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Density Perturbations for Running Cosmological Constant

The dynamics of density and metric perturbations is investigated for the previously developed model where the decay of the vacuum energy into matter (or vice versa) is due to the renormalization group (RG) running of the cosmological constant (CC) term. The evolution of the CC depends on the single parameter ν, which characterizes the running of the CC produced by the quantum effects of matter fields of the unknown high energy theory below the Planck scale. The sign of νindicates whether bosons or fermions dominate in the running. The spectrum of perturbations is computed assuming an adiabatic regime and an isotropic stress tensor. Moreover, the perturbations of the CC term are generated from the simplest covariant form suggested by the RG model under consideration. The corresponding numerical analysis shows that for ν>0 there is a depletion of the matter power spectrum at low scales (large wave numbers) as compared to the standard LCDM model, whereas for ν<0 there is an excess of power at low scales. We find that the LSS data rule out the range |ν|> 10^{-4} while the values |ν|< 10^{-6} look perfectly acceptable. For ν<0 the excess of power at low scales grows rapidly and the bound is more severe. From the particle physics viewpoint, the values |ν|\sim 10^{-6} correspond to the ``desert&#39;&#39; in the mass spectrum above the GUT scale M_X\sim 10^{16} GeV. Our results are consistent with those obtained in other dynamical models admitting an interaction between dark matter and dark energy. We find that the matter power spectrum analysis is a highly efficient method to discover a possible scale dependence of the vacuum energy.