The Universe is too cold.

Our Universe is much too cold. Let me prove it to you. I'll base the proof on the following assumptions:

Over it's entire history, the stars in the universe has produced:

(4 x 1026)(1011) (5 x 1011)(4.4 x 1017) = 8.8 x 1066 Joules

Note that this is the energy from Stars only. The copious radiation from black holes, pulsars, supernovae, interstellar shock fronts, other non thermal sources, and of course, the big bang itself, is ignored here.

If r is the radius of the universe, there are 4/3 pi r3 = 1.15 x 1079 cubic meters in the universe.

Dividing the universe's total energy by its volume gives us it's energy density:

8.8 x 1066 / 1.15 x 1079 = 7.7 x 10-13 Joules/m3

Radiation density is given by the following equation: 2

U = a T4 n 3.

U is the energy density,
a is the radiation density constant = 7.564 x 10-16 Js/m3
n is the index of refraction of the medium, which is 1 for the vacuum of space, so it drops out of our considerations.

Solving for T gives: T = (U / a) 1/4

Plugging in the numbers gives a temperature of 5.6 degrees Kelvin. Now, the observed temperature of space is 2.735 degrees Kelvin3.


I hasten to again point out that my estimates of stellar output are conservative, as the early universe is widely supposed to have been a more energetic place than it is today, and I have ignored all non thermal radiation.

OK, where'd I go wrong? Drop me a line if you have any insights.

1) Data from the Hubble Deep Field exposure.

2) K. R. Lang, Astrophysical Formulae, Springer Verlag, 1980.

3) Mather, et al, GSFC colloquium, data from the COBE spacecraft.

The background image used is of the enigmatic cluster IC1257, from the Palomar Sky survey I.