Early De Sitter Research Articles

Evolution of primordial black holes in an adiabatic FLRW universe with gravitational particle creation

We study the evolution of primordial black holes (PBHs) in an adiabatic FLRW universe with dissipation due to bulk viscosity which is considered to be in the form of gravitational particle creation. Assuming that the process of evaporation is quite suppressed during the radiation era, we obtain an analytic solution for the evolution of PBH mass by accretion during this era, subject to an initial condition. We also obtain an upper bound on the accretion efficiency $\epsilon$ for $a \sim a_r$, where $a_r$ is the point of transition from the early de Sitter era to the radiation era. Furthermore, we obtain numerical solutions for the mass of a hypothetical PBH with initial mass 100 g assumed to be formed at an epoch when the value of the Hubble parameter was, say, 1 km/s/Mpc. We consider three values of the accretion efficiency, $\epsilon=0.23,0.5$, and $0.89$ for our study. The analysis reveals that the mass of the PBH increases rapidly due to the accretion of radiation in the early stages of its evolution. The accretion continues but its rate decreases gradually with the evolution of the Universe. Finally, Hawking radiation comes into play and the rate of evaporation surpasses the accretion rate so that the PBH mass starts to decrease. As the Universe grows, evaporation becomes the dominant phenomenon, and the mass of the PBH decreases at a faster rate. As argued by Debnath and Paul, the evaporated mass of the PBHs might contribute towards the dark energy budget of the late Universe.

Primordial gravitational waves in running vacuum cosmologies

We investigate the cosmological production of gravitational waves in a nonsingular flat cosmology powered by a “running vacuum” energy density described by ρΛ ≡ ρΛ(H), a phenomenological expression potentially linked with the renormalization group approach in quantum field theory in curved spacetimes. The model can be interpreted as a particular case of the class recently discussed by Perico et al. (2013) [25] which is termed complete in the sense that the cosmic evolution occurs between two extreme de Sitter stages (early and late time de Sitter phases). The gravitational wave equation is derived and its time-dependent part numerically integrated since the primordial de Sitter stage. The generated spectrum of gravitons is also compared with the standard calculations where an abrupt transition, from the early de Sitter to the radiation phase, is usually assumed. It is found that the stochastic background of gravitons is very similar to the one predicted by the cosmic concordance model plus inflation except at higher frequencies (ν ≳ 100 kHz). This remarkable signature of a “running vacuum” cosmology combined with the proposed high frequency gravitational wave detectors and measurements of the CMB polarization (B-modes) may provide a new window to confront more conventional models of inflation.

Decaying vacuum inflationary cosmologies: Searching for a complete scenario including curvature effects

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. D88 (2013) 063531]. The early de Sitter phase is characterized by an arbitrary energy scale HI associated to the primeval vacuum energy density. If HI is fixed to be nearly the Planck scale, the ratio between the relic and the present observed vacuum energy density is ρvI/ρv0 ≃ 10118.

Nonsingular decaying vacuum cosmology and entropy production

The thermodynamic behavior of a decaying vacuum cosmology describing the entire cosmological history evolving between two extreme (early and late time) de Sitter eras is investigated. The thermal evolution from the early de Sitter to the radiation phase is discussed in detail. The temperature evolution law and the increasing entropy function are analytically determined. The entropy of the effectively massless particles is initially zero but evolves continuously to the present day maximum value within the current Hubble radius, $S_0 \sim 10^{88}$ in natural units. By using the Gibbons-Hawking temperature relation for the de Sitter spacetime, it is found that the ratio between the primeval and the late time vacuum energy densities is $\rho_{vI}/\rho_{v0} \sim 10^{123}$, as required by some naive estimates from quantum field theory.

Evolution of quantum field, particle content, and classicality in the three stage universe

We study the evolution of a quantum scalar field in a toy universe which has three stages of evolution, viz., (i) an early (inflationary) de Sitter phase (ii) radiation dominated phase and (iii) late-time (cosmological constant dominated) de Sitter phase. Using Schr\"odinger picture, the scalar field equations are solved separately for the three stages and matched at the transition points. The boundary conditions are chosen so that field modes in the early de Sitter evolves from Bunch-Davies vacuum state. We determine the (time-dependent) particle content of this quantum state for the entire evolution of the universe and describe the various features both numerically and analytically. We also describe the quantum to classical transition in terms of a {\it classicality parameter} which tracks the particle creation and its effect on phase space correlation of the quantum field.

Cosmological implications of a viable non-analytical f(R) model

Power-law corrections (having the exponent strictly between 2 and 3) to the Einstein-Hilbert action yield an extended theory of gravity which is consistent with Solar-System tests and properly reproduces the main phases of the Universe thermal history. We find two distinct constraints for the characteristic length scale of the model: a lower bound from the Solar-System test and an upper bound by requiring the existence of the matter-dominated era. We also show how the extended framework can accommodate the existence of an early de Sitter phase. Within the allowed range of characteristic length scales, the relation between the expansion rate and the energy scale of inflation is modified, yielding a value of the rate several orders of magnitude smaller than in the standard picture. The observational implication of this fact is that a tiny value of the tensor-to-scalar ratio is expected in the extended framework. The suppression of primordial tensor modes also implies that the inflationary scale can be made arbitrarily close to the Planck one according to the current limits. Finally, an analysis of the propagation of gravitational waves on a Robertson-Walker background is addressed.

ON VACUUM DENSITY, THE INITIAL SINGULARITY AND DARK ENERGY

Standard cosmology poses a number of important questions. Apart from its singular origin, it possesses early and late accelerating phases required to account for observations. The vacuum energy has been considered as a possible way to resolve some of these questions. The vacuum energy density induced by free fields in an early de Sitter phase has earlier been estimated to be proportional to H4, while more recently it has been suggested that the QCD condensate induces a term proportional to H at late times. These results have been employed in models which are nonsingular and inflationary at early times and accelerating at late times. Here we cast these models in terms of scalar fields and study the corresponding spectrum of primordial perturbations. At early times the spectrum is found to be not scale-invariant, thus implying that slow roll inflation is still required after the phase transition induced by the vacuum. At late times the corresponding scalar field potential is harmonic, with a mass of the order of the Hubble scale — a result that may be understood in the light of the holographic conjecture.

On vacuum density, the initial singularity and dark energy

Standard cosmology poses a number of important questions. Apart from its singular origin, it possesses early and late accelerating phases required to account for observations. The vacuum energy has been considered as a possible way to resolve some of these questions. The vacuum energy density induced by free fields in an early de Sitter phase has earlier been estimated to be proportional to H 4, while more recently it has been suggested that the QCD condensate induces a term proportional to H at late times. These results have been employed in models which are non-singular and inflationary at early times and accelerating at late times. Here we cast these models in terms of scalar fields and study the corresponding spectrum of primordial perturbations. At early times the spectrum is found to be not scale-invariant, thus implying that slow-roll inflation is still required after the phase transition induced by the vacuum. At late times the corresponding scalar-field potential is harmonic, with a mass of the order of the Hubble scale, a result that may be understood in the light of the holographic conjecture.

Cosmological perturbations in the inflationary Universe

Previously defined covariant and gauge-invariant perturbation variables, representing, e.g., the fractional spatial energy density gradient on hypersurfaces of constant expansion, are used to simplify the linear perturbation analysis of a classical scalar field. With the help of conserved quantities on large scales we establish an exact first-order relation between comoving fluid energy density perturbations at ``reentry'' into the horizon and corresponding scalar field energy density perturbations at the first Hubble scale crossing during an early de Sitter phase of a standard inflationary scenario.