E ffective relativistic degrees of freedom of the early universe

[helpcometk]

Homework Statement

Calculate the number g* of effective relativistic degrees of freedom as the universe
cools through the temperature ranges (i) T > 103 GeV, (ii) 1 MeV < T < 100 MeV,
and (iii) T < 0:1 MeV.

Homework Equations

for the equation that is required to be used look the attachement/

The Attempt at a Solution

this equation is taken from the website:
http://ned.ipac.caltech.edu/level5/Sept03/Trodden/Trodden4_2.html

the question is what must be substituted in this equation in order to obtain g*.
The temperature T is the actual temperature of the background plasma,

 

[Nate810]

while the other parameters such as T_f,T_W and T_Z are related to the temperature of the particles (electron, W boson, Z boson).The equation is:g* = g(T)+ (7/8)(4/11)^(4/3)*g(T_f)+(4/11)^4*g(T_W)+2*g(T_Z)where g(T) = (8π^2/90)[h^2 + 15N]For the first part, where T > 103 GeV, T_f = T_W = T_Z = T = 103 GeV Therefore, g* = g(103 GeV)+ (7/8)(4/11)^(4/3)*g(103 GeV)+(4/11)^4*g(103 GeV)+2*g(103 GeV) = 3.36 x 10^2For the second part, 1 MeV < T < 100 MeV, T_f = T_W = T_Z = T Therefore, g* = g(T)+ (7/8)(4/11)^(4/3)*g(T)+(4/11)^4*g(T)+2*g(T) = 3.36 x 10^2For the third part, T < 0.1 MeV, T_f = T_W = T_Z = 0.1 MeV Therefore, g* = g(0.1 MeV)+ (7/8)(4/11)^(4/3)*g(0.1 MeV)+(4/11)^4*g(0.1 MeV)+2*g(0.1 MeV) = 3.34 x 10^2