energy-momentum tensor in the bulk is $\c{T}^i_j$.

For the following it is convenient to introduce the normalized expressions for energy density, pressure and cosmological constant on the brane which all have the same dimensionality $[GeV]$ ł[8a]{} =,=, =, =. The functions $a(y,t)$ and $n(y,t)$ satisfy the junction conditions on the brane [@BDL2] [^3] ł[9a]{} && = --(t)\
&& =2(t) +3p (t) -Using reparametrization of $t$, we set $n(0,t)=1$, i.e. $t$ is the proper time on the brane. Eq. (\[3a\]) can be rewritten as ł[10a]{} = -\^2 -(a\^4 )’ Ţ\_[04]{} + Ţ\_[44]{} .On the brane, using junction conditions and setting $\s\simeq\m$, we have [^4] ł[11a]{} = \^2 +(+) Ţ\_[04]{} + Ţ\_[44]{} . Integrating (\[11a\]) in the interval $(t,\, t_l )$, where the initial time $t_l$ (of the onset of the period of the late cosmology) is defined below, we obtain ł[12a]{} F(0,t)=\^2 a\^4 (0,t) + \_[t\_l]{}\^t dt’ Ţ\_[04]{}(t’ )((t’) +)[a\^4 (0,t’)]{} + \_[t\_l]{}\^t dt’Ţ\_[44]{}(t’ )(0, t’ ) a\^3 (0,t’ ) -C.

Substituting expression (\[4a\]) for $F$ and using the junction conditions, we rewrite (\[12a\]) in a form of the generalized Friedmann equation (cf. [@BDL1; @BDL2]) ł[14a]{} H\^2 (t) = \^2 (t) +2(t) +\_w (t) -\_[t\_l]{}\^t dt’a\^4 (0,t’) .Here we introduced ł[13a]{} 