Friedmann's Assumption: Understanding the Universe's Uniformity

[pvk21]

Let's see.According to friedmann,universe looks same whichever direction we look.but what does it imply exactly.does it like there are equal number of galaxies in all direction?

 

[wabbit]

Yes, broadly / at a large scale. With respect to the observable universe, this is more an observation than an assumption. The most striking illustration of this isotropy is the homogeneity of the cosmic wave background (after correcting for the solar system proper motion), which shows a picture of the universe as it was ~14 billion years ago. The variations are artificially exaggerated in the pictures, otherwise all you'd see would be a prefectly uniform (to within ~0.001%) background.

http://www.britannica.com/EBchecked...-CMB/280807/Isotropy-in-the-cosmic-background

 

[Chronos]

That image portrays a finite universe as viewed by an external observer - very misleading. Observational evidence suggests the universe in which we reside is isotropic and homogeneous in every direction. In other words, yes, we see the same number of galaxies in every direction. The only variable is distance, which disappears if you look 'far' enough into the universe.

 

[wabbit]

That image portrays a finite universe as viewed by an external observer - very misleading.

Ah OK, I like it because it shows a sphere when the usual maps don't obviously do so, but I guess you're right, it can suggest an outside observer... OK, so here is the more usual projection

 

[pvk21]

So our universe is oval in shape?

 

[wabbit]

Ha ha. No, what we observe is a sphere - that's not the shape of the universe, just the shape of our observation: we look around us in every direction, and those directions form a sphere, regardless of what the shape of the universe may be, or if it is finite or infinite.

But of course representing a sphere faithfully isn't feasible on a flat image, and the two projections above are two out of many ways of doing that with some distortion, similarly to different projection used in maps of the Earth (the first one shows only half the sky, the second one the whole sky).

 

[pvk21]

Oh ok I get it.this is just observable universe or is it assumption that our universe would look like?as only sphere would fulfill friedmann's first assumption.

 

[pvk21]

Sorry friedmann's second assumption that its true from whichever point we look.

 

[wabbit]

The picture is what we see from Earth (from sattelites actually), but the assumption is that we would see something similar from anywhere else.

This assumption is supported to some extent by what we see: if the universe was not uniform, chances are that we, from our randomly located vantage point, would see diffrent things in different directions - it would be quite extraordinary to see a uniform image to within 0.001% if the universe wasn't itself uniform.

But as you said, that conclusion only really holds for the observable universe. For what's beyond, we can't see, by definition - so it really becomes an assumption when applied to the whole universe as in Friedman's model. A natural assumption for sure, but still an assumption.

 

[julcab12]

OT...In addiction. Not to be picky here. Let's ignore the pseudocylindrical map projection and include the very small curvature. IF the universe is curved to an approx 0.25% of which it can be sphere or saddle (freeze time). The image above is about 1 in 500. Well the image below is 46.1 bly in radius - centered on us with uncertainty of 98.8%. They can measure asymptotically flat(spacetime) as a bottleneck but you just can't take away that small curvature -- cosmological spacetime aren't asymptotically flat. We don't really know if their is deviation from flatness except from the limit of the eqn.

Image credit: Wikimedia

 

[wabbit]

Not sure what that "25% of being a sphere" means? The universe is known not to be spatially curved more than a sphere of about 100 bn ly at least*, and it could be spatially flat - it is flat within measurement uncertainty, the flat FLRW model is commonly used.

cosmological spacetime aren't asymptotically flat

This is generally true of spacetime curvature (for FLRW spaces), but how is this relevant here?

* edit : actually, greater than 200 bn ly, from the 2015 release http://arxiv.org/abs/1502.01589

 

[julcab12]

Not sure what that "25% of being a sphere" means? The universe is known not to be spatially curved more than a sphere of about 100 bn ly at least, and it could be spatially flat - it is flat within measurement uncertainty, the flat FLRW model is commonly used.

Ops. Sorry typo 0.25%. -- (New constraint from Planck 2015).. As i stated above asymptotically flat is part of the eqn. But cosmological spacetime aren't totally flat. Well, I do agree that it is the simplest..

 

[wabbit]

Ops. Sorry typo 0.25%. -- (New constraint from Planck 2015)

Oh that's "within some small % of being flat", not of being a sphere.

 

[julcab12]

Ops. Sorry typo 0.25%. -- (New constraint from Planck 2015)

Oh that's within 0.25% or so of being flat, not of being a sphere.

..0.25% Of being curved and largely flat. I know it is a very small value and it can account to a glitch -- negligible.

 

[pvk21]

Oh that's "within some small % of being flat", not of being a sphere.

 

[pvk21]

So our universe is almost flat of we ignore that small curve

 

[wabbit]

..0.25% Of being curved and largely flat. I know it is a very small value and it can account to a glitch -- negligible.

Well you can read it either way. It says the equivalent energy density produced by spatial curvature is $0\pm0.005$ as a fraction of total energy density. This is compatible with either flat space or a sphere (or hyperbolic space) of radius greater than some 200 bn ly or so. We just don't know more.

 

[wabbit]

So our universe is almost flat of we ignore that small curve

Right.

 

[pvk21]

So flat universe imply that after a big bang universe expanded unformly in straight line.is that right?

 

[pvk21]

Sorry but I can't imagine universe as flat.

 

[wabbit]

So flat universe imply that after a big bang universe expanded unformly in straight line.is that right?

Hmmm... Yes in a sense* I guess, but what exactly do you mean by that ?

* if you compute the trajectories of very distant galaxies receding away from us, these are undistinguishable from straight lines.

 

[wabbit]

Sorry but I can't imagine universe as flat.

Then take solace in the possibility of a very large sphere* : ) that's what I do

* a 3-sphere that is, not a regular sphere of course.

 

[julcab12]

Well you can read it either way. It says the equivalent energy density produced by spatial curvature is $0\pm0.005$ as a fraction of total energy density. This is compatible with either flat space or a sphere (or hyperbolic space) of radius greater than some 100 bn ly or so.

Of course. We can totally ignore the small curved part and approximate it to be totally flat instead like -- asymptotically flat or Friedman flat solution. Anyways. It depends on what you want with the curve..

 

[julcab12]

So our universe is almost flat of we ignore that small curve

Lol.. I'm not usually that picky nor i have any authority on the subject (just a laymen here) -- but w/out curvature it is flat not almost..

 

[pvk21]

Well its just my imagination but look when big bang happened all material that was at that point expanded all in straight line that mean it only in forward direction not in all directions

 

[wabbit]

Well its just my imagination but look when big bang happened all material that was at that point expanded all in straight line that mean it only in forward direction not in all directions

No, that's not what the model says. First, FLRW does not model what happened "at" the big bang, only at any time after that. And then, from any point "at rest" wrt the expansion, (we are in that case to a reasonable approximation), you see every other point (that is also at rest, or far enough that it doesn't matter) receding away in a straight line (the farther away they are, the faster they recede). There is no preferred direction.

This is actually the case for all FLRW models, not just in the flat case.

Edit: another forum member, phinds, has a nice page about this - have a look at http://phinds.com/balloonanalogy/

 

[marcus]

Sorry but I can't imagine universe as flat.

I sympathize. I can't imagine it as flat and infinite in extent. And I don't enjoy trying to imagine it as zero curvature and finite ( "PacMan" style flatness).
But presumably Nature isn't limited by what we personally can comfortably imagine. So I consult the latest numbers and adapt.

... greater than 200 bn ly, from the 2015 release http://arxiv.org/abs/1502.01589

Wabbit points to where it says "Spatial curvature is found to be |Omega_K| < 0.005." in the abstract. Click on the link. You get the abstract of the relevant Planck mission report and in the middle of the paragraph it says the MOST that |Omega_K| can be, with 95% certainty, is 0.005.

If you like picturing things in your imagination you might want to learn how to translate that into a radius of curvature. The maximum |Omega_K| translates into the SMALLEST radius, i.e. the smallest 3d spherical surface of a 4d ball, that you have to stretch to imagine if you want to picture that kind of finite, round universe.

The way you find the smallest possible radius is you take the present Hubble distance of 14.4 billion light years and you divide by the square root of the largest possible |Omega_K| in other words you take 14.4 billion light years and divide by the square root of 0.005.
The square root of that is 0.0707
and 14.4 divided by 0.0707 is 203.6
Call it 200 for round numbers.

Well you can read it either way. It says the equivalent energy density produced by spatial curvature is $0\pm0.005$ as a fraction of total energy density. This is compatible with either flat space or a sphere (or hyperbolic space) of radius greater than some 200 bn ly or so. We just don't know more.

 

[wabbit]

To be honest, I also think it's fairer to read the results as "very large radius of curvature" rather than "exactly flat". After all "0" is just one number out of the infinite possibilities allowed by the results, so unless we find a reason (a symmetry principle or such) that requires 0, that particular number is not likely at all.

The argument usually goes that, if a number could a priori be anywhere between 0 and 1, and we get an experimental result of "$\leq 0.000000001$", then we should suspect that we were wrong in assuming "anywhere between 0 and 1" and that maybe there is some unknown reason that makes the true number 0.

This is a reasonable argument, but not foolproof, and it fails in other known cases. In fact, the leading theory proposed to explain the (very) small number we get in the case if curvature (together with a few other otherwise weird observations), namely inflation, essentially divides the probable range by a large value, so that our measure falls within the new "natural" range.

But as far as I know (not much, I just started reading about inflation), this theory has no preference for 0 curvature over a very small curvature. So we are back where we started, with no compelling reason to believe the universe is exactly flat, although we know it is nearly flat.

 

[pvk21]

But as far as I know (not much, I just started reading about inflation), this theory has no preference for 0 curvature over a very small curvature. So we are back where we started, with no compelling reason to believe the universe is exactly flat, although we know it is nearly flat.

 

[pvk21]

So although experimentally universe must be somehow curved.but practically its exactly flat.

 

[wabbit]

So although experimentally universe must be somehow curved.

I wouldn't go that far. It is my personal view as a layman that this is more likely than not, but "must" is a big word, there is as far as I know no proof either way.

but practically its exactly flat.

If you mean by that "as good as flat for all (or most) practical purposes" then yes, its curvature is currently estimated to be too low to have any practical consequences.

 

[Chronos]

The CMB is depicted using Mollweide projection, which renders a spherical surface flat with minimal distortion. It looks oval when depicted in this fashion.

 

[Chalnoth]

That image portrays a finite universe as viewed by an external observer - very misleading. Observational evidence suggests the universe in which we reside is isotropic and homogeneous in every direction. In other words, yes, we see the same number of galaxies in every direction. The only variable is distance, which disappears if you look 'far' enough into the universe.

It's the other way around.

The observable universe is extremely homogeneous and isotropic on large scales. But there's no reason to believe that the isotropy and homogeneity extends far beyond the observable universe.

Take inflation, for example. In simple models of inflation, the universe is made to be smooth because of the rapid early expansion. This rapid early expansion doesn't eliminate any variations that existed early-on, it just made it so much larger than the observable universe that we can't detect them. If it were possible to take a sort of "bird's eye" view of the universe on scales much larger than the part we observe, the natural expectation is that pretty large deviations from homogeneity and isotropy would appear.

Of course, it is possible to assume that the universe, not just the observable part, truly is homogeneous and isotropic. But that's an assumption, and I don't think any realistic model of how our universe could have formed produces a perfectly homogeneous or isotropic universe.

 

[wabbit]

It's the other way around.

The observable universe is extremely homogeneous and isotropic on large scales. But there's no reason to believe that the isotropy and homogeneity extends far beyond the observable universe.

Take inflation, for example. In simple models of inflation, the universe is made to be smooth because of the rapid early expansion. This rapid early expansion doesn't eliminate any variations that existed early-on, it just made it so much larger than the observable universe that we can't detect them. If it were possible to take a sort of "bird's eye" view of the universe on scales much larger than the part we observe, the natural expectation is that pretty large deviations from homogeneity and isotropy would appear.

Of course, it is possible to assume that the universe, not just the observable part, truly is homogeneous and isotropic. But that's an assumption, and I don't think any realistic model of how our universe could have formed produces a perfectly homogeneous or isotropic universe.

I would however argue that it is more likely than not for the universe to be homogeneous at a significantly larger scale than our observable universe : it would seem to be an extraordinary coincidence for the homogeneity scale to just match precisely our observable scale - since we know that it is greater, it sounds more reasonable to assume that they are of different magnitude that just too numbers that happened to be close.

This is of course a layman view and perhaps there are arguments that support the idea that the two scales are bound to almost coincide, I just haven't seen them yet.

 

[microtech]

IF the CMB is the light from "the last scattering" at T₀+378,000 years, I don't quite understand how there can be something "behind" that (as the image above implies, where "our" Universe is inside a 46.5 Gly sphere)... Have scientists finally come to their senses, and given up on the "big bang"? That would (should?) have made big news, but I haven't heard a thing... Can someone please explain? Here's my adaptation of a Wikipedia illustration of the "observable" universe, a "zoom in" on the image above. These are the Universe numbers presented in Wikipedia (en.wikipedia.org/wiki/Observable_universe):

Diameter: 93 billion light years (Radius 46.5 Gly)
Volume: 4×10⁸³ liter
Mass (Baryonic): ⁵³ kg
Density: 9.9×10^-30 g/cm³ (equivalent to 6 protons per m³ of space)
Age: 13.798 ± 0.037 billion years

Note that the density given in Wikipedia is for a Universe "a mere" 13.8 Gly radius, whereas the volume is for a 46.5 Gly radius, which would have the much thinner density of 2.45×10^-31 g/cm³ (equivalent to 0.15 protons per m³ of space).

The image above indicates a much larger Universe... Very confusing... Can someone who knows what this is supposed to mean please explain? Bye bye big bang? Hello infinite Universe? What?

https://sites.google.com/site/microtechnonstop/f/Visible%20vs.%20Observable%20Universe%20.png

 

[microtech]

Take inflation, for example. In simple models of inflation, the universe is made to be smooth because of the rapid early expansion. This rapid early expansion doesn't eliminate any variations that existed early-on, it just made it so much larger than the observable universe

This is an oft claimed feature of "inflation," but I have yet to see an explanation of how this would work. What, exactly, becomes "much larger than the observable universe," and at what timeframe? Alan Guth's original (simple?) claim was an expansion factor of "at least 10²⁶," which would make the universe 0.1 m across after 1/10³² second, how can a one meter difference in radius "smooth out" anything?

 

[microtech]

Mass (Baryonic): 53 kg

As I don't know (yet) how to edit earlier posts, I comment my own post: The Mass was of course given as 10⁵³ kg.

 

[Chronos]

I fail to see your point, microtech, Logic does not trump observational evidence and math.

 

[microtech]

observational evidence and math

What observational evidence and math would that be? When I do the math, the "Guth Inflation" blows up a very small universe to one with a radius of 10 cm in a very short time. That is not "logic," it is simple math. How do these 10 extra cm do anything to solve the flatness and the horizon problems? And who was there to observe anything, 13.8 billion years ago? Interpretations of data from observations made today is not evidence of what might have taken place 13.8 Gyr ago.

 

[wabbit]

How do these 10 extra cm do anything to solve the flatness and the horizon problems?

You need to look at the maths / model to see how that question is answered by inflation and determine to what extent that answer is satisfactory. One thing is sure, inflation does address this issue - the key point is probably that what matters for this is not the size of the universe at the end of onflation per se, but the ratio of the size after and before inflation, and this ratio is something like 10^30 or greater in such models, which is big enough to have the required impact (actually that number comes from the required impact, which is a constraint on the model).

Inflation is probably the leading theory for explaining flatness, horizon etc. but not the only game in town either, and it has its own issues. But as far as I can tell, these seem to have to do more with such things as the need to fix parameters at some arbitrary looking value etc, than with observations not matching predictions (inflation seems pretty good at that).

Edit : Regarding such questions, more knowledgeable members directed me to this : http://cern.ch/lesgourg/Inflation_EPFL.pdf , and this http://lanl.arxiv.org/abs/astro-ph/0305179, both are pretty good introductions to inflation, with different style etc.

 

[bahamagreen]

There may be confusion about the meaning and mechanics of homogeneous and isotropic.
The first refers to the overall spacing of things as observed from anywhere (looks to be the same throughout).
The second refers to the lateral but not longitudinal view of things as observed from a particular place (looks the same in every direction).

There are problems about this; first, they both use the phrase "looks the same", which is troublesome.

Taking the second one, saying that the universe "looks the same" in any direction has two possible meanings; it might mean that in any direction you chose the result will be the same as compared to another direction (lateral aspect), but it might also be thought to mean that the results "look the same" in any particular direction comparing segments of that direction to other segments of that same direction - that the observed spacing of objects is constant with increasing distance (the spacing of things in the universe looks the same no matter how far you look in anyone direction)... but this is not true, per Hubble, et al. In this sense the universe does not look the same in every direction; it seems to be changing uniformly with respect to distance in every direction (longitudinal direction)... but doing this the same way for every direction.

The first one says the universe looks the same throughout, but that might mean either it appears so or is inferred to be so after correction for time delay. This is a primary confusion if one knows that the universe is expanding with time... seeing more distant regions as they were from progressively younger more dense states. If they appear to be the same throughout by visual inspection, this suggests that the time delayed views of more distant objects represent some intrinsic correction for their having originated from an earlier scale factor in order to match that of the local observer. On the other hand, if these views are different but accounted for or corrected by knowing of the expansion, the inference is that the universe is the same throughout. It may not be clear whether "looks the same throughout" means "the same as observed" or "the same after correcting for expansion"... it is rarely explained which method is used to develop this snapshot of the universe.

 

[Chronos]

There is no good alternative to inflation that can reasonably explain the extraordinary uniformity of the CMB temperature, since these regions could not have otherwise been in causal contact, thus inflation solves the horizon problem. Inflation also smooths out quantum fluctuations that would otherwise have grown to enormous proportions in the modern universe, thus it also solves the flatness problem. Scientists believe the universe is larger than the observable universe because it is perfectly flat [the largest triangles we can 'draw' in the universe add up to precisely 180 degrees] to the limit of our measurement ability. If the entire universe were a sphere the size of the observable universe, the largest triangles would add up to measurably less than 180 degrees. See http://arxiv.org/abs/1101.5476 for discussion.

 

[Chalnoth]

Have scientists finally come to their senses, and given up on the "big bang"?

Seriously? Don't be a douche.

 

[Chalnoth]

The image above indicates a much larger Universe... Very confusing... Can someone who knows what this is supposed to mean please explain? Bye bye big bang? Hello infinite Universe? What?

https://sites.google.com/site/microtechnonstop/f/Visible%20vs.%20Observable%20Universe%20.png

This graphic is incorrect.

The visible universe and the observable universe are essentially the same thing. The visible universe (that is, the universe visible by using photons) terminates at the surface of last scattering, the surface that emitted the CMB some 13.7 billion years ago or so. This surface is currently about 47 billion light years away. When the CMB was emitted, it was about 43 million light years away. The rapid early expansion carried the light from the CMB away from us at a high speed for billions of years. Since then, the expansion has slowed dramatically, and the light has had a chance to gain ground and start to reach us.

If we ever manage to observe the universe through something other than photons (e.g. neutrinos or gravity waves), we might be able to see to earlier times, which would also give us a window into matter that is currently further away.

 

[Drakkith]

IF the CMB is the light from "the last scattering" at T0+378,000 years, I don't quite understand how there can be something "behind" that (as the image above implies, where "our" Universe is inside a 46.5 Gly sphere)... Have scientists finally come to their senses, and given up on the "big bang"? That would (should?) have made big news, but I haven't heard a thing... Can someone please explain?

Sure, what exactly are you having trouble understanding?