On the initial singularity and extendibility of flat quasi-de Sitter spacetimes

Physical Review D, 1981

The standard model of hot big bang cosmology requires initial conditions which are problematic in two ways: (1) the early universe is assumed to be highly homogeneous, in spite of the fact that separated regions were causally disconnected (horizon problem); and (2) the initial value of the Hubble constant must be fine tuned to extraordinary accuracy to produce a universe as flat (i.e., near critical mass density) as'the one we see today (flatness problem). These problems would disappear if, in its early history, the universe supercooled to temperatures 28 or more orders of magnitude below the critical temperature for some phase transition. A huge expansion factor would then result from a period of exponential growth, and the entropy of the universe would be multiplied by a huge factor when the latent heat is released. Such a scenario is completely natural in the context of grand unified models of elementary particle interactions. In such models, the supercooling is also relevant to the problem of monopole suppression. Unfortunately, the scenario seems to lead to some unacceptable consequences, so modifications must be sought.

Viable models of modified gravity which satisfy both local as well as cosmological tests are investigated. It is demonstrated that some versions of such highly nonlinear models exhibit multiply de Sitter universe solutions, which often appear in pairs, being one of them stable and the other unstable. It is explicitly shown that, for some values of the parameters, it is possible to find several de Sitter spaces (as a rule, numerically); one of them may serve for the inflationary stage, while the other can be used for the description of the dark energy epoch. The numerical evolution of the effective equation of state parameter is also presented, showing that these models can be considered as natural candidates for the unification of early-time inflation with late-time acceleration through dS critical points. Moreover, based on the de Sitter solutions, multiply SdS universes are constructed which might also appear at the (pre-)inflationary stage. Their thermodynamics are studied and free energies are compared. 95.36.+x,

The European Physical Journal C, 2014

In the present work we derive an exact solution of an isotropic and homogeneous Universe governed by f (T ) gravity. We show how the torsion contribution to the FRW cosmology can provide a unique origin for both early and late acceleration phases of the Universe. The three models (k = 0, ±1) show a built-in inflationary behavior at some early Universe time; they restore suitable conditions for the hot Big bang nucleosynthesis to begin. Unlike the standard cosmology, we show that even if the Universe initially started with positive or negative sectional curvatures, the curvature density parameter enforces evolution to a flat Universe. The solution constrains the torsion scalar T to be a constant function at all time t, for the three models. This eliminates the need for dark energy (DE). Moreover, when the continuity equation is assumed for the torsion fluid, we show that the flat and closed Universe models violate the conservation principle, while the open one does not. The evolution of the effective equation of state (EoS) of the torsion fluid implies a peculiar trace from a quintessence-like DE to a phantom-like one crossing a matter and radiation EoS in between; then it asymptotically approaches a de Sitter fate.

Physical Review D, 2010

A large class of the dynamical laws for causal sets described by a classical process of sequential growth yield a cyclic universe, whose cycles of expansion and contraction are punctuated by single 'origin elements' of the causal set. We present evidence that the effective dynamics of the immediate future of one of these origin elements, within the context of the sequential growth dynamics, yields an initial period of de Sitter-like exponential expansion, and argue that the resulting picture has many attractive features as a model of the early universe, with the potential to solve some of the standard model puzzles without any fine tuning.

In the present work we derive an exact solution of an isotropic and homogeneous Universe governed by f (T ) gravity. We show how the torsion contribution to the FRW cosmology can provide a unique origin for both early and late acceleration phases of the Universe. The three models (k = 0, ±1) show a built-in inflationary behavior at some early Universe time; they restore suitable conditions for the hot Big bang nucleosynthesis to begin. Unlike the standard cosmology, we show that even if the Universe initially started with positive or negative sectional curvatures, the curvature density parameter enforces evolution to a flat Universe. The solution constrains the torsion scalar T to be a constant function at all time t, for the three models. This eliminates the need for dark energy (DE). Moreover, when the continuity equation is assumed for the torsion fluid, we show that the flat and closed Universe models violate the conservation principle, while the open one does not. The evolution of the effective equation of state (EoS) of the torsion fluid implies a peculiar trace from a quintessence-like DE to a phantom-like one crossing a matter and radiation EoS in between; then it asymptotically approaches a de Sitter fate.

Modern Physics Letters A

A remarkable property of modern cosmology is that it allows for a special case of symmetry, consisting in the possibility of describing the early-time acceleration (inflation) and the late-time acceleration using the same theoretical framework. In this paper, we consider various cosmological models corresponding to a generalized form for the equation of state for the fluid in a flat Friedmann–Robertson–Walker (FRW) universe, emphasizing cases where the so-called type IV singular inflation is encountered in the future. This is a soft (non-crushing) kind of singularity. Parameter values for an inhomogeneous equation of state leading to singular inflation are obtained. We present models for which there are two type IV singularities, the first corresponding to the end of the inflationary era and the second to a late-time event. We also study the correspondence between the theoretical slow-roll parameters leading to type IV singular inflation and the recent results observed by the Planck...

The European Physical Journal C, 2015

During the inflationary epoch, geometry of the universe may be described by quasi-de Sitter space. On the other hand, maximally extended de Sitter metric in the comoving coordinates accords with a special FLRW model with positive spatial curvature, so in this article we focus on the positively curved inflationary paradigm. For this purpose, first, we derive the power spectra of comoving curvature perturbation and primordial gravitational waves in a positively curved FLRW universe according to the slowly rolling inflationary scenario. It can be shown that the curvature spectral index in this model automatically has a small negative running parameter which is compatible with observational measurements. Then, by taking into account the curvature factor, we investigate the relative amplitude of the scalar and tensor perturbations. It would be clarified that the tensor-scalar ratio for this model against the spatially flat one, depends on the wavelength of the perturbative modes directly.

2013

The inflationary phase of the Universe is explored by proposing a toy model related to the scalar field, termed as {\it inflaton}. The potential part of the energy density in the said era is assumed to have a constant vacuum energy density part and a variable part containing the inflaton. The prime idea of the proposed model constructed in the framework of the closed Universe is based on a fact that the inflaton is the root cause of the orientation of the space. According to this model the expansion of the Universe in the inflationary epoch is not approximately rather exactly exponential in nature and thus it can solve some of the fundamental puzzles, viz. flatness as well as horizon problems. It is also predicted that the constant energy density part in the potential may be associated to the dark energy, which is eventually different from the vacuum energy, at least in the inflationary phase of the Universe. However, the model keeps room for the end of inflationary era.

Quantum Gravity, 1984

It is shown that a equilibrium thermodynamic description of the matter in cosmological models leads to the absence of particle creation. It is proposed to take into account these nonequilibrium processes by introducing a new additional thermodynamic variable, namely explicit time dependence of all thermodynamic potentials into the thermodynamic relations. It is shown that this trick leads to "softening" of the equation of state. It is demonstrated, using a model equation of state, that during a cosmological contraction a de Sitter spacetime may be produced. In recent years the problem of the particle creation by the gravitational field in particular by cosmological field, attracts more attention. The first results obtained by Parker and Fullingl, by Zeldovich and Starobinsky 2 and by Grib, Mamaev and Mostepanenko 3 showed that quantization of the field in a background metric leads to the violation of the energy dominance which is one of the main conditions of the singularity theorems by Penrose and Hawking.~,5 The problem of the avoiding of the cosmological singularity in the past and in the future (if the closed oscillating model is considered) is understood to be particularly important and 173

Modern Physics Letters A, 2018

We consider a very general scenario of our universe where its geometry is characterized by the Finslerian structure on the underlying spacetime manifold, a generalization of the Riemannian geometry. Now considering a general energy–momentum tensor for matter sector, we derive the gravitational field equations in such spacetime. Further, to depict the cosmological dynamics in such spacetime proposing an interesting equation of state identified by a sole parameter [Formula: see text] which for isotropic limit is simply the barotropic equation of state [Formula: see text] ([Formula: see text] being the barotropic index), we solve the background dynamics. The dynamics offers several possibilities depending on this sole parameter as follows: (i) only an exponential expansion, or (ii) a finite time past singularity (big bang) with late accelerating phase, or (iii) a nonsingular universe exhibiting an accelerating scenario at late time which finally predicts a big rip type singularity. We ...

Studying the universe, understanding its origin and evolution has always been of great interest to humanity. In this context, cosmology proposes it, seeking to answer questions related to its structure, composition, and dynamics. Initially, there were various proposed models, but the one that has achieved considerable success when compared with different cosmological observations was the Hot Big Bang model. This implies a universe in expansion, homogeneous and isotropic on a large scale, that is, there are no preferred points or directions in the universe (WEINBERG, 2008). However, despite its great success, it has some problems, among them the horizon and flatness problems can be highlighted. A widely accepted proposal to solve them is that the universe, at its initial moment, underwent a phase of exponential growth. Such a proposal constitutes what is known as inflationary models, which, in addition to solving the problems present in the Hot Big Bang model, provides a good explanation for the formation of the anisotropies of the universe as a result of the expansion of quantum fluctuations in the scalar field generating the inflationary period called inflaton.

General Relativity and Gravitation, 2005

We study a closed model of the universe filled with viscous fluid and quintessence matter components in a Brans-Dicke type cosmological model. The dynamical equations imply that the universe may look like an accelerated flat Friedmann-Robertson-Walker universe at low redshift. We consider here dissipative processes which follow a causal thermodynamics. The theory is applied to viscous fluid inflation, where accepted values for the total entropy in the observable universe is obtained.

1993

A theory of gravitation is constructed in which all homogeneous and isotropic solutions are nonsingular, and in which all curvature invariants are bounded. All solutions for which curvature invariants approach their limiting values approach de Sitter space. The action for this theory is obtained by a higher derivative modification of Einstein's theory. We expect that our model can easily be generalized to solve the singularity problem also for anisotropic cosmologies.

We raise the question of how the curvature parameter k is related to the curvature of the universe. We also show that, for a cosmological model that can be interpreted geometrically as a pseudo-hypersphere with a time-dependent radius, the Einstein field equations are not sufficient to fully describe the model. In addition, the differential equation system of Bianchi identities is required to describe the temporal evolution of the universe. We discuss the facts using the example of the de Sitter universe, the subluminal universe and the h R ct = model by Melia. In particular, we discuss the formal differences between the two latter models and claim that both models are identical. We also examine the possibility of introducing non-comoving coordinates.

General Relativity and Gravitation, 2012

We investigate de Sitter solutions in non-local gravity as well as in non-local gravity with Lagrange constraint multiplier. We examine a condition to avoid a ghost and discuss a screening scenario for a cosmological constant in de Sitter solutions. Furthermore, we explicitly demonstrate that three types of the finite-time future singularities can occur in non-local gravity and explore their properties. In addition, we evaluate the effective equation of state for the universe and show that the late-time accelerating universe may be effectively the quintessence, cosmological constant or phantom-like phases. In particular, it is found that there is a case in which a crossing of the phantom divide from the non-phantom (quintessence) phase to the phantom one can be realized when a finite-time future singularity occurs. Moreover, it is demonstrated that the addition of an R 2 term can cure the finite-time future singularities in non-local gravity. It is also suggested that in the framework of non-local gravity, adding an R 2 term leads to possible unification of the early-time inflation with the late-time cosmic acceleration.