How exactly can CMBR tell us universe age

[azaharak]

HI

Can someone give a good explanation of how we can infer an age of the universe from the CMBR. I was thinking in principle you could get an estimate from determining the rate at which the CMBR is changing, but experimentally that would seem to difficult to observe. Also i guess that assumes a constant rate of expansion.


Also, how does mass effect the expansion? For instance, we often hear that the "space between atoms isn't expanding". I'm assuming this is because mass distorts the expansion?

Thanks to everyone in advance

 

[bapowell]

Hi azaharak,

Can someone give a good explanation of how we can infer an age of the universe from the CMBR. I was thinking in principle you could get an estimate from determining the rate at which the CMBR is changing, but experimentally that would seem to difficult to observe. Also i guess that assumes a constant rate of expansion.

The age of the universe is not read directly from the CMB. The peaks and troughs of the CMB spectrum give detailed information about the expansion rate, the density, and composition of the universe, among other things. Once you have values for these quantities, you use Einstein's general relativity to evolve the universe backwards in time, from today back until the universe reaches (approximately) zero size. This will give the age of the universe. So, it's a theoretical calculation that is based on a few experimentally determined numbers.

Also, how does mass effect the expansion? For instance, we often hear that the "space between atoms isn't expanding". I'm assuming this is because mass distorts the expansion?

The space between atoms is expanding -- all space is expanding. However, the atoms don't grow in size because the atoms are electromagnetically bound.

 

[Naty1]

I disagree with the implied descriptions in post #2...

CMBR IS one way, but not the only way, to estimate the age of the universe...via CMBR current temperature of about 2.7 degrees kelvin...vs theoretically what it was after the big bang...
Try here: http://en.wikipedia.org/wiki/Age_of_the_universe

from above:

Also, how does mass effect the expansion? For instance, we often hear that the "space between atoms isn't expanding". I'm assuming this is because mass distorts the expansion?

The space between atoms is expanding -- all space is expanding. However, the atoms don't grow in size because the atoms are electromagnetically bound.

This is at the least very misleading; aw heck, its just plain wrong...space increases only on intergalactic scales...Try searching for "cosmological constant" here in the forums... and see what turns up here in a closely related thread I just started: https://www.physicsforums.com/showthread.php?t=381205

 

[sylas]

I disagree with the implied descriptions in post #2...

CMBR IS one way, but not the only way, to estimate the age of the universe...via CMBR current temperature of about 2.7 degrees kelvin...vs theoretically what it was after the big bang...

That's not telling you the age of the universe. It is telling you the scale factor in relation to the scale at last scattering, which is not the same thing at all.

Cheers -- sylas

 

[bapowell]

I disagree with the implied descriptions in post #2...
CMBR IS one way, but not the only way

I never said that the CMB was the only way...

This is at the least very misleading; aw heck, its just plain wrong...space increases only on intergalactic scales...Try searching for "cosmological constant" here in the forums...

Thanks for your courteous response. I'm a cosmologist, and I know what the cosmological constant is. Space is expanding everywhere -- the FRW metric is uniform -- a(t) is nonzero everywhere in space. Whether space itself is expanding and whether objects in space are separating are different questions. Galaxies expand along with space because they are weakly bound relative to the expansion. More strongly bound systems do not expand along with space because the expansion is weak relative to the force that binds them. It's well known that if the expansion were more rapid (eg phantom expansion), then a time would come when even atoms would be torn apart.

I just started: https://www.physicsforums.com/showthread.php?t=381205

What does this have to do with the expansion of space?

 

[bapowell]

I never said that the CMB was the only way...
Thanks for your courteous response. I'm a cosmologist, and I know what the cosmological constant is. Space is expanding everywhere -- the FRW metric is uniform -- a(t) is nonzero everywhere in space. Whether space itself is expanding and whether objects in space are separating are different questions. Galaxies expand along with space because they are weakly bound relative to the expansion. More strongly bound systems do not expand along with space because the expansion is weak relative to the force that binds them. It's well known that if the expansion were more rapid (eg phantom expansion), then a time would come when even atoms would be torn apart.

Yikes! Having a touch of schizophrenia here. Immediately after writing this, I realized that I am, indeed, incorrect. This argument does not hold on small scales -- of course, the FRW metric applies to a homogeneous energy distribution -- a good approximation only on large scales. However, the solar system, earth, atoms, people -- these contribute to a locally inhomogenous energy density. The metric within the solar system is closer to Schwarzschild, which is a static spacetime. I don't know what the metric looks like on the scale of an atom, but it's not expanding.

 

[BillSaltLake]

I think the nuts & bolts calculation goes something like this: at around 3000K, plasma (mixed photons, baryons, electrons) waves traveled at about 0.6c. From the first CMB peak, .6c times the age at 3000K has an angular size of about one(?) degree, as we measure it. However the redshift (3000/2.7) is about 1090, so looking back, the "true" size would be 1/1090 degree. If the 3000K surface occurred at time t₀, then our present age is .6ct₀ x 1090 x the inverse of 1 degree in radians.

I think it's actually closer to .9 degree used in the calculation. We believe t₀ is about 380,000yr from other arguments.

 

[George Jones]

Yikes! Having a touch of schizophrenia here. Immediately after writing this, I realized that I am, indeed, incorrect. This argument does not hold on small scales -- of course, the FRW metric applies to a homogeneous energy distribution -- a good approximation only on large scales. However, the solar system, earth, atoms, people -- these contribute to a locally inhomogenous energy density. The metric within the solar system is closer to Schwarzschild, which is a static spacetime.

The Swiss cheese model!

I don't know what the metric looks like on the scale of an atom, but it's not expanding.

Richard Price gives a simplified treatment for a "classical atom" in

http://arxiv.org/abs/gr-qc/0508052.

 

[bapowell]

Thanks for the reference George. According to this work, it appears that my initial response (post #5 above) is closer to the correct answer than my alternate personality's interjected correction (post #6 above). However, Price also begins with the FRW background, then places an atom in it. Then it's just a matter of atomic forces withstanding the efforts of spatial expansion. I guess I'm confused why FRW is relevant on such small scales, where the energy density is far from homogeneous.

 

[George Jones]

Thanks for the reference George. According to this work, it appears that my initial response (post #5 above) is closer to the correct answer than my alternate personality's interjected correction (post #6 above).

Are your posts #5 and #6 really so different? For example, aren't

More strongly bound systems do not expand along with space because the expansion is weak relative to the force that binds them.

However, the solar system, earth, atoms, people -- these contribute to a locally inhomogenous energy density.

really about similar things? The Swiss cheese model cuts out part of a FRW spacetime and inserts a Schwarzschild spacetime that matches on the boundary. It is known more formally as the Einstein-Strauss model. Unfortunately, this model has (at least) a couple of problems: such a matching is perturbatively unstable; for our solar system, the Schwarzschild region would have a radius of about 1000 light-years, and there are many stars within 1000 light-years of the Sun, so Schwarzschild matching is too simplistic.

However, Price also begins with the FRW background, then places an atom in it. Then it's just a matter of atomic forces withstanding the efforts of spatial expansion. I guess I'm confused why FRW is relevant on such small scales, where the energy density is far from homogeneous.

The electromagnetic field in Price's equation (14) contributes an inhomogeneity to to the stress-energy tensor that Price ignores. Price's toy model models something like a solar system by a "classical atom" bound by an electromagnetic force in order to avoid too much GR.

Both models are quite interesting, but both models are really just quantitative plausibility arguments.