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.