f\^[i]{}\_1 (E\_1 ) f\_2\^[i]{} (E\_2 ) |M\^[i]{}\_n |\^2 (2)\^4 \^4 (k\_1 +k\_2 -p ) .Here $f^{i}$ are the Bose/Fermi distributions of colliding particles and $M^{i}_n$ is the amplitude of reaction $\psi^{i} +\b{\psi}^{i}\rightarrow G$, where $\psi$ and $\b{\psi}$ are standard model particles on the brane (vector, spinor, scalar) and $G$ is a state of mass $m_n$ from the graviton Kaluza-Klein tower [^8]. The squared amplitude of annihilation into graviton is [@heb] ł[i2]{} |M\^[i]{}\_n |\^2 =A\_i \_n\^2 (0) s\^4 , where $A_i = A_s ,\, A_v ,\, A_f =2/3,\,4,\,1 $ for scalars, vectors and fermions and $s^2 =(k_1 +k_2 )^2$. The sum over the graviton states is transformed to the integral following (\[en21\]). After integration over the angular variables of the momenta of interacting particles Boltzmann equation takes the form ł[i3]{} && +4H\
&& = - \_m\^2 (0) m\^4 dk\_1 dk\_2 f(k\_1 ) f(k\_2 ) (k\_1 +k\_2 )(1-|1-|) .Integrating over $m$, we obtain ł[i4]{} && +4H = - \_0\^[(2k\_1 k\_2 )\^[1/2]{}]{}dm m\^4 dk\_1 dk\_2 f(k\_1 ) f(k\_2 ) (k\_1 +k\_2 )\
&&=- , where the sum extends over relativistic degrees of freedom ł[i5]{} A=\_i A\_i = +g\_f (1-2\^[-7/2]{})(1-2\^[-9/2]{}) +4g\_v .In the high-energy period, when all the standard model degrees of freedom are 