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 (which are four sets of intersecting M branes) leads to an effectively $3 + 1$ dimensional spacetime as the M theory universe expands, both in the infinite past and future.
We consider alternative inflationary cosmologies in massive gravity with degenerate reference metrics and study the feasibilities of the emergent universe scenario, bouncing and cyclic universes. We focus on the construction of the Einstein static universe, classes of exact solutions of bouncing and cyclic universes in degenerate massive gravity. We further study the stabilities of the Einstein static universe against both homogeneous and inhomogeneous scalar perturbations and give the parameters region for a stable Einstein static universe.
In this paper, employing the modified dispersion relation, we have derived the general modified Friedmann equations and the corresponding modified entropy relations for the Friedmann-Robertson-Walker (FRW) Universe. In this setup, we find that when the big bounce happens, its energy scale and its corresponding modified entropy behavior are sensitive to the value of $k$. In contrast to the previous work with $k=0$, our work mainly demonstrates that the bouncing behavior for the closed Universe with $k=1$ appears at the normal energy limit of the modified dispersion relation introduced, and when…
We investigate the scalar perturbation in the Lee-Wick bouncing universe driven by an ordinary scalar field plus a ghost field. We consider only a symmetric evolution of the universe and the scalar fields about the bouncing point. The gauge invariant Sasaki-Mukhanov variable is numerically solved in the spatially flat gauge. We find a new form of the initial perturbation growing during the contracting phase. After the bouncing, this growing mode stabilizes to a constant mode which is responsible for the late-time power spectrum.
Friedmann-Lemaitre universes driven by a scalar field, spatially closed and bouncing, were recently studied by Martin and Peter in [1], with the conclusion that the spectrum of their large scale matter perturbations was generically modified when going through the bounce. In this Note we give the properties of the scalar field potentials which underly such models.
We investigate a new scenario of dark matter production in a bouncing universe, in which dark matter was produced completely out of equilibrium in the contracting as well as expanding phase. We explore possibilities of using dark matter as a probe of the bouncing universe, focusing on the relationship between a critical temperature of the bouncing universe and the present relic abundance of dark matter.
We consider the possibility to produce a bouncing universe in the framework of scalar-tensor gravity when the scalar field has a nonconformal coupling to the Ricci scalar. We prove that bouncing universes regular in the future with essentially the same dynamics as for the conformal coupling case do exist when the coupling deviates slightly from it. This is found numerically for more substantial deviations as well. In some cases however new features are found like the ability of the system to leave the effective phantom regime.
Bouncing models are alternatives to inflationary cosmology that replace the initial Big-Bang singularity by a `bouncing' phase. A deeper understanding of the initial conditions of the universe, in these scenarios, requires knowledge of quantum aspects of bouncing models. In this work, we propose two classes of bouncing models that can be studied with great analytical ease and hence, provide test-bed for investigating more profound problems in quantum cosmology of bouncing universes. Our model's two key ingredients enable us to do straightforward analytical calculations: (i) a convenient parame…
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 investigate the behaviour of exact closed bouncing Friedmann universes in theories with varying constants. We show that the simplest BSBM varying-alpha theory leads to a bouncing universe. The value of alpha increases monotonically, remaining approximately constant during most of each cycle, but increasing significantly around each bounce. When dissipation is introduced we show that in each new cycle the universe expands for longer and to a larger size. We find a similar effect for closed bouncing universes in Brans-Dicke theory, where $G$ also varies monotonically in time from cycle to cyc…
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.
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 …
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…
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.
In this paper we consider FRW cosmology in modified gravity which contain arbitrary functions $f(ϕ)$. It is shown that the bouncing solution appears in the model whereas the equation of state (EoS) parameter crosses the phantom divider. The reconstruction of the model is also investigated with the aim to reconstruct the arbitrary functions and variables of the model.
The modified field equations are written in logarithmic and power law versions of entropy corrected models in Einstein's gravity in the background of FRW universe. In one section, a brief review of the Ho$\check{\text r}$ava-Lifshitz gravity is discussed and the modified field equations in logarithmic and power law versions of entropy corrected models in Ho$\check{\text r}$ava-Lifshitz gravity are formulated. The stability analysis for these models are performed by describing the dynamical system. In another section, a brief review of the fractal universe is presented and the modified field eq…
In this letter, we study the condition for a generalized DBI action providing a quintom scenario of dark energy. We consider a development of string-inspired quintom by introducing non-minimal coupling. Then we show that the bouncing solution can appear in the universe dominated by the non-minimally coupled quintom matter.
We show that it is possible to realize a cosmological bouncing solution in an anisotropic but homogeneous Bianchi-I background in a class of non-local, infinite derivative theories of gravity. We show that the anisotropic shear grows slower than in general relativity during the contraction phase, peaks to a finite value at the bounce point, and then decreases as the universe asymptotes towards isotropy and homogeneity, and ultimately to de Sitter. Along with a cosmological constant, the matter sector required to drive such a bounce is found to consist of three components - radiation, stiff mat…
We consider the Palatini formalism of the Born-Infeld gravity. In the Palatini formalism, the propagating mode is only graviton, whose situation is different from that in the metric formalism. We discuss about the FRW cosmology by using an effective potential. Especially we consider the condition that the bouncing could occur. We also give some speculations about the black hole formation
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 dynamics of bouncing universes is characterized by violating certain coordinate invariant restrictions on the total energy-momentum tensor, customarily referred to as energy conditions. Although there could be epochs where the null energy condition is locally violated, it may perhaps be enforced in an averaged sense. Explicit examples of this possibility are investigated in different frameworks.
We consider the possibility to produce a bouncing universe in the framework of scalar-tensor gravity models in which the scalar field potential may be negative, and even unbounded from below. We find a set of viable solutions with nonzero measure in the space of initial conditions passing a bounce, even in the presence of a radiation component, and approaching a constant gravitational coupling afterwards. Hence we have a model with a minimal modification of gravity in order to produce a bounce in the early universe with gravity tending dynamically to general relativity (GR) after the bounce.
We examine the evolution of a closed, homogeneous and anisotropic cosmology subject to a variation of the fine structure 'constant', α, within the context of the theory introduced by Bekenstein, Sandvik, Barrow and Magueijo, which generalises Maxwell's equations and general relativity. The variation of αpermits an effective ghost scalar field, whose negative energy density becomes dominant at small length scales, leading to a bouncing cosmology. A thermodynamically motivated coupling which describes energy exchange between the effective ghost field and the radiation field leads to an expanding…
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…
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 investigate the stability of a spatially homogeneous and isotropic non-singular cosmological model. We show that the complete set of independent perturbations (the electric part of the perturbed Weyl tensor and the perturbed shear) are regular and well behaved functions which have no divergences, contrary to previous claims in the literature.
For the anisotropic Universe filled with massless vector field in the General Relativity frame we obtain bouncing solution for one of scale factors. We obtain the Universe with finite maximal energy density, finite value of $R,R^{μν}R_{μν},R^{μναβ}R_{μναβ}$ and non-zero value of a scale factor for directions transverse to a vector field. Such a bounce can be also obtained for a massive vector field with kinetic initial conditions, which gives isotropic low energy limit. We discuss the existence of a bounce for a massless vector field with additional matter fields, such as cosmological constant…
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 …
Using the simplest model for a bouncing universe, namely that for which gravity is described by pure general relativity, the spatial sections are positively curved and the matter content is a single scalar field, we obtain the transition matrix relating cosmological perturbation modes between the contracting and expanding phases. We show that this case provides a specific example in which this relation explicitely depends on the perturbation scale whenever the null energy condition (NEC) is close to be violated.
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 the tensor and the scalar perturbations in the symmetric bouncing universe driven by one ordinary field and its Lee-Wick partner field which is a ghost. We obtain the even- and the odd-mode functions of the tensor perturbation in the matter-dominated regime. The tensor perturbation grows in time during the contracting phase of the Universe, and decays during the expanding phase. The power spectrum for the tensor perturbation is evaluated and the spectral index is given by $n_{\rm T} =6$. We add the analysis on the scalar perturbation by inspecting the even- and the odd-mode func…
In a recent paper [Phys. Rev. D{\bf 85}, 023528 (2012)] the authors proposed a generalized Born-Infeld electrodynamics coupled to general relativity which produces a nonsingular bouncing universe. For a magnetic universe the resulting cosmic evolution inevitably interpolates between asymptotic de Sitter states. Here we shall show that (i) the above theory does not have the standard weak field Maxwell limit, (ii) a sudden curvature singularity -- not better than the big bang -- arises, (iii) the speed of sound squared is a negative quantity signaling instability against small perturbations of t…
In this paper we study quantum dynamics of the bouncing cosmological model. We focus on the model of the flat Friedman-Robertson-Walker universe with a free scalar field. The bouncing behavior, which replaces classical singularity, appears due to the modification of general relativity along the methods of loop quantum cosmology. We show that there exist a unitary transformation that enables to describe the system as a free particle with Hamiltonian equal to canonical momentum. We examine properties of the various quantum states of the Universe: boxcar state, standard coherent state, and solito…
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…
Motivated by the recent works of Refs. \cite{R1, R2} where a model of inflation has been suggested with non-minimally coupled massive vector fields, we generalize their work to the study of the bouncing solution. So we consider a massive vector field, which is non-minimally coupled to gravity. Also we consider non-minimal coupling of vector field to the scalar curvature. Then we reconstruct this model in the light of three forms of parametrization for dynamical dark energy. Finally we simply plot reconstructed physical quantities in flat universe.
We construct a quintom dark energy model with two non-minimally coupled scalar fields, one quintessence and the other phantom field, confined on the warped DGP brane. We study some important issues such as phantom divide line crossing, existence of the bouncing solutions and the stability of the solutions in this framework. We show that this model accounts for crossing of the phantom divide line and realization of the bouncing solutions. This model allows for stability of the solutions in separate regions of the $ω$-$ω'$ phase-plane.
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…
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 …
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 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…
Bouncing scenarios offer an alternative to the inflationary paradigm for the generation of perturbations in the early universe. Recently, there has been a surge in interest in examining the issue of primordial magnetogenesis in the context of bouncing universes. As in the case of inflation, the conformal invariance of the electromagnetic action needs to be broken in bouncing scenarios in order to generate primordial magnetic fields which correspond to observed strengths today. The non-minimal coupling, which typically depends on a scalar field that possibly drives the homogeneous background, l…
We find a class of solutions for a homogeneous and isotropic universe in which the initially expanding universe stops expanding, experiences contraction, and then expands again (the "bounce"), in the framework of Einstein gravity with a real scalar field without violating the null energy condition nor encountering any singularities. Two essential ingredients for the bouncing universe are the positive spatial curvature and the scalar potential which becomes flatter at large field values. Depending on the initial condition, either the positive curvature or the negative potential stops the cosmic…
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 introduce a string-inspired model for a bouncing/cyclic universe, utilizing the scalar-tachyon coupling as well as contribution from curvature in a closed universe. The universe undergoes the locked inflation, tachyon matter dominated rolling expansion, turnaround and contraction, as well as the subsequent deflation and "bounce" in each cycle of the cosmological evolution. We perform extensive analytic and numerical studies of the above evolution process. The minimum size of the universe is nonzero for generic initial values. The smooth bounce are made possible because of the negative contr…
The present article discusses about the effect of a Lee-Wick partner infested radiation phase of the early universe. As Lee-Wick partners can contribute negative energy density so it is always possible that at some early phase of the universe when the Lee-Wick partners were thermalized the total energy density of the universe became very small making the effective Hubble radius very big. This possibility gives rise to the probability of a bouncing universe. As will be shown in the article that a simple Lee-Wick radiation is not enough to produce a bounce. There can be two possibilities which c…
Preheating describes the stage of rapidly depositing the energy of cosmological scalar field into excitations of other light fields. This stage is characterized by exponential particle production due to the parametric resonance. We study this process in the frame of matter bounce cosmology. Our results show that the preheating process in bouncing cosmology is even more efficient than that in inflationary cosmology. In the limit of weak coupling, the period of preheating is doubled. For the case of normal coupling, the back-reaction of light fields can lead to thermalization before the bouncing…
We consider the introduction of anisotropy in a class of bouncing models of cosmology. The presence of anisotropy often spells doom on bouncing models, since the energy density due to the anisotropic stress outweighs that of other matter components, as the universe contracts. Different suggestions have been made in the literature to resolve this pathology, classically. Here, we introduce a family of bouncing models, in which the shear density can be tuned to either allow or forbid classical bouncing scenarios. Following this, we show that quantum cosmological considerations can drastically cha…
Recently, we had numerically shown that, for a non-minimal coupling that is a simple power of the scale factor, scale invariant magnetic fields arise in a class of bouncing universes. In this work, we {\it analytically} evaluate the spectrum of magnetic and electric fields generated in a sub-class of such models. We illustrate that, for cosmological scales which have wavenumbers much smaller than the wavenumber associated with the bounce, the shape of the spectrum is preserved across the bounce. Using the analytic solutions obtained, we also illustrate that the problem of backreaction is sever…
We study bouncing and cyclic universes from an (n+1)-dimensional brane in the (n+2)-dimensional charged AdS bulk background. In the moving domain wall (MDW) approach this picture is clearly realized with a specified bulk configuration, the 5D charged topological AdS (CTAdS_5) black hole with mass M and charge Q. The bulk gravitational dynamics induces the 4D Friedmann equations with CFT-radiation and exotic stiff matters for a dynamic brane. This provides bouncing universes for k=0, -1 and cyclic universe for k=1, even though it has an exotic stiff matter from the charge Q. In this work we use…
The Asymptotically Safe Gravity provides a framework for the description of gravity from the trans-Planckian regime to cosmological scales. According to this scenario, the cosmological constant and Newton's coupling are functions of the energy scale whose evolution is dictated by the renormalization group equations. The formulation of the renormalization group equations on foliated spacetimes, based on the Arnowitt-Deser-Misner (ADM) formalism, furnishes a natural way to construct the RG energy scale from the spectrum of the laplacian operator on the spatial slices. Combining this idea with a …
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 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…
Bouncing cosmologies, suggested by String/M-theory, may provide an alternative to standard inflation to account for the origin of inhomogeneities in our universe. The fundamental question regards the correct way to evolve the scalar perturbations through the bounce. In this work, we determine the evolution of perturbations and the final spectrum for an arbitrary (spatially flat) bouncing cosmology, with the only assumption that the bounce is governed by a single physical scale. In particular, we find that the spectrum of the pre-bounce growing mode of the Bardeen potential (which is scale-inva…
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 consider f(Q) extended symmetric teleparallel cosmologies, where Q is the non-metricity scalar, and constrain its functional form through the order reduction method. By using this technique, we are able to reduce and integrate the field equations and thus to select the corresponding models giving rise to bouncing cosmology. The selected Lagrangian is then used to develop the Hamiltonian formalism and to obtain the Wave Function of the Universe which suggests that classical observable universes can be recovered according to the Hartle Criterion.
What happens to the most general closed oscillating universes in general relativity? We sketch the development of interest in cyclic universes from the early work of Friedmann and Tolman to modern variations introduced by the presence of a cosmological constant. Then we show what happens in the cyclic evolution of the most general closed anisotropic universes provided by the Mixmaster universe. We show that in the presence of entropy increase its cycles grow in size and age, increasingly approaching flatness. But these cycles also grow increasingly anisotropic at their expansion maxima. If the…
