Narrow Results

To clarify the issue of obtaining the scale invariant CMB spectrum in bouncing cosmology, we examine the matching condition between the metric perturbations before and after the bounce. We prove a no-go theorem: independent of the details of the matching condition, a scale invariant spectrum is impossible as long as the local causality condition is satisfied. In our framework, it is easy to show that a violation of local causality around the bounce is needed in order to give a scale invariant spectrum. We study a specific scenario of this possibility by considering a nonlocal effective theory inspired by noncommutative geometry around the bounce and show that a scale invariant spectrum is possible.

This paper presents modeling of matter bounce in the framework of $f(R,T)$ gravity, where $f(R,T)=R+2\lambda T$. 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 $f(R,T)$ gravity but the perturbations decay out rapidly away from the bounce safeguarding its stability at late-times.

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, ${\rho }_x=n_0+n_2{H}^2+n_4{H}^4$, 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 $(n_0$, $n_2$, $n_4)$, 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 $H^2$, is studied, and we see that by increasing its coefficient, $n_2$, the transition point leads to lower values.

This work deals with an exhaustive study of bouncing cosmology in the background of homogeneous and isotropic Friedmann–Lemaître–Robertson–Walker spacetime. The geometry of the bouncing point has been studied extensively and used as a tool to classify the models from the point of view of cosmology. Raychaudhuri equation (RE) has been furnished in these models to classify the bouncing point as regular point or singular point. Behavior of time-like geodesic congruence in the neighborhood of the bouncing point has been discussed using the Focusing Theorem which follows as a consequence of the RE. An analogy of the RE with the evolution equation for a linear harmonic oscillator has been made and an oscillatory bouncing model has been discussed in this context.

This paper examines the behavior of the universe around the bouncing point in the background of $f(\mathcal{𝒬},\mathcal{𝒯})$ theory, where $\mathcal{𝒬}$ is the non-metricity and $\mathcal{𝒯}$ is the trace of the energy–momentum tensor. We derive the field equations that describe gravitational phenomena in the existence of non-metricity and matter source terms. By applying the reconstruction method for the Hubble parameter, a phenomenon of the bouncing universe for homogeneous spacetime filled with perfect fluid is studied. We consider specific models of this modified theory to evaluate the behavior of various cosmic parameters such as the Hubble, deceleration, equation of state and fluid parameters. When the null energy condition is violated, it follows a bouncing behavior. It is found that spacetime is composed of isotropic fluid, where a big bounce can occur and the universe turns into extremely unstable. We conclude that $f(\mathcal{𝒬},\mathcal{𝒯})$ gravity successfully explains the early and late time cosmic expansion and evolution.

In this paper, we study $F(R)$ gravity by Hu–Sawicki model in Friedmann–Lemaître–Robertson–Walker (FLRW) background. The Friedmann equations are calculated by modified gravity action, and then the obtained Friedmann equations are written in terms of standard Friedmann equations. Next, the behavior of bouncing cosmology is investigated in the modified gravity model, i.e. this behavior can solve the problem of nonsingularity in standard big bang cosmology. We plot the cosmological parameters in terms of cosmic time and then the bouncing condition is investigated. In what follows, we reconstruct the modified gravity by redshift parameter, and also graphs of cosmological parameters are plotted in terms of redshift, in which the figures show us an accelerated expansion of universe. Finally, the stability of the scenario is investigated by a function as sound speed, and the graph of sound speed versus redshift shows us that there is the stability in late-time.

The observed value of the Higgs mass indicates an instability of the Higgs scalar at large energy scales, and hence also at large field values. In the context of early universe cosmology, this is often considered to lead to problems. Here, we point out that we can use the instability of the Higgs field to generate an ekpyrotic phase of contraction. In the context of string theory, it is possible that at very high energy densities, extra states become massless leading to an $S$-brane which causes the transition between a contracting phase in the past and the current expanding phase. Thus, the Higgs field may be useable to generate a nonsingular bouncing cosmology in which the anisotropy problem of usual bouncing scenarios is mitigated.

The perturbations in the early universe are generated as a result of the interplay between quantum field theory and gravitation. Since these primordial perturbations lead to the anisotropies in the cosmic microwave background and eventually to the inhomogeneities in the Large Scale Structure (LSS), they provide a unique opportunity to probe issues which are fundamental to our understanding of quantum physics and gravitation. One such fundamental issue that remains to be satisfactorily addressed is the transition of the primordial perturbations from their quantum origins to the LSS which can be characterized completely in terms of classical quantities. Classical bouncing universes provide an alternative to the more conventional inflationary paradigm as they can help overcome the horizon problem in a fashion very similar to inflation. While the problem of the quantum-to-classical transition of the primordial perturbations has been investigated extensively in the context of inflation, we find that there has been a rather limited effort toward studying the issue in classical bouncing universes. In this work, we analyze certain aspects of this problem with the example of tensor perturbations produced in classical matter and near-matter bouncing universes. We investigate the issue mainly from two perspectives. First, we approach the problem by examining the extent of squeezing of a quantum state associated with the tensor perturbations with the help of the Wigner function. Second, we analyze the issue from the perspective of the quantum measurement problem. In particular, we study the effects of wave function collapse, using a phenomenological model known as continuous spontaneous localization, on the tensor power spectra. We conclude with a discussion of results.

This paper investigates the possibility of reconstruction of the generic function in $F({ℛ},T)$ gravitational theory by considering some well-known cosmological bouncing models, namely, exponential evaluation, oscillatory, power law and matter bounce model, where ${ℛ}$ and $T$ are Ricci scalar and trace of energy–momentum tensor, respectively. Due to the complexity of dynamical field equations, we propose some ansatz forms of function $F({ℛ},T)$ in perspective models and examine which type of Lagrangian is capable of reproducing bouncing solution via analytical expression. It is seen that for some cases of exponential, oscillatory and matter bounce models, it is possible to get analytical solution while in other cases, it is not possible to achieve exact (general) solutions so only complementary solutions can be discussed. However, for power-law model, all forms of generic function can be reconstructed analytically. Next we analyze the energy conditions and stability of these reconstructed cosmological bouncing models which have analytical forms. It is found that these models are stable for linear forms of Lagrangian only but the reconstructed solutions for power law are unstable for some nonlinear forms of Lagrangian. Further, we determine the observable quantities like spectral index ($n_s$) and tensor-to-scalar ratio ($r$) for the simplest reconstructed form of $f(R,T)$ function. As a result, we directly confront the reconstructed linear form of Lagrangian in $F({ℛ},T)$ model with 2018 Planck observations. Furthermore, we analyze that $F({ℛ},T)$ gravity with dark energy epoch is consistent with Sne-Ia+BAO+H(z)+CMB data and show that bounce can unify with dark energy epochs in $F({ℛ},T)$ gravity.

In this paper, our interest lies in investigating the possibilities of reconstructing analytical solutions for some familiar bouncing models in the flat Friedmann–Lemaître–Robertson–Walker (FLRW) geometry. We inspect the various gravitational Lagrangians, which are efficient enough for reproducing analytical solutions for symmetric, oscillatory, power law and bounce from loop quantum cosmology settings. Equation of state parameter, energy conditions, stability analysis have been performed for each model to examine its validity. The outcomes determine that the $f(T,{𝒯})$ modified theory is the competitive candidate of extended theories on the cosmological scale.

In the Emergent scenario, the Universe should evolve from a nonsingular state replacing the typical singularity of General Relativity, for any initial condition. For the scalar field model by Ellis and Maartens [Class. Quantum Grav. 21 (2003) 223] we show that only a set of measure zero of trajectories leads to emergence, either from a static state (an Einstein model), or from a de Sitter state. Assuming a scenario based on CDM interacting with a Dark Energy fluid, we show that in general flat and open models expand from a nonsingular unstable de Sitter state at high energies; for some closed models this state is a transition phase with a bounce, other closed models are cyclic. A subset of these models are qualitatively in agreement with the observable Universe, accelerating at high energies, going through a matter-dominated decelerated era, then accelerating toward a de Sitter phase.

Assuming that a cosmological model can describe the whole Universe history, we look for the conditions of a cosmological bounce that thus have to be in agreement with late time observations. Our approach involves casting such a theory into General Relativity with curvature (${\mathrm{\Omega }}_{\kappa }$), matter (${\mathrm{\Omega }}_m$), radiation (${\mathrm{\Omega }}_r$) and an effective dark fluid (${\mathrm{\Omega }}_d$) and formulating the corresponding field equations as a 2D dynamical system, wherein phase space points corresponding to extrema of the metric function are constrained by observational data on the aforementioned parameters densities. We show that if this effective dark fluid density is positive at the bounce, these observational constraints imply its occurrence in the future at a redshift $z<-0.81$ whatever the cosmological model (dark energy, brane, $f(R)$, etc.) corresponding to this effective dark fluid and even in the presence of positive curvature. Hence, the effective dark fluid density must be negative at the bounce such as it arises for $z>-0.81$ and thus possibly in the past. Observations also impose that the dark fluid effective density can change sign only within the redshift range $0.54<z<0.61$. We then proceed by examining three distinct cosmological models: a nonlinear dark fluid model, a Randall Sundrum brane model and a $f(R)=R+m{R}^n+\mathrm{\Lambda }$ model. For each of them, we examine the conditions for (1) a bounce at early time (when radiation dominates over matter), (2) with a negative effective dark fluid energy density, (3) this having to change sign within the above specified redshift interval (to be positive at present time). We find that none of the three models under consideration satisfy all three constraints. We therefore conclude that while a negative effective dark fluid energy density required by observational constraints on ${\mathrm{\Omega }}_m$, ${\mathrm{\Omega }}_r$ and ${\mathrm{\Omega }}_k$ for a bounce at early times facilitates this bounce, the requirement for ${\mathrm{\Omega }}_d$ to change sign and become positive within the above specified narrow redshift interval proves exceedingly challenging to satisfy these same constraints.

In this work, we use the Loop Quantum Cosmology (LQC) modified scalar–tensor reconstruction techniques in order to investigate how bouncing and inflationary cosmologies can be realized. With regard to the inflationary cosmologies, we shall be interested in realizing the intermediate inflation and the Type IV singular inflation, while with regard to bouncing cosmologies, we shall realize the superbounce and the symmetric bounce. In all the cases, we shall find the kinetic term of the LQC holonomy corrected scalar–tensor theory and the corresponding scalar potential. In addition, we shall include a study of the effective Equation of State (EoS), emphasizing at the early- and late-time eras. As we demonstrate, in some cases it is possible to have a nearly de Sitter EoS at the late-time era, a result that could be interpreted as the description of a late-time acceleration era. Also, in all cases we shall examine the dynamical stability of the LQC holonomy corrected scalar-tensor theory, and we shall confront the results with those coming from the corresponding classical dynamical stability theory. The most appealing cosmological scenario is that of a Type IV singular inflationary scenario, in which the singularity may occur at the late-time era. As we demonstrate, for this model, during the dark energy era, a transition from non-phantom to a phantom dark energy era occurs.

In this work, we have investigated the cosmological bouncing solution in LRS Bianchi-I space-time in framework of $f(R,T)$ 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 $f(R,T)$ theory proposed by Harko et al. [f(R, T) gravity, Phys. Rev. D84 (2011) 024020], whose functional form is as $f(R,T)=R+2\mu T,$ where $R$ is Ricci scalar, $T$ is trace of energy–momentum tensor and $\mu$ 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 $\omega$ 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.

This paper is devoted to explore bouncing cosmology in $f(T,{𝒯})$ modified gravity. In the background of $f(T,{𝒯})$ modified theory with $T$ being Torsion scalar and ${𝒯}$ being the trace of energy–momentum tensor, the Hubble parameter is considered for the isotropic, flat, and homogenous universe. The standard bouncing scale factor has employed the exponential term to unify bounce with late-time acceleration. Phase portrait analysis reveals us that Minkowskian origin transfers to de Sitter origin in $(H,Ḣ)$-plane and as past infinite time $t\to -\infty$$\Rightarrow$$a(t)\to 0$ and $(H,Ḣ)\to$ constant which corresponds to some physical cosmological scenarios. Since field equations of $f(T,{𝒯})$ gravity are of second order, a one-dimensional autonomous system has been extracted. Finally, outcomes have been plotted graphically, and any type of singular behavior has not been experienced. The study of the equation of state parameter against cosmic time reveals that phantom phase is quite significant for both models. The inertial force in terms of Hubble parameter and cosmic time gives rise to pseudo Rip. The study of cosmographic parameters tells us that the present model corresponds to $\mathrm{\Lambda }$CDM at a large value of cosmic time.

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 the 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 analyzed. The violation of strong energy condition further supports the behavior of extended gravity. As the bouncing cosmology suffers with instability, this model also shows the similar behavior.

This work aims to study the bouncing universe under f(G, T) theory of gravity (where G and T are the Gauss–Bonnet invariance and trace of energy–momentum tensor, respectively). We construct modified field equations (MFEs) to analyze the behavior of Hubble parameter (HP) for $f(G,T)=G+\alpha G^n+2\lambda T$ with $\alpha$, $\lambda$ and $(n>0)$ are constant terms. Different constraints are applied, engaging HP to examine the accelerating universe and to test initial singularity. The graphical analysis is made for different values of n to explain bouncing process more precisely with respect to cosmic time that also provides an indication of null energy condition (NEC) violation. Resultantly, all mandatory conditions are fulfilled indicating that our proposed model provides good bouncing solutions.

In this paper, we investigate the bouncing behavior of the universe within the framework of $f(R,L_m)$ gravity, using a simple form of $f(R,L_m)=\frac{R}{2}+L_m^{\gamma }$ (where $\gamma$ is a free model parameter) as previously studied. The model predicts a vanishing Hubble parameter in the early and late times, with the deceleration parameter approaching a specific limit at the bouncing point. The EoS parameter is observed to cross the phantom divide line ($\omega =-1$) near the bouncing point, indicating a significant transition from a contracting to an expanding phase. The model satisfies the necessary energy conditions for a successful bouncing scenario, with violations indicating exotic matter near the bouncing point. Stability conditions are satisfied for certain values of $\gamma$ near the bouncing point, but potential instabilities in late-time evolution require further investigation. Finally, we conclude that the $f(R,L_m)$ gravity model is promising for understanding the universe’s dynamics, especially during events like the bouncing phase.

The general matter bounce scenario, including an Ekpyrotic field to avoid anisotropic instabilities, is studied in a loop quantized isotropic and homogeneous FLRW setting. The matter bounce scenario provides a convenient way to include quantum corrections from the bounce in the perturbations originating in the far past, which also produce a scale invariant power spectrum. LQC provides the right setting for studying quantum corrections in a matter bounce scenario as the bounce in LQC occurs entirely due to quantum geometrical effects without needing any exotic matter fields to avoid the singularity. A detailed exploration of this general matter-Ekpyrotic scenario in spatially flat FLRW spacetime in LQC filled with minimally coupled dust and Ekpyrotic scalar field is studied with the help of numerical simulations. Various features of the background dynamics are shown to be robust under variations in initial conditions and choice of parameters. We use the dressed metric approach for the perturbations and obtain a scale invariant power spectrum for modes exiting the horizon in the dust dominated contracting phase. In contrast to previous studies considering a constant equation of state for the Ekpyrotic field, we found that the magnitude of the power spectrum changes during the evolution. The scale invariant section of the power spectrum also undergoes a rapid increase in its magnitude in the bounce regime, while its scale invariance is unaffected. We argue that apart from increasing the magnitude, the bounce regime may only substantially affect the modes outside the scale invariant regime. However, the spectral index is found to be too close to unity, thus inconsistent with the observational constraints, necessitating further modifications of the model.

We review recent developments in the primordial power spectra of two modified loop quantum cosmological models (mLQCs) which originate from the quantization ambiguities while loop quantizing the spatially-flat Friedmann-Lemaître-Robertson-Walker (FLRW) universe. The properties of the background dynamics and the primordial scalar power spectra in two modified models, namely mLQC-I and mLQC-II, are reported. In both models, the inflationary scenario can be naturally extended to the Planck regime when a single scale field is minimally coupled to gravity with an inflationary potential and the big bang singularity is replaced with a quantum bounce. The qualitative difference lies in the behavior of the contracting phase where a quasi de Sitter phase emerges in mLQC-I. When applying the dressed metric approach and the hybrid approach to mLQCs, we find the most distinguishable differences between these models and the standard loop quantum cosmology (LQC) occur in the infrared and intermediate regimes of the power spectra.