In the present mainstream cosmology, matter and spacetime emerged from a singularity and evolved through four distinct periods: early inflation, radiation, dark matter and late-time inflation (driven by dark energy). During the radiation and dark matter dominated stages, the universe is decelerating while the early and late-time inflations are accelerating stages. A possible connection between the accelerating periods remains unknown, and, even more intriguing, the best dark energy candidate powering the present accelerating stage (Λ-vacuum) is plagued with the cosmological constant and coincidence puzzles. Here we propose an alternative solution for such problems based on a large class of time-dependent vacuum energy density models in the form of power series of the Hubble rate, Λ = Λ(H). The proposed class of Λ(H)-decaying vacuum model provides: i) a new mechanism for inflation (different from the usual inflaton models), (ii) a natural mechanism for a graceful exit, which is universal for the whole class of models; iii) the currently accelerated expansion of the universe, iv) a mild dynamical dark energy at present; and v) a final de Sitter stage. Remarkably, the late-time cosmic expansion history of our class of models is very close to the concordance ΛCDM model, but above all it furnishes the necessary smooth link between the initial and final de Sitter stages through the radiation-and matter-dominated epochs.PACS numbers:

Modified gravity (MG) theories aim to reproduce the observed acceleration of the Universe by reducing the dark sector while simultaneously recovering General Relativity (GR) within dense environments. Void studies appear to be a suitable scenario to search for imprints of alternative gravity models on cosmological scales. Voids cover an interesting range of density scales where screening mechanisms fade out, which reaches from a density contrast δ ≈ −1 close to their centers to δ ≈ 0 close to their boundaries. We present an analysis of the level of distinction between GR and two modified gravity theories, the Hu-Sawicki f (R) and the symmetron theory. This study relies on the abundance, linear bias, and density profile of voids detected in n-body cosmological simulations. We define voids as connected regions made up of the union of spheres with a mean density given by ρ v = 0.2 ρ m , but disconnected from any other voids. We find that the height of void walls is considerably affected by the gravitational theory, such that it increases for stronger gravity modifications. Finally, we show that at the level of dark matter n-body simulations, our constraints allow us to distinguish between GR and MG models with | f R0 | > 10 −6 and z S S B > 1. Differences of best-fit values for MG parameters that are derived independently from multiple void probes may indicate an incorrect MG model. This serves as an important consistency check.

We propose a large class of nonsingular cosmologies of arbitrary spatial curvature whose cosmic history is determined by a primeval dynamical Λ(t)-term. For all values of the curvature, the models evolve between two extreme de Sitter phases driven by the relic time-varying vacuum energy density. The transition from inflation to the radiation phase is universal and points to a natural solution of the graceful exit problem regardless of the values of the curvature parameter. The flat case recovers the scenario recently discussed in the literature [Perico et al., Phys. Rev. D 88 (2013) 063531]. The early de Sitter phase is characterized by an arbitrary energy scale H I associated to the primeval vacuum energy density. If H I is fixed to be nearly the Planck scale, the ratio between the relic and the present observed vacuum energy density is ρ vI /ρ v0 10 118 .

In cosmology, phenomenologically motivated expressions for running vacuum are commonly parametrized as linear functions Λ(H 2 ) or Λ(R). Such kind of models assume an equation of state for vacuum given by P Λ = − ρ Λ , relating their background pressure P Λ and mean energy density ρ Λ ≡ Λ/8πG. This equation of state requires that the dynamic for vacuum is due to the energy exchange with the material species. Most of the approaches to background level consider only the energy exchange between vacuum and the transient dominant material component of the universe. We extend such models assuming the running vacuum as the sum of independent contributions ρ Λ = i ρ Λi , associated with (and interacting with) each of the i material species. We derive the linear scalar perturbations for two running scenarios, modeling its cosmic evolution and identifying their different imprints on the cosmic microwave background anisotropies and the matter power spectrum. In the Λ(H 2 ) scenario the running vacuum are coupled with all the material species in the universe, whereas the Λ(R) description only leads to coupling between vacuum and the non-relativistic matter components; which produces different imprints of the two models on the matter power spectrum. A comparison with the Planck 2015 data was made in order to constrain the free parameters of the models. In the case of the Λ(H 2 ) model, it was found that Ω Λ = 0.705 ± 0.027 and H 0 = 69.6 ± 2.9 km M pc −1 s −1 , which diminish the tension with the low redshift expectations. * elduartep@usp.br †