Matter Bounce Scenario Research Articles

Scalar field induced dynamical evolution in teleparallel gravity

In this paper, we investigate the role of scalar field potentials in the dynamical evolution of the Universe. A gravity theory with a non-minimally coupled scalar field with torsion in the geometrical action simulating effective dark energy is considered to study an extended matter bounce scenario. The dynamical behaviour of the equation of state parameter has been studied near the bouncing epoch. Keeping in mind the inflationary behaviour near the bounce, five different scalar field potential functions are explored, and their effect on the equation of state parameter is investigated.

Cosmographic and matter bounce scenario in modified torsion gravity

In this manuscript, we investigate the matter bounce cosmological implications in the context of f(T,τ) gravity (T represents the torsion scalar whereas τ is the trace of the energy–momentum tensor). We construct the field equations for spatially flat homogeneous and isotropic space–time with perfect fluid configuration. We consider the two particular forms of scale factor inspired by loop-quantum cosmology to investigate the matter bounce mechanism. In this regard, we examine the graphical behavior of cosmological as well as dynamical parameters at and in the neighborhood of bounce point. Furthermore, the stability via perturbation technique and energy conditions are also discussed. It is concluded that all the cosmographic tests favor the bouncing cosmology for an appropriate choice of model parameters. It is worth mentioning that considered models are stable and energy conditions are violated at the bouncing point as well as in its vicinity leading to a successful bouncing scenario.

Matter bounce scenario in matter geometry coupled theory

This paper studies the cosmographic and matter bounce scenario in modified theory. The corresponding field equations are evaluated after considering special corrections of a Hubble parameter. The linear corrections to the Gauss-Bonnet gravity are being taken to analyze the behavior of Hubble and deceleration parameters. We derive dynamical parameters in a very general way to analyze different energy conditions that would lead to understanding the behavior of the equation of state parameters in cosmography. Finally, the removal of the initial singularity is observed to understand the late-time cosmic acceleration.

Matter bounce scenario in extended symmetric teleparallel gravity

In this paper, we have shown the matter bounce scenario of the Universe in an extended symmetric teleparallel gravity, the f(Q) gravity. Motivated from the bouncing scenario and loop quantum cosmology (LQC), the form of the function f(Q) has been obtained at the backdrop of Friedmann–Lema{hat{i}}tre–Robertson Walker (FLRW) space time. Considering the background cosmology dominated by dust fluid, the e-folding parameter has been expressed, which contains the nonmetricity term. Since the slow roll criterion in the bouncing context is not valid, we used a conformal equivalence between f(Q) and scalar-tensor model to apply the bottom-up reconstruction technique in the bouncing model. The dynamics of the model has been studied through the phase space analysis, where both the stable and unstable nodes are obtained. Also, the stability analysis has been performed with the first order scalar perturbation of the Hubble parameter and matter energy density to verify the stability of the model.

Imprints of anisotropy on the power spectrum in matter dominated bouncing universe as background

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 the scale invariance. Having set up this background, we consider a test massless scalar field and work out the correlations for the field, 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 power spectrum for the range of modes which are of cosmological interest. Using both techniques, we get an upper bound on the deviation in the power spectrum from the scale invariance. We also work out the power spectrum for much smaller modes and look at whether it is possible to explain the observed anomalies in CMB via the matter bounce scenario.

Observational constraints on anisotropies for bouncing alternatives to inflation

We calculate how primordial anisotropies in the background space-time affect the evolution of cosmological perturbations for bouncing alternatives to inflation, like ekpyrosis and the matter bounce scenario. We find that the leading order effect of anisotropies in the contracting phase of the universe is to induce anisotropies in the cosmic microwave background with a very concrete form: a scale-invariant quadrupolar angular distribution. Sub-leading effects are the generation of higher-order moments in the angular distribution, as well as cross-correlations between scalar and tensor modes. We also find that observational constraints from the cosmic microwave background on the quadrupole moment provide strong bounds on allowed anisotropies for bouncing alternatives to inflation that are significantly more constraining than the bounds previously obtained using scaling arguments based on the conjectured Belinski-Khalatnikov-Lifshitz instability.

Unifying turnaround-bounce cosmology in a cyclic universe considering a running vacuum model

Among many models which can describe the bouncing cosmology, a matter bounce scenario that is deformed by a running vacuum model of dark energy (RVM-DE) has been interested. In this research, I show that a class of RVM-CDM (cold dark matter) model can also describe a cyclical cosmology in which the universe undergoes cycles of expansion to the contraction phase and vice versa. To this end, following our previous work, I consider one of the most successful classes of RVM-CDM model in bouncing cosmology, [Formula: see text], in which the power spectral index gets a red tilt and the running of the spectral index may give a negative value by choosing the appropriate value of parameters [Formula: see text], [Formula: see text], [Formula: see text], which is consistent with the cosmological observations. It is worthwhile to mention that most matter bounce models do not produce this negative value. However, the main purpose of this paper is to investigate the RVM-CDM model in the turnaround phase. Far from the bounce in a phantom expanding universe, the turnaround conditions are investigated before the occurrence of a sudden big rip. By analyzing the Hubble parameter, equation of state (EoS) parameter, and deceleration parameter around the turnaround, we show that a successful turnaround may occur after an expansion in an interacting case of RVM-CDM by choosing the appropriate value of parameters. A minimum value for the interaction parameter is obtained and also find any relation between other model parameters. Finally, the effect of each parameter on a turnaround is studied, and we see that the transition time from accelerating to decelerating expansion can occur earlier for larger values of interaction parameter. Also, in several graphs, the effect of the second term in DE density, including [Formula: see text], is studied, and we see that by increasing its coefficient, [Formula: see text], the transition point leads to lower values.

Kalb-Ramond field-induced cosmological bounce in generalized teleparallel gravity

One of the important open questions in high-energy physics is to understand the lack of evidence of the Kalb-Ramond (KR) field, in particular in present day cosmology. In this paper we aim to address this issue by showing that a bounce scenario in the evolution of the Universe strongly advocates their elusiveness, even if their energy density was very large to start with. We consider the Kalb-Ramond field and its effects in the context of generalized teleparallel gravity in ($3+1$) dimensions. Teleparallel gravity is a description of gravitation in which the tetrads are the dynamical degrees of freedom, and the torsion arising from fields with spin are accommodated naturally as field strength tensors. In order to describe the coupling prescription, we address the correct generalization of the Fock-Ivanenko derivative operator for an $n$-form tensor field. By varying with respect to the tetrads, this rank-2 field is shown to source the teleparallel equivalent of Einstein's equations. We study the possibility of reproducing two well-known cosmological bounce scenarios; namely, symmetric bounce and matter bounce in four-dimensional spacetime with the Friedmann-Lema\^{\i}tre-Robertson-Walker metric, and observe that the solution requires the KR field energy density to be localized near the bounce. The crucial result in our work is that this feature also naturally explains the lack of cosmological evidence of the rank-2 field in the present day Universe for the matter-bounce scenario. Thus, among the bouncing cosmologies, the latter is favored over the former.

Matter bounce scenario and the dynamical aspects in f(Q,T) gravity

In the context of the late time cosmic acceleration phenomenon, many geometrically modified theories of gravity have been proposed in recent times. In this paper, we have investigated the role of a recently proposed extension of symmetric teleparallel gravity dubbed as f(Q,T) gravity in getting viable cosmological models, where Q and T respectively denote the non-metricity and the trace of energy momentum tensor. We stress upon the mathematical simplification of the formalism in the f(Q,T) gravity and derived the dynamical parameters in more general form in terms of the Hubble parameter. We considered two different cosmological models mimicking non-singular matter bounce scenario. Since energy conditions play a vital role in providing bouncing scenario, we have analyzed different possible energy conditions to show that strong energy condition and null energy condition be violated in this theory. The models considered in the work are validated through certain cosmographic tests and stability analysis.

Primordial power spectrum from a matter-ekpyrotic bounce scenario in loop quantum cosmology

A union of matter bounce and Ekpyrotic scenarios is often studied in an attempt to combine the most promising features of these two models. Since non-perturbative quantum geometric effects in loop quantum cosmology (LQC) result in natural bouncing scenarios without any violation of energy conditions or fine tuning, an investigation of matter-Ekpyrotic bounce scenario is interesting to explore in this quantum gravitational setting. In this work, we explore this unified phenomenological model for a spatially flat Friedmann-Lema\^itre-Robertson-Walker (FLRW) universe in LQC filled with dust and a scalar field in an Ekpyrotic scenario like negative potential. Background dynamics and the power spectrum of the comoving curvature perturbations are numerically analyzed with various initial conditions and a suitable choice of the initial states. By varying the initial conditions we consider different cases of dust and Ekpyrotic field domination in the contracting phase. We use the dressed metric approach to numerically compute the primordial power spectrum of the comoving curvature perturbations which turns out to be almost scale invariant for the modes which exit the horizon in the matter-dominated phase. But, in contrast with a constant magnitude power spectrum obtained under approximation of a constant Ekpyrotic equation of state using deformed algebra approach in an earlier work, we find that the magnitude of power spectrum changes during evolution. Our analysis shows that the bouncing regime only leaves imprints on the modes outside the scale-invariant regime. However, an analysis of the spectral index shows inconsistency with the observational data, thus making further improvements in such a model necessary.

LRS Bianchi type-I bouncing cosmological models in f(R,T) gravity

In this work, we have investigated the cosmological bouncing solution in LRS Bianchi-I space-time in framework of [Formula: see text] gravity. Our study in this paper is based on the modeling of matter bounce scenario in which the universe starts with a matter-dominated contraction phase and transitions into an ekpyrotic phase. Mathematical simulations have been done in the modified general theory of relativity in the form of [Formula: see text] theory proposed by Harko et al. [f(R, T) gravity, Phys. Rev. D 84 (2011) 024020], whose functional form is as [Formula: see text] where [Formula: see text] is Ricci scalar, [Formula: see text] is trace of energy–momentum tensor and [Formula: see text] is constant. Taking the non-vanishing scale factor in LRS Bianchi-I space-time, the geometrical parameters such as Hubble parameter and deceleration parameter have been derived and their subsequent use in the expression of pressure, density and EoS parameter [Formula: see text] confirms qualitatively the initial conditions of the universe at the bounce. With the non-vanishing nature of scale factor, initial universe in finite means ruled out the initial singularity problem. The analysis of violation of energy conditions near the bouncing region and stability of the model shows that the matter bounce approach is highly unstable at the bounce but the rapid decay of perturbations away from the bounce supports the stability of the model.

Planck residuals anomaly as a fingerprint of alternative scenarios to inflation

Planck's residuals of the CMB temperature power spectrum present a curious oscillatory shape that resembles an extra smoothing effect of lensing and is the source of the lensing anomaly. The smoothing effect of lensing to the CMB temperature power spectrum is, to some extent, degenerate with oscillatory modulations of the primordial power spectrum, in particular if the frequency is close to that of the acoustic peaks. We consider the possibility that the lensing anomaly reported by the latest Planck 2018 results may be hinting at an oscillatory modulation generated by a massive scalar field during an alternative scenario to inflation or by a sharp feature during inflation. We use the full TTTEEE+low E CMB likelihood from Planck to derive constraints on these two types of models. We obtain that in both cases the AL anomaly is mildly reduced to slightly less than 2σ, to be compared with the 2.8σ deviation from AL=1 in ΛCDM. Although the oscillatory features are not able to satisfactorily ease the lensing anomaly, we find that the oscillatory modulation generated during an alternative scenario alone, i.e. with AL=1, presents the lowest value of χ2, with Δχ2=−13 compared to ΛCDM. Furthermore, the Akaike Information Criterion suggests that such an oscillation constitutes an attractive candidate since it has a value ΔAIC=−5 with respect to ΛCDM, comparable to the AL parameter. We also obtain that the equation of state parameter in the alternative scenario is given at 1σ by w=0.13±0.17. Interestingly, the matter bounce and radiation bounce scenarios are compatible with our results. We discuss how these models of oscillatory features can be tested with future observations.

Extended matter bounce scenario in ghost free [formula omitted] gravity compatible with GW170817

In the context of a ghost free f(R,G) model, an extended matter bounce scenario is studied where the form of the scale factor is given by a(t)=(a0t2+1)n. The ghost free character of the model is ensured by the presence of a Lagrange multiplier, as developed in [1]. The conditions under which, in this model, the speed of gravitational waves becomes equal to the speed of light (equal to one, in natural units), thus becoming compatible with the striking event GW170817, is investigated. It is shown that this happens for a class of Gauss-Bonnet (GB) coupling functions (h(t)) which satisfies a constraint equation of the form h¨=h˙H, with H the Hubble parameter. This constraint is then imposed on the ghost free f(R,G) gravity theory to be consistent with the GW170817 event, subsequently, the corresponding non-singular bouncing cosmology with the aforementioned scale factor is extensively studied. The forms of the coupling function and Lagrange multiplier in the “low curvature limit” of the theory are reconstructed, yielding a viable approximation for n<1/2. Correspondingly, by solving the cosmological perturbation equation, the main observable quantities, namely the spectral index, tensor to scalar ratio, and the running index are determined and confronted with the latest Planck 2018 data. Consistency with the data is proven for those parametric regimes that which correspond to n<1/2. This makes the low curvature approximation a viable one for calculating the scalar and tensor power spectra.

Bouncing scenario in f(R,T) gravity

This paper presents modeling of matter bounce in the framework of [Formula: see text] gravity, where [Formula: see text]. We start by defining a parametrization of scale factor which is non-vanishing. The geometrical parameters such as the Hubble parameter and deceleration parameter are derived, from which expressions of pressure, density and Equation of State (EoS) parameter and a qualitative understanding of the initial conditions of the universe at the bounce are ascertained. We found that the initial conditions of the universe are finite owing to the non-vanishing nature of the scale factor thus eliminates the initial singularity problem. Furthermore, we show the violation of energy conditions near the bouncing region and analyze the stability of our model with respect to linear homogeneous perturbations in Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime. We found that our model and hence matter bounce scenarios in general are highly unstable at the bounce in the framework of [Formula: see text] gravity but the perturbations decay out rapidly away from the bounce safeguarding its stability at late-times.

Viable non-singular cosmic bounce in holonomy improved F(R) gravity endowed with a Lagrange multiplier

Matter and quasi-matter bounce scenarios are studied for an F(R) gravity model with holonomy corrections and a Lagrange multiplier, with a scale factor a(t) = left( a_0t^2 + 1 right) ^n, where the Hubble parameter squared has a linear and a quadratic dependence on the effective energy density. Provided n < 1/2, it is shown that the primordial curvature perturbations are generated deeply into the contracting era, at large negative time, which makes the low-curvature limit a good approximation for calculating the perturbation power spectrum. Moreover, it is shown that, for n within this range, the obtained cosmological quantities are fully compatible with the Planck constraints, and that the “low curvature limit” comes as a viable approximation to calculate the power spectra of both scalar and tensor perturbations. Using reconstruction techniques for F(R) gravity with the Lagrange multiplier, the precise form of the effective F(R) gravity is found, from which one determines the power spectra of scalar and tensor perturbations in such bouncing scenario. Correspondingly, the spectral index for curvature perturbations and the tensor to scalar ratio are obtained, and these values are successfully confronted with the latest Planck observations. Further, it is shown that both the weak and the null energy conditions are satisfied, thanks to the holonomy corrections performed in the theory–which are then proven to be necessary for achieving this goal. In fact, when approaching the bouncing era, the holonomy corrections become significant and play a crucial role in order to restore the energy conditions. Summing up, a cosmological bouncing scenario with the scale factor above and fulfilling the energy conditions can be adequately described by the F(R) model with a Lagrange multiplier and holonomy corrections, which prove to be very important.

Viable scalar spectral tilt and tensor-to-scalar ratio in near-matter bounces

In a recent work, we had constructed a model consisting of two fields---a canonical scalar field and a non-canonical ghost field---that had sourced a symmetric matter bounce scenario. The model had involved only one parameter, viz. the scale associated with the bounce. For a suitable value of the parameter, the model had led to strictly scale invariant power spectra with a COBE normalized scalar amplitude and a rather small tensor-to-scalar ratio. In this work, we extend the model to achieve near-matter bounces, which contain a second parameter apart from the bounce scale. As the new model does not seem to permit analytical evaluation of the scalar modes near the bounce, with the aid of techniques which we had used in our earlier work, we compute the scalar and the tensor power spectra numerically. For appropriate values of the additional parameter, we find that the model produces red spectra with a scalar spectral tilt and a small tensor-to-scalar ratio which are consistent with the recent observations of the anisotropies in the cosmic microwave background by Planck.

Gauge invariant prescription to avoid a γ -crossing instability in a Galileon bounce

We revisit the evolutions of scalar perturbations in a non-singular Galileon bounce. It is known that the second order differential equation governing the perturbations is numerically unstable at a point called $\gamma$-crossing. This instability is usually circumvented using certain gauge choices. We show that the perturbations can be evolved across this point by solving the first order differential equations governing suitable gauge invariant quantities without any instabilities. We demonstrate this method in a matter bounce scenario described by the Galileon action.

The Dapor\u2013Liegener model of loop quantum cosmology: a dynamical analysis

The Dapor–Liegener model of loop quantum cosmology (LQC), which depicts an emergent universe from a de Sitter regime in the contracting phase is studied from the mathematical viewpoint of dynamical systems and compared with the standard model of LQC. Dealing with perturbations, on the contrary to standard LQC where at early times all the scales are inside the Hubble radius, we show that it is impossible to implement the matter bounce scenario due to the fact that an emergent de Sitter regime in the contracting phase implies that all the scales are outside of the Hubble radius in a past epoch.

Bouncing cosmologies via modified gravity in the ADM formalism: Application to loop quantum cosmology

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. Moreover, choosing multivalued $f$ functions, bouncing backgrounds emerge in a natural way. In fact, the simplest is the one corresponding to holonomy corrected Loop Quantum Cosmology. The final goal of this work is to provide the equations of perturbations which, unlike the full equations, become gauge invariant in this theory, and apply them to the so-called matter bounce scenario.

Running of the spectral index in deformed matter bounce scenarios with Hubble-rate-dependent dark energy

As a deformed matter bounce scenario with a dark energy component, we propose a deformed one with running vacuum model (RVM) in which the dark energy density rho _{Lambda } is written as a power series of H^2 and dot{H} with a constant equation of state parameter, same as the cosmological constant, w=-1. Our results in analytical and numerical point of views show that in some cases same as Lambda CDM bounce scenario, although the spectral index may achieve a good consistency with observations, a positive value of running of spectral index (alpha _s) is obtained which is not compatible with inflationary paradigm where it predicts a small negative value for alpha _s. However, by extending the power series up to H^4, rho _{Lambda }=n_0+n_2 H^2+n_4 H^4, and estimating a set of consistent parameters, we obtain the spectral index n_s, a small negative value of running alpha _s and tensor to scalar ratio r, which these reveal a degeneracy between deformed matter bounce scenario with RVM-DE and inflationary cosmology.