2.2 The Big Bang 16 where A = 1 for bosons and A = 3 4 for fermions and g is the number of spin states of the particle (relativistic degrees of freedom). The energy density is given by where B =1 for bosons and B = 7 8 for fermions. For the Universe, the energy density is given by the weighted sum of all the particles as with being the total number of spin states of all of the constituent particles (the effective number of relativistic degrees of freedom). As the temperature of the Universe falls due to the expansion, Γ for a particular particle species will fall below H at some time. Different particle species will start to fall out of thermal equilibrium at different times and thus decouple from each other. One of the big successes of the HBB is the agreement between analyti- cal/numerical calculations and observation of Big Bang Nucleosynthesis , hereafter referred to as BBN. After an excess of $^{1}$H (over anti- $^{1}$H ) had been ρ = π 2 30 $^{g}$∗T 4 (2.38) $^{g}$∗ ≡ bosons ∑ i g$_{i}$ + 7 8 fermions ∑ j g$_{j}$ (2.39) ρ = g 2 π 2 ∫ ∞ 0 f ( p ) p $^{3}$d p (2.36) = B π $^{2}$g 30 T 4 (2.37)