Effective growth of matter density fluctuations in the running LCDM and LXCDM models

Abstract

We investigate the matter density fluctuations δρ/ρfor two dark energy (DE) models in the literature in which the cosmological term Λis a running parameter. In the first model, the running LCDM model, matter and DE exchange energy, whereas in the second model, the LXCDM model, the total DE and matter components are conserved separately. The LXCDM model was proposed as an interesting solution to the cosmic coincidence problem. It includes an extra dynamical component, the "cosmon" X, which interacts with the running Λ, but not with matter. In our analysis we make use of the current value of the linear bias parameter, b^2(0)= P_{GG}/P_{MM}, where P_{MM} ~ (δρ/ρ)^2 is the present matter power spectrum and P_{GG} is the galaxy fluctuation power spectrum. The former can be computed within a given model, and the latter is found from the observed LSS data (at small z) obtained by the 2dF galaxy redshift survey. It is found that b^2(0)=1 within a 10% accuracy for the standard LCDM model. Adopting this limit for any DE model and using a method based on the effective equation of state for the DE, we can set a limit on the growth of matter density perturbations for the running LCDM model, the solution of which is known. This provides a good test of the procedure, which we then apply to the LXCDM model in order to determine the physical region of parameter space, compatible with the LSS data. In this region, the LXCDM model is consistent with known observations and provides at the same time a viable solution to the cosmic coincidence problem.