Carried along by the Hubble flow.

[Naty1]

Marcus:

So if you have some massive particle with a certain momentum p measured relative to universal rest and if it is flying free not interacting much if any with other stuff then its momentum will tend to taper off gradually to zero and it will decline as 1/a where a(t) is the scale factor...beautifully enough that is exactly what happens to a photon of light ..

yes, So that explains the Tamara Davis one liner :

...matter particles have the same proportional redshift as photons...

or something very close...

very nice!

Marcus:

...So it is momentum measured by isotropic observers which very gradually tapers off as the spatial geometry expands. ...as 1/a...

I will try and read, er, that is, 'understand', the Zhang paper but before I do, can you confirm that this result is applicable for all cosmological time...in other words, in earlier matter dominated expansion as well as our current energy dominated expansion...a[t] varies over time so the redshift pattern of momentum decline [redshift] also varies over time, right...that also provides a nice insight about the cumulative effects of expansion on redshift that I did not really appreciate previously.

edit: sure. it is ok for varying cosmological time periods and the Hubble parameter is related since H[t] = a'[t]/a[t]...

[This almost makes sense!.]

PS: Wasn't that you who previously mentioned 'isotropic observers' in another thread??...no "hotspots'...anyway, somebody did and that perspective made it into my personal notes! [ If you try and deny it I will be forced to look it up in my notes and see if I have an attribution!]

 

[marcus]

I wouldn't urge anyone to read Hongbao Zhang's paper, too technical. But on page 2 it has equation (2.7) which says that, as measured by isotropic observers
p ~ 1/a

After that, he goes into how the distribution of energies remains THERMAL which is kind of interesting. But not essential.
You know that lop-sided bell curve mound that Planck discovered describes the distribution of energies of photons in thermal equilibrium (say in a hot box).
It is a kind of beautiful fact that the CMB still has that thermal shape after all these years.
The shape was established when the photons actually were in equilibrium with hot gas. But they have kept that same distribution for 13.7 billion years during which they have NOT been in contact and have not been thermalized and made to be in equilibrium with anything. Just flying free.

Well, he goes thru some math to show that neutrinos, even though they lose energy and momentum differently, would ALSO retain a thermal distribution. If we could ever see the cosmic neutrino background, we would find that it too (like the CMB) had a nice lopsided bellcurve distribution.

But that, tho nice to know, is not essential. I would just read (2.7) and glance at some verbal context, and be lazy about the rest. Life is short.

In answer to your questions: I confirm as well as I can (as non-expert retired guy who loves cosmology) that equation (2.7) would work for all the time that cosmology normally covers.

(Up to near the start of expansion where the classical GR geometry fails and you need a quantum cosmology extension.)

And I don't recall having used the phrase isotropic observers before, but I could have and forgotten. You might find the phrase in your notes if you took the time to look. It's great you keep notes.

 

[Naty1]

I wouldn't urge anyone to read Hongbao Zhang's paper, too technical.

I skimmed the paper...if you like advanced math, go for it; otherwise, there are few additional insights described beyond what Marcus posted...