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Antonio Bibiano added section_Perturbations_The_linear_perturbations__.tex
almost 9 years ago
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\section{Perturbations}
The linear perturbations for this model where thoroughly studied in \cite{Grande_2010} where the perturbations of the matter components of the universe where considered alongside the perturbations for $\rho_\Lambda$ and $G$.
This is necessary to grasp the different dynamics present in this model compared to the $\Lambda CDM$ model.
If fact in both these models matter is covariantly conserved and the density contrast $D \equiv \delta\rho_m/\rho_m$ satisfies the following second order differential equation:
\begin{equation}
D''(a) + \left( \frac{3}{a} + \frac{H'(a)}{H(a)} \right) D'(a) = \frac{3 \tilde{\Omega}_m(a)}{2 a^2} \left( D(a) + \frac{\delta G}{G},
\end{equation}
where a prime denotes differentiation with respect to the scale factor.
