Matter Perturbations in Scaling Cosmology

Abstract

A suitable nonlinear interaction between dark matter with an energy density ${\rho }_M$ and dark energy with an energy density ${\rho }_X$ is known to give rise to a non-canonical scaling ${\rho }_M\propto {\rho }_X{a}^{-\xi }$ where $\xi$ is a parameter which generally deviates from $\xi =3$. 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 $\xi =3.25$ which corresponds to a decay of dark matter into the cosmological term. Our results are compatible with the $\Lambda$CDM model at the 2$\sigma$ confidence level.

Updated revised version, degeneracy substantially reduced, accepted for publication in MNRAS

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