Constraints on a special running vacuum model

Abstract

We study a special running vacuum model (RVM) with Lambda = 3 alpha H^2+3beta H_0^4 H^{-2}+Lambda _0, where alpha , beta and Lambda _0 are the model parameters and H is the Hubble one. This RVM has non-analytic background solutions for the energy densities of matter and radiation, which can only be evaluated numerically. From the analysis of the CMB power spectrum and baryon acoustic oscillation along with the prior of alpha >0 to avoid having a negative dark energy density, we find that alpha <2.83times 10^{-4} and beta =(-0.2^{+3.9}_{-4.5})times 10^{-4} (95% C.L.). We show that the RVM fits the cosmological data comparably to the Lambda hbox {CDM}. In addition, we relate the fluctuation amplitude sigma _8 to the neutrino mass sum Sigma m_nu .