relativistic, $A=166,2$. Eq.(\[i4\]) has the same form as Eq.(\[22a\]) and the expression in the rhs of (\[i4\]) is the component $\c{T}_{04}$ of the bulk energy-momentum tensor [@lan2] (see (\[i6\]) in the next section). The physical content of both equations is that the energy loss on the brane is due to graviton production.

The energy-momentum tensor in the bulk
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Corrections to the leading-order solution to the Einstein equation are expressed through the components of the energy-momentum tensor of the emitted gravitons in the bulk. In this section we determine the $y$-dependence of the components of the energy-momentum tensor in the bulk in the period of late cosmology.

After being produced in reactions on the brane, gravitons move freely following the null geodesics in the bulk. Coordinates of particles on the geodesics are parametrized by an affine parameter $\la$. In the region $0<y<\b{y}$ we integrate geodesic equations using the approximate metric (\[ap\]) $$ds^2 = dy^2 +e^{-2\m y}\b{g}_{\m\n}(x)dx^\m dx^\n
.$$ Geodesic equations are ł[g1]{} && +2\^a\_[by]{}+ 2\^a\_[b [0]{}]{}=0\
ł[g2]{} && +2\^[0]{}\_[[0]{} y]{}+ 2\^[0]{}\_[ab]{}=0\
ł[g3]{} && +\^y\_[[0]{} [0]{}]{}()\^2+ \^[y]{}\_[ab]{}=0 ,where connections are $$\Gamma^a_{by}=-\d^a_b\m,\quad \Gamma^a_{b
{0}}=\d^a_b\f{\dot{a}}{a},\quad
\Gamma^{0}_{{0} y}=-\m,\quad \Gamma^{0}_{ab}=\eta_{ab}\dot{a}a,\quad
\Gamma^y_{{0} {0}}=-\m e^{-2\m y},\quad \Gamma^{y}_{ab}= a^2\eta_{ab}\m
e^{-2\m y}.$$ Integrating the geodesic equations, we obtain ł[g4]{} 