Thermodynamical aspects of running vacuum models

Abstract

The thermal history of a large class of running vacuum models in which the effective cosmological term is described by a truncated power series of the Hubble rate, whose dominant term is (H ) ∝ H n+2 , is discussed in detail. Specifically, by assuming that the ultrarelativistic particles produced by the vacuum decay emerge into space-time in such a way that its energy density ρ r ∝ T 4 , the temperature evolution law and the increasing entropy function are analytically calculated. For the whole class of vacuum models explored here we find that the primeval value of the comoving radiation entropy density (associated to effectively massless particles) starts from zero and evolves extremely fast until reaching a maximum near the end of the vacuum decay phase, where it saturates. The late-time conservation of the radiation entropy during the adiabatic FRW phase also guarantees that the whole class of running vacuum models predicts the same correct value of the present day entropy, S 0 ∼ 10 87 -10 88 (in natural units), independently of the initial conditions. In addition, by assuming Gibbons-Hawking temperature as an initial condition, we find that the ratio between the late-time and primordial vacuum energy densities is in agreement with naive estimates from quantum field theory, namely, ρ 0 /ρ I ∼ 10 −123 . Such results are independent on the power n and suggests that the observed Universe may evolve smoothly between two extreme, unstable, non-singular de Sitter phases.

Starobinsky Inflation: From Non-SUSY to SUGRA Realizations

“…It would be nice to obtain a complete and predictable transition to the radiation dominated era. An alternative graceful exit can be achieved in the running vacuum models, as described in the fourth paper of [77][78][79][80][81][82][83][84].…”

“…An alternative framework is provided by the running vacuum models [77][78][79][80][81][82][83][84] which turn out to yield a quality fit to observations, significantly better than that of ΛCDM. In this case, the acceleration of the universe, either during inflation or at late times, is not attributed to a scalar field but rather arises from the modification of the vacuum itself, which is dynamical.…”

Starobinsky-Like Inflation and Running Vacuum in the Context of Supergravity

“…However, in other important aspects, they are different. We should mention that the RVM model provides a simple description of the graceful exit and reheating problem; see [23][24][25]27,87] for details. As for the Starobinsky model, the reheating of the Universe after the exit of the inflationary phase has been discussed for example in [88][89][90].…”

Primordial gravitational waves in running vacuum cosmologies

“…which has two limiting cases: at very early times it is a de Sitter solution, a ∝ |η| −1 , whereas at late time (t >> H −1 I ) , it enters in the radiation phase, a ∝ η [25,28]. The reduced Hubble parameter, H(η) = a ′ /a, for this stage…”

“…This class of models has some interesting features, among them: a nonsingular origin for the expanding universe (no horizon problem) with a deflationary process also without "exit problem", that is, the model evolves smoothly from the primeval nonsingular de Sitter state to the radiation phase; its late-time cosmic expansion history is very close to the concordance model and it also furnishes a smooth link between the initial and final de Sitter stages through the radiation and matter dominated phases. The temperature behavior and the entropy generation during the continuous non-adiabatic transition from de Sitter to the radiation phase has also been investigated [27,28] and a comparison with the late time observations has also been carried out in detail by GomezValent and Solà [29].…”