calculated with the metric (\[ap\]) is ł[4f]{} R\_\^= -( + )+\_\^() = \_\^(-4\^2 + 2(y) )+ [R]{}\_\^() ,where we used the relations $b'/b=-2\m\, \mbox{sign} (y)$ and $ b'' /b =4\m^2 -4\m \d (y)$. Prime is derivative over $y$.

Using (\[25\]), we obtain the estimate of the components of the tensor $\b{R}_\m^\n (\b{g})$ $${R}_\m^\n (\b{g})\sim1/t^2  \sim \m^2\f{\r}{\m}.$$ The components of the tensor $\k^2 \tau_\m^\n$ are of order $\r$. Comparing the expressions for $R_\m^\n$ calculated with the exact and approximate metrics, we find that in the period of late cosmology when $\r/\m< 1$ and $\m^2 > {R}_\m^\n (\b{g}),\,\,\,
 \m> \k^2 \tau_\m^\n$, both expressions for the Ricci tensor coincide up to the terms of order $\r/\m$, which is the precision of our calculations in the period of late cosmology.

Written with the approximate metric, the equations of motion are considerably simpler than with the exact metric. The (44) and (4$\m$) and contracted $(\m\n )$ components of equations of motion which follow from the action (\[2f\]) are (cf. [@vol]) ł[44]{} && D\^D\^h\_ - D\^2 h -h’ =0,\
ł[m4]{} && (D\_h - D\^h\_ )’ =0\
ł[con]{} && D\^D\^h\_ -h’-h” =0 ,where $h=h_{\m\n}\b{g}^{\m\n}$. From the Eqs. (\[44\]) and (\[con\]) it follows that $$h'' +\f{b'}{b}h' =0,$$ or 