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.