In this letter, we argue that the past of the Universe, extrapolated from standard physics and measured cosmological parameters, might be a non-singular bounce. We also show that, in this framework, quite stringent constraints can be put on the reheating temperature and number of inflationary e-folds, basically fixing $T_{RH}\sim T_{GUT}$ and $N\sim 70$. We draw some conclusions about the shape of the inflaton potential and raise the "naturalness" issue in this context. Finally, we argue that this could open a very specific window on the "pre big bounce" universe.
We study how a cosmological bounce with a Type IV singularity at the bouncing point, can be generated by a classical vacuum $F(G)$ gravity. We focus our investigation on the behavior of the vacuum $F(G)$ theory near the Type IV singular bouncing point and also we address the stability of the resulting solution, by treating the equations of motion as a dynamical system. In addition, we investigate how the scalar perturbations of the background metric evolve, emphasizing to cosmological times near the Type IV singular bouncing point. Finally, we also investigate which mimetic vacuum $F(G)$ gravi…
In this paper, we study a class of higher derivative, non-local gravity which admits homogeneous and isotropic non-singular, bouncing universes in the absence of matter. At the linearized level, the theory propagates only a scalar degree of freedom, and no vector or tensor modes. The scalar can be made free from perturbative ghost instabilities, and has oscillatory and bounded evolution across the bounce.
We complement the low-energy gravi-dilaton effective action of string theory with a non-local, general-covariant dilaton potential, and obtain homogeneous solutions describing a non-singular (bouncing-curvature) cosmology. We then compute, both analytically and numerically, the spectrum of amplified scalar and tensor perturbations, and draw some general lessons on how to extract observable consequences from pre-big bang and ekpyrotic scenarios.
We investigate bouncing scenario in the modified $f(T)$ gravity, $T$ being the torsion scalar. Attention is attached to the reconstruction of $f(T)$ able to describe type IV singular bouncing evolution, where we adopt as assumption that the bouncing and type IV singularity points coincide. In the context of the reconstructed $f(T)$ model we calculate the Hubble slow-roll parameters in order to determine the dynamical evolution of the cosmological system under study. The results show that the Hubble slow-roll parameters become singular at the type IV singularity indicating a dynamical instabili…
We choose a modified Chaplygin Gas Dark energy model for considering some its cosmological behaviors. In this regards, we study different Rip singularity scenarios and bouncing model of the universe in context of this model. We show that by using suitable parameters can explain some cosmological aspects of the model.
The observed temperature fluctuations in the cosmic microwave background can be traced back to primordial curvature modes that are sourced by adiabatic and/or entropic matter perturbations. In this paper, we explore the entropic mechanism in the context of non-singular bouncing cosmologies. We show that curvature modes are naturally generated during `graceful exit,' i.e., when the smoothing slow contraction phase ends and the universe enters the bounce stage. Here, the key role is played by the kinetic energy components that come to dominate the energy density and drive the evolution towards t…
Although inflation is a natural candidate to generate the lengths of coherence of magnetic fields needed to explain current observations, it needs to break conformal invariance of electromagnetism to obtain significant magnetic amplitudes. Of the simplest realizations are the kinetically-coupled theories $f^2(ϕ)F_{μν}F^{μν}$ (or $IFF$ theories). However, these are known to suffer from electric fields backreaction or the strong coupling problem. In this work we shall confirm that such class of theories are problematic to support magnetogenesis during inflationary cosmology. On the contrary, we …
We present a model for a classical, non-singular bouncing cosmology without violation of the null energy condition (NEC). The field content is General Relativity plus a real scalar field with a canonical kinetic term and only renormalizable, polynomial type self-interaction for the scalar field in the Jordan frame. The universe begins vacuum-energy dominated and is contracting at $t=-\infty$. We consider a closed universe with a positive spatial curvature, which is responsible for the universe bouncing without any NEC violation. An $Rϕ^2$ coupling between the Ricci scalar and the scalar field …
We study a cosmological scenario in which inflation is preceded by a bounce. In this scenario, the primordial singularity, one of the major shortcomings of inflation, is replaced by a non-singular bounce, prior to which the universe undergoes a phase of contraction. Our starting point is the bouncing cosmology investigated in Falciano et al. (2008), which we complete by a detailed study of the transfer of cosmological perturbations through the bounce and a discussion of possible observational effects of bouncing cosmologies. We focus on a symmetric bounce and compute the evolution of cosmologi…
In this paper, we show how the proper choice of gauge is critical in analyzing the stability of non-singular cosmological bounce solutions based on Horndeski theories. We show that it is possible to construct non-singular cosmological bounce solutions with classically stable behavior for all modes with wavelengths above the Planck scale where: (a) the solution involves a stage of null-energy condition violation during which gravity is described by a modification of Einstein's general relativity; and (b) the solution reduces to Einstein gravity both before and after the null-energy condition vi…
We construct a simple non singular cosmological model in which the currently observed expansion phase was preceded by a contraction. This is achieved, in the framework of pure general relativity, by means of a radiation fluid and a free scalar field having negative energy. We calculate the power spectrum of the scalar perturbations that are produced in such a bouncing model and find that, under the assumption of initial vacuum state for the quantum field associated with the hydrodynamical perturbation, this leads to a spectral index n=-1. The matching conditions applying to this bouncing model…
We propose a new scenario for the bouncing universe in a simple five-dimensional braneworld model in the framework of Einstein-Gauss-Bonnet gravity, which works even with ordinary matter on the brane. In this scenario, the so-called branch singularity located at a finite physical radius in the bulk spacetime plays an essential role. We show that a three-brane moving in the bulk may reach and pass through it in spite of the fact that it is a curvature singularity. The bulk spacetime is extended beyond the branch singularity in the C^0 sense and then the branch singularity is identified as a mas…
In this note, we construct a family of non-singular time-dependent solutions of a six-dimensional gravitational theory that are warped products of a four dimensional bouncing cosmological solution and a two dimensional internal manifold. The warp factor is time-dependent and breaks translation invariance along one of the internal directions. When the warp factor is periodic in time, the non-compact part of the geometry bounces periodically. The six dimensional geometry is supported by matter that does not violate the null energy condition. We show that this 6D geometry does not admit a closed …
A matter bouncing entropy-corrected cosmological model has been suggested. The model allows only positive curvature with negative pressure and no violation of the null energy condition. The result obtained in this paper is supported by some recent theoretical works where the combination of positive spatial curvature and vacuum energy leads to non-singular bounces with no violation of the null energy condition. An important feature of the current model is that evolutions of the cosmic pressure, energy density and equation of state parameter are independent of the values of the prefactors $α$ an…
We propose a set of equations as a simple model for non singular evolutions of a $10 + 1$ dimensional M theory universe. Our model uses ideas from Loop Quantum Cosmology and offers a solution to the important problem of singularity resolutions. We solve the equations numerically and find that an M theory universe in this model evolves non singularly and with a bounce : going back in time, its density reaches a maximum and decreases thereafter whereas its physical size reaches a non vanishing minimum and increases thereafter. Taking the constituents of the universe to be the most entropic ones …
We study cosmological braneworld models with a single timelike extra dimension. Such models admit the intriguing possibility that a contracting braneworld experiences a natural bounce without ever reaching a singular state. This feature persists in the case of anisotropic braneworlds under some additional and not very restrictive assumptions. Generalizing our study to braneworld models containing an induced brane curvature term, we find that a FRW-type singularity is once again absent if the bulk extra dimension is timelike. In this case, the universe either has a non-singular origin or commen…
The present paper is devoted to the study of bouncing cosmology in $f(R,T)$ modified gravity where we presume $f(R,T) = R + 2 λT$, with $R$ the Ricci scalar, $T$ the trace of energy momentum tensor and $λ$ the model parameter. We present here a novel parametrization of Hubble parameter which is apt in representing a successful bouncing scenario undergoing no singularity. We proceed to present a complete analysis of the proposed bouncing model by studying the evolution of primordial curvature perturbations, energy conditions and stability against linear homogeneous perturbations in flat space-t…
Homogeneous and isotropic, nonsingular, bouncing world models are designed to evade the initial singularity at the beginning of the cosmic expansion. Here, we study the thermodynamics of the subset of these models governed by general relativity. Considering the entropy of matter, radiation and that the entropy of the apparent horizon is proportional to its area, we argue that these models do not respect the generalised second law of thermodynamics, also away from the bounce.
The spectrum and amplitude of the stochastic background of relic gravitons produced in a bouncing universe is calculated. The matter content of the model consists of dust and radiation fluids, and the bounce occurs due to quantum cosmological effects when the universe approaches the classical singularity in the contracting phase. The resulting amplitude is very small and it cannot be observed by any present and near future gravitational wave detector. Hence, as in the ekpyrotic model, any observation of these relic gravitons will rule out this type of quantum cosmological bouncing model.
Hořava-Lifshitz gravity is a potentially UV complete theory with important implications for the very early universe. In particular, in the presence of spatial curvature it is possible to obtain a non-singular bouncing cosmology. The bounce is realized as a consequence of higher order spatial curvature terms in the gravitational action. Here, we extend the study of linear cosmological perturbations in Hořava-Lifshitz gravity coupled to matter in the case when spatial curvature is present. As in the case without spatial curvature, we find that there is no extra dynamical degree of freedom for sc…
This work is concerned to study the bouncing nature of the universe for an isotropic configuration of fluid $\mathcal{T}_{αβ}$ and Friedmann-Lemaître-Robertson-Walker metric scheme. This work is carried out under the novel $f(\mathcal{G},\mathcal{T}_{αβ} \mathcal{T}^{αβ})$ gravitation by assuming a specific model i.e, $f(\mathcal{G},\mathcal{T}^2)=\mathcal{G}+α\mathcal{G}^2+2λ\mathcal{T}^2$ with $α$ and $λ$ are constants, serving as free parameters. {The terms $\mathcal{G}$ and $\mathcal{T}^2$ served as an Gauss-Bonnet invariant and square of the energy-momentum trace term as an inclusion in t…
Alternative scenarios to the Big Bang singularity have been subject of intense research for several decades by now. Most popular in this sense have been frameworks were such singularity is replaced by a bounce around some minimal cosmological volume or by some early quantum phase. This latter scenario was devised a long time ago and referred as an "emergent universe" (in the sense that our universe emerged from a constant volume quantum phase). We show here that within an improved framework of canonical quantum gravity (the so called Quantum Reduced Loop Gravity) the Friedmann equations for co…
The bouncing universe provides a possible solution to the Big Bang singularity problem. In this paper we study the bouncing solution in the universe dominated by the Quintom matter with an equation of state (EoS) crossing the cosmological constant boundary. We will show explicitly the analytical and numerical bouncing solutions in three types of models for the Quintom matter with an phenomenological EoS, the two scalar fields and a scalar field with a modified Born-Infeld action.
We derive the arrows of time of our universe that follow from the no-boundary theory of its quantum state (NBWF) in a minisuperspace model. Arrows of time are viewed four-dimensionally as properties of the four-dimensional Lorentzian histories of the universe. Probabilities for these histories are predicted by the NBWF. For histories with a regular `bounce' at a minimum radius we find that fluctuations are small at the bounce and grow in the direction of expansion on either side. For recollapsing classical histories with big bang and big crunch singularities we find that the fluctuations are s…
We describe string frame bouncing universe scenarios involving the creation and annihilation of a non-BPS D9-brane in type IIA superstring theory. We find several classes of solutions, in which the bounce is driven by the tachyon dynamics of the non-BPS brane. The metric and the dilaton are consistently described in terms of the lowest order effective action. The bounce solutions interpolate between contracting and expanding pre-big bang (or post-big bang) solutions. The singular behavior of our bounce solutions is the same as that of the pre-big bang (or post-big bang) solution. Upon adding a…
We present exact non-singular bounce solutions of general relativity in the presence of a positive cosmological constant and an electromagnetic field, without any exotic matter. The solutions are distinguished by being spatially inhomogeneous in one direction, while they can also contain non-trivial electromagnetic field lines. The inhomogeneity may be substantial, for instance, there can be one bounce in one region of the universe and two bounces elsewhere. Since the bounces are followed by a phase of accelerated expansion, the metrics described here also permit the study of (geodesically com…
In this paper we calculate $\mathcal{O}(μ^4)$ corrections from holonomies in the Loop Quantum Gravity, usually not taken into account. Allowance of the corrections of this kind is equivalent with the choice of the new quatization scheme. Quantization ambiguities in the Loop Quantum Cosmology allow for this additional freedom and presented corrections are consistent with the standard approach. We apply these corrections to the flat FRW cosmological model and calculate the modified Friedmann equation. We show that the bounce appears in the models with the standard $\mathcal{O}(μ^2)$ quantization…
In this work, we analyzed the improved Deser-Woodard non-local gravity over the background of five different bouncing cosmologies, whose premise is avoid the initial singular state of the universe. We developed the numerical solution for the non-local distortion function, which encompass the modifications to the Einstein-Hilbert action, using the reconstruction procedure and we have found that they have a viable cosmological solution. Afterwards, we discussed the physical aspects and outcomes of the evolution of the distortion function throughout the bouncing point for these models, specifical…
A non-local modified gravity model with an analytic function of the d'Alembert operator is considered. This model has been recently proposed as a possible way of resolving the singularities problem in cosmology. We present an exact bouncing solution, which is simpler compared to the already known one in this model in the sense it does not require an additional matter to satisfy all the gravitational equations.
A non-singular bouncing cosmology is generically obtained in loop quantum cosmology due to non-perturbative quantum gravity effects. A similar picture can be achieved in standard general relativity in the presence of a scalar field with a non-standard kinetic term such that at high energy densities the field evolves into a ghost condensate and causes a non-singular bounce. During the bouncing phase, the perturbations can be stabilized by introducing a Horndeski operator. Taking the matter content to be a dust field and an ekpyrotic scalar field, we compare the dynamics in loop quantum cosmolog…
We consider the early time cosmology of f(R) theories in Palatini formalism and study the conditions that guarantee the existence of homogeneous and isotropic models that avoid the Big Bang singularity. We show that for such models the Big Bang singularity can be replaced by a cosmic bounce without violating any energy condition. In fact, the bounce is possible even for pressureless dust. We give a characterization of such models and discuss their dynamics in the region near the bounce. We also find that power-law lagrangians with a finite number of terms may lead to non-singular universes, wh…
It is generically believed that higher-order curvature corrections to the Einstein-Hilbert action might cure the curvature singularities that plague general relativity. Here we consider Einstein-scalar-Gauss-Bonnet gravity, the only four-dimensional, ghost-free theory with quadratic curvature terms. For any choice of the coupling function and of the scalar potential, we show that the theory does not allow for bouncing solutions in the flat and open Friedmann universe. For the case of a closed universe, using a reverse-engineering method, we explicitly provide a bouncing solution which is never…
Non-perturbative quantum geometric effects in Loop Quantum Cosmology predict a $ρ^2$ modification to the Friedmann equation at high energies. The quadratic term is negative definite and can lead to generic bounces when the matter energy density becomes equal to a critical value of the order of the Planck density. The non-singular bounce is achieved for arbitrary matter without violation of positive energy conditions. By performing a qualitative analysis we explore the nature of the bounce for inflationary and Cyclic model potentials. For the former we show that inflationary trajectories are at…
A bouncing universe is a viable candidate to solve the initial singularity problem. Here we consider bouncing solutions in the context of $f(R,\mathcal{G})$ gravity by using an order reduction technique which allows one to find solutions that are perturbatively close to General Relativity. This procedure also acts as a model selection approach. Indeed, several covariant gravitational actions leading to a bounce are directly selected by demanding that the Friedmann equation derived within such gravity theories coincides with the one emerging from Loop Quantum Cosmology.
We illustrate a general reconstruction procedure for mimetic gravity. Focusing on a bouncing cosmological background, we derive general properties that must be satisfied by the function $f(\Boxϕ)$ implementing the limiting curvature hypothesis. We show how relevant physical information can be extracted from power law expansions of $f$ in different regimes, corresponding e.g. to the very early universe or to late times. Our results are then applied to two specific models reproducing the cosmological background dynamics obtained in group field theory and in loop quantum cosmology, and we discuss…
We present a nonsingular scenario in which an inflation era goes after a bounce from a contracting scenario in the early universe. The contracting of the universe is supposed to be slow, such that the initial anisotropies will not grow too fast to become dominant and destroy the bounce. After the bounce, the universe enters into an inflationary region and reheating phase, where primordial perturbations are generated. The tensor-to-scalar ratio of the perturbations are expected to be consistent with the newly released data, $r=0.2^{+0.07}_{-0.05}$. The addition of the bounce process is aimed at…
The investigation of quantum gravity effects in order to avoid the big bang singularity is a requisite, so that the idea of oscillating universes is introduced as an alternative for standard cosmological model. Therefore, the Friedmann equations arising from the quantum corrections of entropy-area relation provide the possibility of studying the oscillating universes. Addition to necessity of surveying the bouncing solutions, however, the values of unknown constant parameters are still a matter of open debate. In this paper, we consider modified Friedmann equations with logarithmic entropy cor…
The big bang singularity could be understood as a breakdown of Einstein's General Relativity at very high energies. Adopting this viewpoint, other theories, that implement Einstein Cosmology at high energies, might solve the problem of the primeval singularity. One of them is Loop Quantum Cosmology (LQC) with a small cosmological constant that models a universe moving along an ellipse, which prevents singularities like the big bang or the big rip, in the phase space $(H,ρ)$, where $H$ is the Hubble parameter and $ρ$ the energy density of the universe. Using LQC when one considers a model of un…
We study the conditions under which thermal fluctuations generated in the contracting phase of a non-singular bouncing cosmology can lead to a scale-invariant spectrum of cosmological fluctuations at late times in the expanding phase. We consider point particle gases, holographic gases and string gases. In the models thus identified, we also study the thermal non-Gaussianities of the resulting distribution of inhomogeneities. For regular point particle radiation, we find that the background must have an equation of state $w = 7/3$ in order to obtain a scale-invariant spectrum, and that the non…
Cosmological bounces occur in many gravity theories. We define singularity scattering maps relating large scale geometries before and after the bounce (assuming no BKL oscillations) and encoding microscopic details of the theory. By classifying all suitably local maps we uncover three universal laws: scaling of Kasner exponents, canonical transformation of matter, directional metric scaling. These are indeed obeyed by Bianchi I bounces in string theory, loop quantum cosmology and modified matter models; our classification then determines how inhomogeneities and anisotropies traverse bounces, a…
We present the graviton propagator for an infinite derivative, $D$-dimensional, non-local action, up to quadratic order in curvature around a Minkowski background, and discuss the conditions required for this class of gravity theory to be ghost-free. We then study the gravitational entropy for de-Sitter and Anti-de Sitter backgrounds, before comparing with a recently derived result for a Schwarzschild blackhole, generalised to arbitrary $D$-dimensions, whereby the entropy is given simply by the area law. A novel approach of decomposing the entropy into its $(r, t)$ and spherical components is …
This work explains how the presence of a Type-IV singularity (a mild singularity) can influence the dynamics of a bouncing universe. In particular, we examine bounce cosmology that appears with a Type-IV singularity in the context of a ghost free Gauss-Bonnet theory of gravity. Depending on the time of occurrence of the Type-IV singularity, three different cases may arise -- when the singularity occurs before the bounce or after the bounce or at the instant of the bounce respectively. However in all of these cases, we find that in the case when the singularity "globally" affects the spacetime,…
We consider the effects on cosmology of higher-derivative modifications of (effective) gravity that make it asymptotically free without introducing ghosts. The weakening of gravity at short distances allows pressure to prevent the singularity, producing a solution with contraction preceding expansion.
We compute the level of non-gaussianities produced by a cosmological bouncing phase in the minimal non-singular setup that lies within the context of General Relativity when the matter content consists of a simple scalar field with a standard kinetic term. Such a bouncing phase is obtained by requiring that the spatial sections of the background spacetime be positively curved. We restrict attention to the close vicinity of the bounce by Taylor expanding the scale factor, the scalar field and its potential in powers of the conformal time around the bounce. We find that possibly large non-gaussi…
Cosmological bouncing solutions and their stability in teleparallel gravity
University of South China（南华大学）；University of Management and Technology（管理科技大学）；Khazar University（哈扎尔大学）；Fukushima University（福岛大学）；Princess Nourah Bint Abdulrahman University（公主努拉·宾特·阿卜杜勒·拉赫曼大学）
We study the dynamics of a homogeneous and isotropic Friedmann-Robertson-Walker universe in the context of the Eddington-inspired Born-Infeld theory of gravity. We generalize earlier results, obtained in the context of a radiation dominated universe, to account for the evolution of a universe permeated by a perfect fluid with an arbitrary equation of state parameter $w$. We show that a bounce may occur for $κ>0$, if $w$ is time-dependent, and we demonstrate that it is free from tensor singularities. We argue that Eddington-inspired Born-Infeld cosmologies may be a viable alternative to the inf…
We review the general features of nonsingular universes ({\em i.e.} those that go from an era of accelerated collapse to an expanding era without displaying a singularity) as well as cyclic universes. We discuss the mechanisms behind the bounce, and analyze examples of solutions that implement these mechanisms. Observational consequences of such regular cosmologies are also considered, with emphasis in the behavior of the perturbations.
The question of how perturbations evolve through a bounce in the Cyclic and Ekpyrotic models of the Universe is still a matter of ongoing debate. In this report we show that the collision between boundary branes is in most cases singular even in the full 5-D formalism, and that first order perturbation theory breaks down for at least one perturbation variable. Only in the case that the boundary branes approach each other with constant velocity shortly before the bounce, can a consistent, non singular solution be found. It is then possible to follow the perturbations explicitly until the actual…
We analyze the causal structure of McVittie spacetime for a classical bouncing cosmological model. In particular, we compute the trapping horizons of the metric and integrate the trajectories of radial null geodesics before, during, and after the bounce takes place. In the contracting phase up to the occurrence of the bounce, a dynamical black hole is present. When the universe reaches a certain minimum scale, the trapping horizons disappear and the black hole ceases to exist. After the bounce, the central weak singularity becomes naked. In the expanding phase, for large positive values of the…
By studying some bouncing universe models dominated by a specific class of hydrodynamical fluids, we show that the primordial cosmological perturbations may propagate smoothly through a general relativistic bounce. We also find that the purely adiabatic modes, although almost always fruitfully investigated in all other contexts in cosmology, are meaningless in the bounce or null energy condition (NEC) violation cases since the entropy modes can never be neglected in these situations: the adiabatic modes exhibit a fake divergence that is compensated in the total Bardeen gravitational potential …
Scenario bouncing can give the cosmology singularity problem a possible way out. Finding a solution for the universe's bouncing model requires proper estimation of the state equation. We present two such state equations that give us the solution for a bounce. One such case is the exotic radiation, where we assumed that exotic radiation dominated the universe during the bounce occurrence. We also considered another case where quintom matter scenario existed previously, and the newly proposed exotic radiation scenario coexisted. In these two cases, we have shown that all the necessary conditions…
According to classical GR, Anti-de Sitter (AdS) bubbles in the multiverse terminate in big crunch singularities. It has been conjectured, however, that the fundamental theory may resolve these singularities and replace them by nonsingular bounces. This may have important implications for the beginning of the multiverse. Geodesics in cosmological spacetimes are known to be past-incomplete, as long as the average expansion rate along the geodesic is positive, but it is not clear that the latter condition is satisfied if the geodesic repeatedly passes through crunching AdS bubbles. We investigate…
