Narrow Results

The analytical bounce solution is derived in terms of the polygamma function in the Caldeira–Leggett's dissipative quantum tunneling model. The classical action for the bounce solution lies between the upper and lower bounds in the full range of α, where α is a dissipation coefficient. The bounce peak point increases from 1 to 4/3 with the increase of α. In spite of various nice features, we have shown that the solution we have derived is not exact one by making use of the zero-mode argument in the linearized fluctuation equation. However, our solution can be a starting point for approximate computation of the prefactor in this model.

We present and expand the simplest possible quantum cosmological bouncing model already discussed in previous works: the trajectory formulation of quantum mechanics applied to cosmology (through the Wheeler–De Witt equation) in the Friedmann–Lemaître–Robertson–Walker (FLRW) minisuperspace without spatial curvature. The initial conditions that were previously assumed were such that the wave function would not change its functional form but instead provide a dynamics to its parameters. Here, we consider a more general situation, in practice consisting of modified Gaussian wave functions, aiming at obtaining a nonsingular bounce from a contracting phase. Whereas previous works consistently obtain very symmetric bounces, we find that it is possible to produce highly non-symmetric solutions, and even cases for which multiple bounces naturally occur. We also introduce a means of treating the shear in this category of models by quantizing in the Bianchi I minisuperspace.

Many cosmological scenarios envisage either a bounce of the universe at early times, or a collapse locally to form a black hole which re-expands into a new expanding universe region. Energy conditions preclude this phenomena for ordinary matter in general relativistic universe, but scalar or other types of fields can violate some of these conditions, and so can, possibly, provide conditions for a bouncing universe. In this paper, we have investigated the necessary conditions for a bounce in Kantowski–Sachs (KS) and Bianchi type models in some modified theories of gravity like Hoyle–Narlikar creation field theory, Lyra geometry, general class of scalar–tensor theories, Einstein's theory with variable cosmological term.

We discuss again the approach to cyclic cosmology based on the 2007 Baum–Frampton model. By introducing the relationship between entanglement entropy and space–time connectivity first introduced by Van Raamsdonck (2010) we show how vanishing entropy at the turnaround, and hence at the bounce after adiabatic contraction, can be better understood in this solution to the Tolman entropy conundrum.

In this paper, we investigate the possibility of a nonsingular model of universe in the framework of general relativity in nonflat FRW geometries with quadratic equation of state and bulk viscosity. We study whether a nonsingular bounce requires violation of energy conditions. We discuss the thermodynamical aspects of the resulting models with equilibrium description. In particular, we discuss the validity of the generalized second law of thermodynamics for resulting cosmologies.

The time evolution of total entropy including the entropy associated with horizon and entropy of matter inside the horizon in homogeneous and isotropic Jordan frame (dilatonic) Brans–Dicke cosmologies is examined. We show that the bouncing Brans–Dicke cosmologies do not satisfy the generalized second law of thermodynamics during the contracting phase of evolution.

In this work, we have examined the metric affine-based geometric model $f(Q)=Q+m{Q}^n$ to investigate inflationary cosmology and bouncing cosmology. The four bouncing models we have examined are the exponential, matter, symmetric and super-bounce models. Furthermore, in the inflationary situation, we have employed a scalar field to test whether or not kinetic energy is dominated and whether or not all of the bouncing models are consistent with inflationary conditions. We have investigated various energy conditions for various scale factors and verified whether or not these scale factors are consistent with inflationary scenarios within the framework of inflationary cosmology under $f(Q)\text{gravity}$. In the end, we have shown that the bouncing scale factor under the polynomial model ($Q+m{Q}^n$) of $f(Q)$ gravity in a single scalar field is compatible with the inflationary scenario.

A cosmological model with two phantom scalar fields with a special choice of the field potential is considered. The obtained regular solution describes a bounce with a subsequent transition to the de Sitter stage of the expansion of the universe. This solution could also be interpreted as an S-brane solution.

In teleparallel gravity, we apply Lorenz type gauge fixing to cope with redundant degrees of freedom in the vierbein field. This condition is mainly to restore the Lorentz symmetry of the teleparallel torsion scalar. In cosmological application, this technique provides standard cosmology, turnaround, bounce or $\mathrm{\Lambda }$CDM as separate scenarios. We reconstruct the $f(T)$ gravity which generates these models. We study the stability of the solutions by analyzing the corresponding phase portraits. Also, we investigate Lorenz gauge in the unimodular coordinates, it leads to unify a nonsingular bounce and Standard Model cosmology in a single model, where crossing the phantom divide line is achievable through a finite-time singularity of Type IV associated with a de Sitter fixed point. We reconstruct the unimodular $f(T)$ gravity which generates the unified cosmic evolution showing the role of the torsion gravity to establish a healthy bounce scenario.

Cosmological inflation is a popular paradigm for understanding Cosmic Microwave Background Radiation (CMBR); however, it faces many conceptual challenges. An alternative mechanism to inflation for generating an almost scale-invariant spectrum of perturbations is a bouncing cosmology with an initial matter-dominated contraction phase, during which the modes corresponding to currently observed scales exited the Hubble radius. Bouncing cosmology avoids the initial singularity but has fine-tuning problems. Taking an agnostic view of the two early-universe paradigms, we propose a quantum measure — Dynamical Fidelity Susceptibility (DFS) of CMBR — that distinguishes the two scenarios. Taking two simple models with the same power-spectrum, we explicitly show that DFS behaves differently for the two scenarios. We discuss the possibility of using DFS as a distinguisher in the upcoming space missions.

Cosmological models with inflation and those with bounce have their own strengths and weaknesses. Here, we construct a model in which a phase of bounce is followed by a viable inflationary phase. This incorporates several advantages of both and hence, is a more viable model for cosmic evolution. We explore scenarios wherein the bouncing phase smoothly transits to an inflationary one, with the pivot scale leaving the Hubble horizon during the latter era, thereby maintaining consistency with observations. Staying within the ambit of Einstein–Hilbert gravity augmented by the inflation, we ensure a pre-inflationary bounce by introducing a second scalar field that helps engineer the requisite violation of the null energy condition. Potential ghost instabilities can be mitigated by invoking a nontrivial coupling between the two scalar fields.

The present paper reports a study on the bouncing behavior of the viscous modified Chaplygin gas (MCG) in Einstein as well as modified gravity framework. For a bouncing scale factor proposed by Cai et al., Class. Quantum Grav.28 (2011) 215011, we have studied the cosmology of MCG in presence of bulk viscosity. In Einstein gravity framework, we have studied the equation of state parameter and it has been found to cross $-1/3$ indicating the end of the early accelerated expansion and it has also been observed that for flat FRW universe the presence of bulk viscosity induces the crossing of phantom boundary. Role of the model parameters of the MCG has also been investigated before and after the bounce. A Hubble flow dynamics has been carried out and, it was revealed that MCG is capable of realizing inflationary phase as well as an exit from inflation. A $f(T)$ gravitational paradigm has also been considered, where the MCG density has been reconstructed in presence of bulk viscosity. Role of $\sigma$ of the bouncing scale factor, describing how fast the bounce takes place, has also been studied in this framework.

The present study reports a reconstruction scheme for $f(T)$ gravity considering the scale factor in the power law form. The equation of state parameter has been studied for this reconstructed model along with the deceleration parameter and the statefinder pair $\{r,s\}$. The statefinder trajectory has been found to interpolate between dust and $\mathrm{\Lambda }$CDM phase of the universe. Cosmological evolution of primordial perturbations has been studied through scalar metric fluctuations and finally the reconstructed $f(T)$ model has been tested for its consistency with the generic expansion of the universe.

In this paper, a cosmological model with linear equation of state in the framework of General relativity is studied. We explore the thermodynamical aspects of the cosmological model with equilibrium description. In particular, we discuss the validity of generalized second law of thermodynamics for resulting cosmologies. General conditions for this model to satisfy the slow roll conditions for inflation are discussed.

In this paper, we explore the homogeneous and isotropic flat Friedmann–Robertson–Walker (FRW) model in Chameleon cosmology. By considering a non-minimal coupling between the scalar field and matter, we present a non-singular bouncing cosmological scenario of the universe. The universe initially exhibits the ekpyrotic phase during the contracting era, undergoes a non-singular bounce, and then in expanding era, it smoothly transits to the decelerating era having matter and radiation-dominated phases. Further, this decelerating era is smoothly connected to the late-time dark energy-dominated era of the present epoch. We use numerical solution techniques to solve non-minimally coupled gravity equations for understanding the evolution of scalar field along with other quantities like effective potential in the model. The model thus unifies an ekpyrotic, non-singular, asymmetric bounce with the dark energy era of the present epoch. We study the evolution of bouncing model and confront the model with observational results on the equation of state parameter by constraining the model parameters.

We investigate the role of bulk and shear viscosity in the spatially homogeneous anisotropic spacetime, in particular, the Kantowski–Sachs (KS) spacetime. General conditions for the bouncing evolution of universe in anisotropic background have been obtained by using the derived propagation equations of expansion scalar, shear scalar and spatial 3-curvature. We show that the presence of shear viscosity in the model prohibits the energy density to attain its extremum in the bouncing model. We explore the qualitative behavior of KS cosmologies by formulating the Einstein’s field equations into a plane-autonomous system of equations by taking dimensionless equation of state. The stability of the system has been investigated by evaluating and analyzing the eigenvalues at the critical points. The stable solutions exist for the system composed of bulk and shear viscosity. The present analysis through dynamical system method illustrates that the universe does not exhibit synchronous bounce with perfect fluid and/or viscous fluids in the KS spacetime.

It is shown that taking into consideration vorticity-related component of cosmological motion averts singularity and explains acceleration of the expansion. No mystic matter with dark energy is needed. That energy belongs to the local rotational motion (vorticity). Einstein's idea on static universe occurs to be encompassing conception for the standard cosmology, as well as for the emerging new (oscillating) one. Alexander Friedman gave to us its verbal model and was the most well prepared to give mathematical one.

Bounce inflation denotes the scenario that a bouncing process occurs preceding the traditional inflation in the early universe. In this talk I present a new bounce inflation model which can not only realize the background evolution of the bounce and inflationary phases, but also get rid of the problems of “ghost” and “anisotropy” that bothers the usual bounce models. Observable primordial cosmological perturbations can be generated during the inflationary phase after the bounce, therefore can naturally generate the scale-invariant scalar power spectrum and gravitational waves that fits the data. Moreover, the blue-tilted spectrum at large scales generated during the contracting phase can provide characteristic predictions for the bounce inflation scenario.