Reference level of the vacuum energy density of the Universe and astrophysical data

Abstract

An extended framework of gravity, in which the first Friedmann equation is satisfied up to some constant due to violation of gauge invariance, is tested against astrophysical data: Supernovae Type-Ia, Cosmic Chronometers, and Gamma-ray bursts. A generalized expression for the Friedmann equation, including the possible vacuum contributions, is suggested, and two particular cosmological models with two independent parameters are considered within this framework and compared on the basis of the likelihood analysis. One of the models considered includes contribution of the residual vacuum fluctuations to the energy density and places the limit on the UV cutoff scale as $k_{max} = 12.43^{+0.9}_{-1.6} [M_p/\sqrt{2+N_{sc}}]$, where $N_{sc}$ is the number of minimally coupled scalar fields. Model comparison using the Akaike information criteria and Bayesian evidence shows a preference for the conventional $\Lambda$CDM over the extended models. A more general model with three parameters is considered within which an anti-correlated behavior between the dynamical vacuum fluctuations contribution and a negative cosmological constant was found. The result is an upper limit of $\Omega_{\Lambda} \lesssim -0.14$ at $95\%$ C.L., which is only mildly disfavored ($\ln\mathcal{B} = -1.8$) with respect to $\Lambda$CDM.