jackal0206 said:
One question I want to know though, isn't rho_matter/rho_rad = Scale factor and not redshift?
I think yes, you're right, if I understand you. To paraphrase what I think you mean:
rho_matter/rho_rad
is the ratio of scalefactor now and scalefactor then (when matter and radiation were in balance).
In other words the ratio by which distances have expanded since that time.
So instead of being exactly the redshift z, it is 1+z.
Because the answer is large there is not much percentage difference if add or take away one, but you're right to keep the concepts clear like that and make the distinction. Good luck with your astro course!
Chronos said:
A thought to consider - can photons remain homogenously distributed throughout the universe without redshift?
I think the answer might depend somewhat on the model, Chronos. If I understand you, it is a kind of "what if" question. What if, after year 380,000, there had been no expansion? Suppose some genii had frozen the geometry of the universe at that moment, so that distances could neither expand further or begin to re-collapse. Imagine you are the light. What would happen to you?
I think eventually you would be scattered. Re-absorbed and your energy re-emitted. Because the density of year 380,000 is just too high.
The reason that, for us, year 380,000 (approx.) works as a "moment of last scattering" of the great majority of CMB light is that by that time the mean-free-path or the expected free flight time for a photon is long enough, that by the time it would have been absorbed or scattered (barring expansion) there will have been enough additional expansion to extend its flight still more. When you solve the equation that gives 380,000 it takes into account that kind of feedback (or synergy or cooperation among the variables).
Part of the reason 380,000 works IOW is precisely because distances are expanding fast enough---density is declining fast enough--- so that the photon can "recalculate its own mean free path as it goes along", continually getting a new lease on life, and make it to mathematical infinity. It is the point where the half-life blows up so to speak. I hope this sloppy explanation is not making things worse. I looked at the derivation a couple of decades ago and wouldn't be able to re-produce it, just retain the vague idea. Popular accounts simplify by saying that 380,000 was the moment that the medium became transparent. But it didn't become perfectly transparent---just transparent enough that, allowing for future expansion, you had infinite path expectancy.
Like. Density determines your life expectancy as a photon. If density is decreasing fast enough it's like medical science progressing fast enough. We come to a point where you can live forever. Because you will almost surely make it for another five years and by that time medical science will have improved and given you another ten years and so on.
So the whole microwave background thing depends on there being expansion. Not just the homogeneity but even having all that ancient light around at all.
