Running vacuum cosmological models: linear scalar perturbations

Abstract

In cosmology, phenomenologically motivated expressions for running vacuum are commonly parameterized as linear functions typically denoted by Λ(H²) or Λ(R). Such models assume an equation of state for the vacuum given by bar P_Λ = - bar rho_Λ, relating its background pressure bar P_Λ with its mean energy density bar rho_Λ ≡ Λ/8πG. This equation of state suggests that the vacuum dynamics is due to an interaction with the matter content of the universe. Most of the approaches studying the observational impact of these models only consider the interaction between the vacuum and the transient dominant matter component of the universe. We extend such models by assuming that the running vacuum is the sum of independent contributions, namely bar rho_Λ = Σ_ibar rho_Λi. Each Λ i vacuum component is associated and interacting with one of the i matter components in both the background and perturbation levels. We derive the evolution equations for the linear scalar vacuum and matter perturbations in those two scenarios, and identify the running vacuum imprints on the cosmic microwave background anisotropies as well as on the matter power spectrum. In the Λ(H²) scenario the vacuum is coupled with every matter component, whereas the Λ(R) description only leads to a coupling between vacuum and non-relativistic matter, producing different effects on the matter power spectrum.