Effective growth of matter density fluctuations in the runningΛ CDMand Λ XCDM models

Abstract

We investigate the matter density fluctuationsδρM/ρM for two dark energy (DE) models in the literature in which the cosmological termΛ is a running parameter. In the first model, the runningΛCDM model, matter and DE exchange energy, whereas in the second model, theΛXCDM model, the total DE and matter components are conserved separately. TheΛXCDM model was proposed as an interesting solution to the cosmic coincidenceproblem. It includes an extra dynamical component, the ‘cosmon’X, which interactswith the running Λ, but not with matter. In our analysis we make use of the current value of the linear bias parameter,b2(0) = PGG/PMM, where is the present matter power spectrum andPGG is the galaxy fluctuation power spectrum. The former can be computed withina given model, and the latter is found from the observed LSS data (at smallz) obtained by the 2dF Galaxy Redshift Survey. It is found that within a 10% accuracyfor the standard ΛCDM model. Adopting this limit for any DE model and using a method based on the effective equationof state for the DE, we can set a limit on the growth of matter density perturbations for the runningΛCDM model,the solution of which is known. This provides a good test of the procedure, which we then apply to theΛXCDM modelin order to determine the physical region of parameter space, compatible with the LSS data. In this region,the ΛXCDM model is consistent with known observations and provides at the same time a viablesolution to the cosmic coincidence problem.