Growth index of matter perturbations in running vacuum models

摘要: We derive for the first time growth index of matter perturbations Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) flat cosmological models in which vacuum energy depends on redshift. A particularly well-motivated model this type is so-called quantum field vacuum, which, apart from a leading constant term ${\mathrm{\ensuremath{\Lambda}}}_{0}$, there also an ${H}^{2}$ dependence functional form namely, $\mathrm{\ensuremath{\Lambda}}(H)={\mathrm{\ensuremath{\Lambda}}}_{0}+3\ensuremath{\nu}({H}^{2}\ensuremath{-}{H}_{0}^{2})$. Since $|\ensuremath{\nu}|\ensuremath{\ll}1$, endows mild dynamics affects evolution main observables at background and perturbation levels. Specifically, level, we find that running ${\ensuremath{\gamma}}_{{\mathrm{\ensuremath{\Lambda}}}_{H}}\ensuremath{\approx}\frac{6+3\ensuremath{\nu}}{11\ensuremath{-}12\ensuremath{\nu}}$, thus it nicely extends analytically result $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model, ${\ensuremath{\gamma}}_{\mathrm{\ensuremath{\Lambda}}}\ensuremath{\approx}6/11$.