Complete cosmic history with a dynamicalΛ=Λ(H)term

Abstract

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:

Primordial gravitational waves in running vacuum cosmologies

“…[25,26], the very late time behavior of the model analized here is exactly ΛCDM. The GW equation is derived and its time-dependent part numerically integrated since the primordial de Sitter stage.…”

“…The dynamical Λ(H)-term was phenomenologically modeled as Λ(H) = Λ b + H 3 /H I . This kind of model undergone a smooth transition from an early inflation to the standard radiation phase which can analytically be described [3,4,25,26]. Interestingly, the model explain the present day entropy content of the Universe stored in the relic radiation [27,28] without necessity of a highly non-adiabaticreheating stage.…”

“…As remarked before, it will be assumed here that the Λ(H)-term is given by a particular case of the general class studied by Perico et al [25,26] (for closely related works see also [3,4])…”

“…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…”

“…In this connection, a large class of nonsingular models, where the vacuum energy density evolves phenomenologically as a truncated power-series in the Hubble parameter, has been proposed a couple of years ago [25,26] (its dominant term ρ vac (H) ∝ H n , n > 2). 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.…”