\\ \hline 7.943&0.13&48.534&17.2923&14.324&113.777&17.292&0.99&6.58\\ \hline 10.000&0.10&52.516&17.2961&14.772&147.715&17.296&1.03&8.54\\ \hline \end{array}}[/tex]

The wavelengths being enlarged by factor of S=2.0 tells us that the galaxy is NOW at distance of 11 Gly. We look down the D column to find where a target's distance is approximately the same. If we flash a message today to a galaxy that is now at distance 11 Gly it will get there in year 32.6 billion. That is, about 19 billion years from now. But yes, it will get there.

The galaxy is within communication range because its distance now (11 Gly) is less than the current value of the horizon distance Dhor = 16.47 Gly. (Look in the S=1 row.)

Incidental intelligence: our return message will be wavestretched by a factor of about 3.16.

Current State of the Big Freeze end of the Universe Theory.

raluu — Wed, 08 May 2013 22:50:36 GMT

I was trying to find an updated view on the plausibility of the Big Freeze. I believe that a couple of years ago, it was considered the most likely end of the world scenario and I was just wondering if it still is.

Also as a side question: I understand that Big Freeze happens with an indefinite expansion of the universe. Does this occur exclusively with a Wq value of -1 exactly or any value below -1/3, given that it stays below -1/3 indefinitely.

can we create ourselves?

mtasquared — Wed, 08 May 2013 20:22:33 GMT

Is it possible for technology to advance such that we can travel back in time and be the ones to set the universe into motion? Would such circularity have any meaning for us living beings?

Which: scale or years? as parameter of change

marcus — Tue, 07 May 2013 15:34:47 GMT

The first stars formed when distances were 9% of their present size.
The solar system began forming when distances were 70% of what they are now.
Andromeda galaxy will make a first pass through Milkyway when they're 129% of present.

Which do you find more meaningful and intuitive for tracking the evolution of the universe, percentages like those or numbers of years?

Universe history (say from recombination onwards) is often laid out using years to parametrize event, but in some of Lineweaver's diagrams the scale factor (denoted "a") is used as well. If you have any thoughts about this: reasons to prefer one or the other, I'd be interested to learn what you think--and which parametrization is more intuitive for you.

If you have some other parameter that works better please post it, and discuss. We are not talking about the first few milliseconds of expansion, or the first three minutes, here, but about history after recombination and the emission of the ancient CMB light.

I've finally accept that the universe is unimaginable

MathJakob — Tue, 07 May 2013 07:47:26 GMT

Everyday I sit and think about the universe, and after some thinking I always end up letting my imagination run wild with what could be out there, what space is and is there a creator ect.

Then it's like getting smashed in the face with a wake up call... I can't possibly imagine anything in the universe.

The size of the universe is literally unimaginable, our brains can not comprehend the distances.
The size of objects is unimaginable, even our own sun is extremely hard to visualise and that's absolutely tiny on the grand scale of things.
The speed of light is impossible to imagine, travelling around the Earth 7 times per second.
The enormous energy produced by universal explosions such as supernovae, which is equivalent to about 10 octillion megatons of TNT.

And finally the most brain crushing question of them all, this is where I'm hoping I can get some help. Does anyone find it absolutely impossible to grasp the concept of something (energy) having always existed, the "stuff" that created that tiny peice of infinitely dense matter that turnt into the big bang.

Sometimes I think it's like a mouse trying to figure out the workings of a jet engine. It's just impossible! Although a caveman trying to figure out the workings of a jet engine would have been impossible too so hopefully if humans live long enough and our understanding becomes greater it may not be too difficult to not only visualise this stuff but actually grasp it.

There should be a word specifically created for describing how ridiculously massive the universe is. Maybe that word is universe... come to think of it xD

Switch to scale factor "time" (universe its own clock)

marcus — Mon, 06 May 2013 21:27:25 GMT

In a sense the universe is its own clock and the pointer-hand is the scalefactor, as in:
"when distances were 0.1 what they are today"

"when distances were 0.3 what they are today"

"when distances were 0.9 what they are today"

For some purposes I think it's good to be able to switch over to thinking of time with the scalefactor (commonly denoted "a") serving as the index of change and marker of events, rather than numbers of thousand, millions and billions of years.
There is a sense in which our earth years are not so meaningful, talking about the expansion process of the universe, and in which "a" is a more convenient way to keep track.

Plus over much of history, from formation of the first galaxies up to present, the relation is roughly LINEAR. So, should the need arise, one might quickly reckon translations from one method of counting to the other.

After thinking it over I decided to try it out. I already was doing some of that anyway: mentally marking a time or era by how big distances were compared with today.

If you also want to try the experiment, the first thing we need to do is get used to thinking of recombination occurring at scale 1/1090 whatever that is, rather than at year 373,000 or whenever it was--I think using latest model parameters it was 373,000.
And the first galaxies forming at around scale 1/11, rather than some number of millions of years.

This might not be so easy. Let's see. 1/11 is 9 percent. Distances were 9 percent of today's.
Proto-galaxies were forming, not grand spirals with thin disks like we have today, but more modest blobs of stars. That was the 9 percent "era".

Maybe the most difficult number to get used to is 0.092 percent. This is the moment of recombination, when the ancient CMB light was released.
When that happened, distances were 0.092 percent of present size. This could be the Achilles heel of the whole idea, 0.092 is such a dinky number. Easier to think of it as 1/1090.

The prospect of having to go through life thinking of the CMB being released at scale 0.092% is discouraging, but I want to give this a fair trial. Let's figure out when the Milkyway galaxy's thin disk formed.

The thin disk formed fairly recently actually, at scale 44% (translating from Wikipedia article on Milkyway formation). Milkyway has some very old stars in it, going back to the 9% era of protogalaxy formation. But its present size and structure (thin disk, flat spiral) are supposed to be more recent developments.

lightcone 1.0 basic redshift article development

Mordred — Mon, 06 May 2013 18:49:24 GMT

Developing a basic explanatory manual for the Light cone 1.0 calculator. This is as a supplement to give a basic understanding on what the terms used in the calculator mean. The user manual is separate as is the advanced manual which shows the math forms used in the calculator.

The CMB, (Cosmic Microwave Background) The CMB is thermal radiation filling the Observable universe almost uniformly. The CMB provides an excellent reference point in distance measurements and corresponds to a stretch of 1090

Doppler shift and redshift are the same phenomenon in general relativity. However you will often see Doppler factored into components with different names used. 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.

[tex]\frac{\Delta_f}{f} = \frac{\lambda}{\lambda_o} = \frac{v}{c}=\frac{E_o}{E}=\frac{hc}{\lambda_o} \frac{\lambda}{hc}[/tex]

However the only form of redshift we need to concern ourselves with is called the cosmological 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.
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 [itex]\Lambda[/itex]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 (red) shift proportional to distance. 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. 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
z = (Observed wavelength - Rest wavelength)/(Rest wavelength) or more accurately

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

[tex]1+Z=\frac{\lambda}{\lambda_o}[/tex] or [tex]1+Z=\frac{\lambda-\lambda_o}{\lambda_o}[/tex]

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 blue shift 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.

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)

[tex]Proper distance =\frac{\stackrel{.}{a}(t)}{a}[/tex]

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.

[tex]H(t)=\frac{\stackrel{.}{a}(t)}{a(t)}[/tex]

Expansion velocity
[tex] v=\frac{\stackrel{.}{a}(t)}{a}[/tex]

This shows that Hubble's constant is time dependant.

Luminosity: absolute luminosity is the amount of energy emitted per second.
is often measured in flux where flux is

[tex]f=\frac{L}{4\pi r^2}[/tex]

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.

N-Body Simulations

Madster — Mon, 06 May 2013 13:20:13 GMT

Hi.

I read due interest papers in Arxiv. There is many times refereed to so called N-Body Simulations.

Is that for Matter or Dark Matter? How does it work, can someone explain or suggest good readings?

THX

About imaginary time

tmv3v — Sun, 05 May 2013 22:45:38 GMT

http://www.youtube.com/watch?v=VZiWKmhuaZE

At about 7:00 he talked about imaginary time. Does that account for parallel universe? Also is there an imaginary mass as well?