content_image/324936.jpg content_image/324933.jpg content_image/324934.jpg content_image/324932.jpg content_image/324935.jpg content_image/324937.jpg content_image/324931.jpg
verse is matter-dominated (ignoring dark energy). Therefore we have 

Therefore, from the Friedmann equation, we have 

This gives 

We now obtain $^{N}$∗ as 

<img src='content_image/324936.jpg'>

<img src='content_image/324933.jpg'>

<img src='content_image/324934.jpg'>

<img src='content_image/324932.jpg'>

<img src='content_image/324935.jpg'>

<img src='content_image/324937.jpg'>

<img src='content_image/324931.jpg'>

where we have used $^{g}$∗ ≈ 10 2 as the number of spin states (effective relativistic degrees of freedom) of all of the particles in the thermal bath, at the time of 

