Matter density fluctuations in the running ΛCDM and ΛXCDM models

We have investigated the matter density fluctuations, δM(a), in the running ΛCDM and ΛXCDM models. The latter was proposed as an interesting solution to the cosmic coincidence problem. It includes an extra dynamical component, the “cosmon” X, which interacts with a running Λ, but not with matter. Adopting a dark energy (DE) “picture”, in which the total DE and matter components are conserved separately, the growth of density fluctuations ${\cal G}(a) = δM(a)/a can be written in terms of the effective equation of state. We made use of the measured galaxy fluctuation power spectrum, PGG, and of the linear bias parameter b2(z = 0) = PGG/PMM, where PMM ∝ δM2 is the matter power spectrum of the model under consideration. According to the 2dFGRS survey, bΛ2(z $\simeq$ 0) = 1 within a 10% accuracy for the ΛCDM model. We adopted this limit to put constraints on the fundamental parameter, ν, of the running ΛCDM model. We found an agreement with previous estimates obtained by a number of different methods and authors. This provided a good test of the procedure, which we used then to determine the physical region of the ΛXCDM parameter space