In Loop Quantum Gravity mathematically rigorous models of full quantum gravity were proposed. In this paper we study a cosmological sector of one of the models describing quantum gravity with positive cosmological constant coupled to massless scalar field. In our previous research we introduced a method to reduce the model to homogeneous-isotropic sector at the quantum level. In this paper we propose a method to restrict to the spatially flat sector. After this restriction the number of degrees of freedom gets substantially reduced. This allows us to make numerical calculations. Remarkably, the resulting model shares some structural similarities with the Loop Quantum Cosmological models and therefore sheds some new light on the relation between Loop Quantum Gravity and Loop Quantum Cosmology. According to our model the evolution of the Universe is periodic. The quantum gravity effects resolve the Big Bang singularity leading to a Big Bounce and cause the Universe to contract after a classical expansion phase (Big Crunch).
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…
In this work, we have considered the Friedmann-Robertson-Walker (FRW) model of the universe where bounce occurs and the universe is filled with Generalized Cosmic Chaplygin Gas (GCCG) or Variable Modified Chaplygin Gas (VMCG). We have studied the stability analysis through dynamical system for both models and found the critical points in flat, open and closed universe. In presence of scalar field, the dynamical behavior of scale factor and Hubble parameter is described in both models. Finally, we have analyzed the energy conditions for both the models in bouncing universe.
We have investigated some bouncing models in the framework of an extended gravity theory where the usual Ricci scalar in the gravitational action is replaced by a sum of the Ricci scalar and a term proportional to the trace of the energy momentum tensor. The dynamical parameters of the model are derived in most general manner. We considered two bouncing scenarios through an exponential and a power law scale factor. The non singular bouncing models also favour a late time cosmic speed up phenomenon. The dynamical behaviour of the equation of state parameter is studied for the models. It is obse…
In this paper, we have studied the bouncing behavior of the cosmological models formulated at the background of the Hubble function in the F(R, G) theory of gravity, where R and G denote the Ricci scalar and Gauss-Bonnet invariant. The actions of bouncing cosmology are studied under consideration of different viable models and can resolve the difficulty of singularity in standard Big-Bang cosmology. Both models show bouncing behavior and satisfy the bouncing cosmological properties. Models based on dynamical, deceleration, and energy conditions indicate the accelerating behavior at the late ev…
Bouncing Cosmological Models and Energy Conditions in $f(Q, L_m)$ gravity
Centre for Interdisciplinary Studies and Research, D Y Patil International University（D Y Patil国际大学跨学科研究与中心）；JSPM’s Bhivarabai Sawant Institute of Technology and Research（JSPM Bhivarabai Sawant技术与研究所）；Department of Mathematics, SR University（SR大学数学系）
In the present work we revisit a model consisting of a scalar field with a quartic self-interaction potential non-minimally (conformally) coupled to gravity [1]. When the scalar field vacuum is in a broken symmetry state, an effective gravitational constant emerges which, in certain regimes, can lead to gravitational repulsive effects when only ordinary radiation is coupled to gravity. In this case, a bouncing universe is shown to be the only cosmological solution admissible by the field equations when the scalar field is in such a broken symmetry state.
In this paper, a bouncing cosmological scenario is studied in the background of a flat FLRW model with a specific parametrized hyperbolic form of scale factor $ a $ in terms of $ t $, where $ λ$ is taken as the model parameter. This model is discussed in $ f(R,G) $ formalism having structured as $ f(R,G)=R+F(G) $, where $ R $ is Ricci scalar and $ G $ is the Gauss-Bonnet invariant. The proposed functional form of the Hubble parameter is considered in such a way that it satisfies the bouncing criteria of the model, which is free from the initial singularity. The physical consequences of the mod…
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…
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…
In a Bohmian quantum cosmology scenario, we investigate some quantum effects on the evolution of the primordial universe arising from the adoption of an alternative non-trivial ordering to the quantization of the constrained Hamiltonian of a minimally coupled scalar field. The Wheeler-DeWitt equation has a contribution from the change in factor ordering, hence there are new quantum effects. We compare the results between the non-trivial and the trivial ordering cases, showing that the classical limit is valid for both orderings, but new bouncing and cyclic solutions are present in the non-triv…
We consider the field equations for a flat FRW cosmological model, in a generic $f(R)$ gravity model and cast them into a, completely normalized-dimensionless, system of O.D.Es for the scale factor and the function $f(R)$, with respect to the scalar curvature $R$. It is shown that under reasonable assumptions one can produce simple analytical and numerical solutions describing bouncing cosmological models where in addition there are late-time accelerating. Possibility of extending these results is briefly discussed.
In this work we explore the quantum Bianchi type IX-model, its semi-classical features, and its relevance in early cosmology to tentatively explain inflation and production of primordial structures. We specially focus on the analytical and numerical exploration of the dynamical system derived from the phase-space portraits. Afterwards we investigate the reliability of our results with regard to inflation and post inflation scenarii commonly accepted nowadays.
Modeling of matter bounce in $f(R,T)$ gravity has been presented with no violation of the null energy condition. Only a closed universe with negative pressure is allowed in good agreement with some recent observations which favor a universe with positive curvature. Our results agree with some recent works in which a combination of positive curvature and vacuum energy leads to non-singular bounces with no violation of the null energy condition. The stability of the model has been discussed. The cosmographic parameters are developed for the derived model to explain the accelerated expansion of t…
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.
A 1-parameter class of quadratic equations of state is confronted with the Hubble diagram of supernovae and Baryonic Acoustic Oscillations. The fit is found to be as good as the one using the LambdaCDM model. The corresponding universe has no initial singularity, only a mild bounce at a temperature well above the Planck temperature.
A cosmological model with a specific form of the Hubble parameter is constructed in a flat homogeneous, and isotropic background in the framework of $f(R, T)$ gravity, where $R$ is the scalar curvature and $T$ is the trace of the stress-energy-momentum tensor. The proposed functional form of the Hubble parameter is taken in such a way that it fulfills the successful bouncing criteria to find the solution of the gravitational field equations provided the Universe is free from initial singularity. The various constraints on the parameters are involved in the functional form of the Hubble paramet…
Teleparallel Gravity offers the possibility of reformulating gravity in terms of torsion by exchanging the Levi-Civita connection with the Weitzenböck connection which describes torsion rather than curvature. Surprisingly, Teleparallel Gravity can be formulated to be equivalent to general relativity for a appropriate setup. Our interest lies in exploring an extension of this theory in which the Lagrangian takes the form of $f(T,B)$ where T and B are two scalars that characterize the equivalency with general relativity. In this work, we explore the possible of reproducing well-known cosmologica…
In this study, cosmological models with perfect fluid and a gravitational framework f(Q) will be examined. In this modified theory of gravity, the gravitational force has the form f(Q), where Q stands for the non-metricity scalar. I create two bouncing cosmological models, one in which the Lagrangian f(Q) is assumed to have a linear dependence on Q and the other in which it has a polynomial functional form. It has been discovered that the parameters of the individual models largely determine how they will behave. The resulting models' equation of state (EoS) parameter captures the universe's i…
An important property of the three-point functions generated in the early universe is the so-called consistency condition. According to the condition, in the squeezed limit wherein the wavenumber of one of the three modes (constituting the triangular configuration of wavevectors) is much smaller than the other two, the three-point functions can be completely expressed in terms of the two-point functions. It is found that, while the consistency condition is mostly satisfied by the primordial perturbations generated in the inflationary scenario, it is often violated in the bouncing models. The v…
As our understanding of the past in a bouncing universe is limited, it becomes difficult to propose a cosmological model which can give some understanding of the causal structure of the bouncing universe. In this article we address the issue related to the particle horizon problem in the bouncing universe models. It is shown that in many models the particle horizon does not exist, and consequently the horizon problem is trivially solved. In some cases a bouncing universe can have a particle horizon and we specify the conditions for its existence. In the absence of a particle horizon the Hubble…
To understand the dynamics of loop quantum gravity, the deparametrized model of gravity coupled to a scalar field is studied in a simple case, where the graph underlying the spin network basis is one loop based at a single vertex. The Hamiltonian operator $\hat{H}_v$ is chosen to be graph-preserving, and the matrix elements of $\hat{H}_v$ are explicitly worked out in a suitable basis. The non-trivial Euclidean part $\hat{H}_v^E$ of $\hat{H}_v$ is studied in details. It turns out that by choosing a specific symmetrization of $\hat{H}_v^E$, the dynamics driven by the Hamiltonian gives a picture …
We consider certain aspects of cosmological dynamics of a spatially curved Universe in $f(T)$ gravity. Local analysis allows us to find conditions for bounces and for static solutions; these conditions appear to be in general less restrictive than in general relativity. We also provide a global analysis of the corresponding cosmological dynamics in the cases when bounces and static configurations exist, by constructing phase diagrams. These diagrams indicate that the fate of a big contracting Universe is not altered significantly when bounces become possible, since they appear to be inaccessib…
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…
The theory of inflation is one of the fundamental and revolutionary developments of modern cosmology that became able to explain many issues of early universe in the context of the standard cosmological model (SCM). However, the initial singularity of the universe, where physics is indefinite, is still obscure in the combined `SCM+inflation' scenario. An alternative to `SCM+inflation' without the initial singularity is thus always welcome, and bouncing cosmology is an attempt of that. The current work is thus motivated to investigate the bouncing solutions in modified gravity theories when the…
It was recently shown that black holes could be bouncing stars as a consequence of quantum gravity. We investigate the astrophysical signals implied by this hypothesis, focusing on primordial black holes. We consider different possible bounce times and study the integrated diffuse emission.
We consider the ADM formalism as a tool to build bouncing cosmologies. In this approach, the foliation of the spacetime has to be fixed in order to go beyond General Relativity modifying the gravitational sector. Once a preferred slicing, which we choose based on the matter content of the universe following the spirit of Weyl's postulate, has been fixed, $f$ theories depending on the extrinsic and intrinsic curvature of the slicing are covariant for all the reference frames preserving the foliation, i.e., the constraint and dynamical equations have the same form for all these observers. Moreov…
In this paper, we aim to investigate the effects of the anisotropy on the scale-invariant power spectrum considering the matter-dominated collapsing universe as background and look for the deviations from this scale invariance. Having set up this background, we consider a massless scalar field and work out the correlations, first by using the perturbative approach in which the anisotropic background is approximated with an effective isotropic metric represented by the metric of matter dominated collapsing universe, second by directly solving the field equation numerically, and then obtain the …
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…
In this paper, we have presented a bouncing cosmological model of the Universe in an extended theory of gravity. The dynamical behaviour of the model obtained from the flat FLRW space-time along with the violation of null energy condition have been shown. The geometrical parameters show singularity behaviour at the bouncing epoch. The parameters involved in the scale factor play a major role in the bouncing behaviour. In addition, the coupling parameter that resulted in the minimal matter-geometry coupling in the extended gravity has significant role to avoid the singularity of equation of sta…
In this paper, in an extended theory of gravity, we have presented bouncing cosmological model at the backdrop of an isotropic, homogeneous space-time, in presence of general relativistic hydrodynamics (GRH). The scale factor has been chosen in such a manner that with appropriate normalization, the quintom bouncing scenario can be assessed. Accordingly, the bounce occurs at $t=0$ and the corresponding Hubble parameter vanishes at the bounce epoch. The equation of state (EoS) parameter and the energy conditions of the model have been analysed. The violation of strong energy condition further su…
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.
We reconstruct $F(\mathcal{G})$ gravity theory with an exponential scale factor to realize the bouncing behavior in the early universe and examine the asymptotic behaviour of late-time solutions in this model. We propose an approach to the construction of asymptotic expansions of solutions of the Friedmann equations on the basis of Puiseux series.
Symmetric Teleparallel Gravity is an exceptional theory of gravity that is consistent with the vanishing affine connection. This theory is an alternative and a simpler geometrical formulation of general relativity, where the non-metricity $Q$ drives the gravitational interaction. Our interest lies in exploring the cosmological bouncing scenarios in a flat Friedmann-Limaître-Robertson-Walker (FLRW) spacetime within this framework. We explore bouncing scenarios with two different Lagrangian forms of $f(Q)$ such as a linearly and non-linearly dependence on $Q$. We have successfully examined all t…
