Matter Perturbations in Scaling Cosmology

A suitable nonlinear interaction between dark matter with an energy density $ρ_{M}$ and dark energy with an energy density $ρ_{X}$ is known to give rise to a non-canonical scaling $ρ_{M} \propto ρ_{X}a^{-ξ}$ where $ξ$ is a parameter which generally deviates from $ξ=3$. Here we present a covariant generalization of this class of models and investigate the corresponding perturbation dynamics. The resulting matter power spectrum for the special case of a time-varying Lambda model is compared with data from the SDSS DR9 catalogue. We find a best-fit value of $ξ= 3.25$ which corresponds to a decay of dark matter into the cosmological term. Our results are compatible with the $Λ$CDM model at the 2$σ$ confidence level.

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