Radiation in cosmology

Cosmological radiation has equation of state

P_{r} = ρ_{r} /3

and density scaling

ρ_{r} \propto a^{- 4}

.

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- Effective number of relativistic energy degrees of freedom Radiation in cosmology
  - Radiation mass density Effective number of relativistic energy degrees of freedom

Effective number of relativistic energy degrees of freedom ( $g_{*}$ )

For relativistic species in thermal equilibrium at a common temperature

T

, the total energy density can be written

ϵ = \frac{4 π ^{5}}{15 ( h c ) ^{3}} g_{*} (k_{B} T)^{4}, g_{*} = \sum_{bosons} g_{i} + \frac{7}{8} \sum_{fermions} g_{i} .

The factor

7/8

is the fermion-to-boson thermal integral ratio for energy density.

Radiation mass density ( $ρ_{rad}$ )

For relativistic species at a common temperature, the mass-equivalent energy density is

ρ = π^{2} g_{*} (k_{B} T)^{4} / (30 ℏ^{3} c^{5})

. Using mass rather than energy density accounts for the powers of

c

in the Friedmann equation.

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