is independent of $\b{y}$. The same measure of integration was obtained in [@lan1], where the authors used the graviton modes of the RS2 model without matter, in which case the integration over $y$ extends to infinity and the spectrum is continuous. Similarity of the results can be traced to the fact that we performed calculations in the period of late cosmology neglecting the terms of order $O(\r/\m)$ as compared to unity. This result can be anticipated also from the equation for the eigenmodes which does not contain matter terms. Time (temperature) dependence of the Universe enters only through the $\b{y}$ , and calculations of appendix B are effectively performed by taking the limit $\b{y}\rightarrow \infty$.

Production of Kaluza-Klein gravitons
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Let us calculate the rate of production of Kaluza-Klein gravitons in interactions of particles in hot matter on the brane in the radiation-dominated period.

Production of Kaluza-Klein gravitons in reactions of particles localized on the brane is calculated with the interaction Lagrangian $$I =\k\int d^4x\,\sqrt{-\b{g}}\,{h}_{\m\n}(0,x)T^{\m\n}(x) ,$$ where $T^{\m\n}$ is the energy-momentum of particles on the brane. The Boltzmann equation which determines evolution of the energy density $\h{\r}(t)$ of matter on the brane is [@kolb; @heb; @lan2] [^7] ł[i1]{} +4H =-\_n\_i 