Aidan Karley .group wrote:
A discussion elsewhere lead me to wonder what the temperature
of the CMB was at about the time that Jupiter was forming. (I was
wondering how the different background temperature would affect the
rate at which the initial gravitational infall energy was radiated.)
I'd guess that the temperature is declining exponentially, so I
should be able to work out an expression from the decomposition
temperature of hydrogen (ca. 5,000 K ? ), the present age of the
universe (13.7 Gyr) and the present CMB temperature (3.7 K). But it
would only be a guess.
Does anyone have an expression that would give the CMB's
temperature as a function of time - either time after the hydrogen
recombination/ big bang, or back from the present day? Doesn't have to
be too accurate - give or take a factor of two would be fine.


At the epoch from which we now see radiation at redshfift z, the
CMB had temperature 2.73(1+z). The time-z mapping depends on
the cosmological parameters, and doesn't necessarily have
a nice closed form. Ned Wright's calculator at
http://www.astro.ucla.edu/~wright/CosmoCalc.html
will deliver lookback times (which is what you need) for
various z and cosmologies. For the popular WMAP "consensus"
values, 4.6 Gyr back corresponds to z=0.44, for a CMB temperature
of 3.9 K.

Bill Keel