'Density' of 2.73K Cosmic Microwave Background

[tasp77]

Never seen this addressed anywhere, and maybe it doesn't matter;

but, regarding the cosmic background radiation, in any given instant, how many 2.73K (on average) photons are in a given volume ?

See, we would measure the same background temperature with our instruments over a range of 'densities', but the actual energy content could vary.

(or does the temperature finding of 2.73K take that into account ?)

And then a follow up, what would the total energy content in the entire observable universe be for the CMB? And then what is the mass equivalent of that ? (solve for M instead of E in E=MC\
2)


I know this hasn't been overlooked in the field of cosmology, it just hasn't filtered down to my level.

 

[yenchin]

To answer your first question, it is around 400 CMB photons per 1 cm^3. This can be found as an exercise in Pathria and Beale's Statistical Mechanics [Problem 7.24].

 

[Chronos]

The CMB temperature of 2.73K is the temperature at t = 13.7 billion years. It increases with redshift by a factor of 1+z, meaning the CMB temperature at z=1 is twice that of our local [z=0] universe. This has been observationally confirmed - e.g., http://arxiv.org/abs/astro-ph/0012222

 

[marcus]

Never seen this addressed anywhere, and maybe it doesn't matter;

but, regarding the cosmic background radiation, in any given instant, how many 2.73K (on average) photons are in a given volume ?

See, we would measure the same background temperature with our instruments over a range of 'densities', but the actual energy content could vary.

(or does the temperature finding of 2.73K take that into account ?)

And then a follow up, what would the total energy content in the entire observable universe be for the CMB? And then what is the mass equivalent of that ? (solve for M instead of E in E=MC\
2)I know this hasn't been overlooked in the field of cosmology, it just hasn't filtered down to my level.

This is a pretty interesting bunch of questions, which HAVE in fact been addressed by cosmologists. It would be nice to respond at more length. Yenchin's answer of about 400 photons per cubic centimeter is almost surely right, but one could say more.

The CMB is "black body" radiation or "cavity" radiation and that kind of radiation follows a beautifully simply laws that were worked out over 100 years ago by people like Ludwig Boltzmann and Max Planck. It is the generic radiation that fills a box and depends only on the temperature of the walls of the box. The temperature tells everything: the energy density, the number of photons per unit volume, the average energy of an individual photon, and even the statistical distribution curve of how many photons in each energy bracket, or if you plot the curve on a wavelength scale, the number of of them in each wavelength bracket. So the temperature tells everything.

These are all old results, from before or around 1900, but some of the finest in all of physics. Worth looking up in Wikipedia and learning about.

=====================
You ask other questions. You ask about the observable universe. Probably the best approach there is to get your answers PER UNIT VOLUME first, and then multiply by the volume of the currently observed region. Of course the volume of the observable universe is constantly growing as more light comes in from more and more distant matter. And we only know what it is at the present era in an APPROXIMATE way.

It is approximately a spherical volume with a radius between 45 and 46 billion LY, centered at the Milkyway galaxy. That is how far away, now, the farthest matter is that we can see the glow of, or that we could detected the neutrinos coming from, if we had a good enough neutrino instrument.

But that volume is a bit fuzzy. You can find out the DENSITIES (amount per unit volume) of different species of energy much more precisely. So that is probably the way to go.

An astronomer named PEEBLES published an ENERGY INVENTORY a few years back that has all these energy densities. You might be curious and want to take a look. I'll see if I can find it. It has the energy density of the CMB listed in there along with the rest.

Yeah. I just googled "peebles energy inventory" and got this:
http://ned.ipac.caltech.edu/level5/March04/Fukugita/frames.html
and the archived preprint:
http://arxiv.org/abs/astro-ph/0406095

There's more to be said about all this. I imagine that if you keep asking questions you will be told more stuff. Incidentally Chronos link is to a very beautiful paper about the temperature of a certain distant gas cloud measured by observing a molecular transition happening in the cloud, as if one could read a remote thermometer using special imaginary eyeglasses. It's related to this discussion too, but rather advanced for starters.