H(t) =,\_w (t) =\_[w0]{}()\^4 where $\r_w (t)$ is the so-called Weyl radiation term [@maart], $\m\r_{w0}=C/a^4 (0,t_0 )$. To comply with the observational data, the Weyl radiation term, which appears in the leading-order solution to the Einstein equations should be small [^5]. Assuming that the terms with the bulk energy-momentum tensor can be treated perturbatively, we neglect corrections to the Weyl radiation term due to graviton emission from the brane.

Substituting from the junction conditions the expressions for $n'/n$ and $a'/a$ at $y=0$, we transform the (04) component of the Einstein equations (\[5\]) to the form ł[22a]{} +3H(+p )= .On the other hand, the same equation, which is a generalization of the conservation equation for the energy-momentum tensor of the matter confined to the brane to the case with the energy-momentum flow in the bulk, is obtained by integration across the brane of the 5D conservation law $\nabla_i T^i_0 =0$ [@tan].

Some relevant equations following from general approach to the 3-brane embedded in the AdS bulk are found in the appendix A.

Period of late cosmology
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Graviton production by hot matter is sufficiently intensive in the radiation-dominated period of cosmology. In the period of late cosmology the terms linear in 