Graceful Exit Research Articles

Non-extensive entropy and power-law inflation: Implications for observations

This study explores the interaction between non-extensive entropic FLRW cosmology and the power-law inflationary model, with a focus on the overlap between the scalar spectral index “[Formula: see text]” and the tensor-to-scalar ratio “r”. Based on a conjecture that non-extensive entropy alters the energy–momentum content of the cosmic fluid, the analysis examines how these overlaps shift with different model parameters and compares the findings to those from Bekenstein–Hawking (BH) entropic cosmology. The study highlights the impact of Tsallis, Rényi, and Sharma–Mittal entropies, uncovering a significant correlation between “[Formula: see text]” and “r” that suggests a deeper connection in power-law inflationary dynamics. The results demonstrate that non-extensive entropies not only enable viable inflation with a graceful exit but also address limitations inherent in the standard BH entropic framework, emphasizing the importance of precise parameter estimation. Specifically, Tsallis entropy allows for power-law inflation with [Formula: see text] to [Formula: see text] in alignment with Planck 2018 data. Moreover, the [Formula: see text] parameter in Rényi and Sharma–Mittal entropy models must be extremely small ([Formula: see text] in Planck mass units) to achieve successful power-law inflation with an e-folding number around 55–65, suggesting a unified thermodynamic perspective in cosmological studies.

Scalar perturbations in nonsingular universes from interacting vacuum

In this paper we examine the stability of scalar perturbations in nonsingular models which emerge from an interacting vacuum component. The analysis developed in this paper relies on two phenomenological choices for the energy exchange between a nonrelativistic fluid and a vacuum component. In both scenarios it can be shown that closed models may furnish nonsingular orbits of physical interest in phase space once a decelerated past era is connected to a graceful exit to late-time acceleration. Regarding such configurations as background spacetimes we introduce scalar perturbations in order to examine the stability of these models in a high energy domain. We explicitly show that the vacuum perturbation is not an independent variable and diverges as dynamics approaches the bounce. This feature assigns a rather unstable signature to the dynamics making the choices for the energy transfer ill defined at least for nonsingular configurations at the bounce scale.

Entropic Inflation in Presence of Scalar Field

In spirit of the recently proposed four-parameter generalized entropy of apparent horizon, we investigate inflationary cosmology where the matter field inside of the horizon is dominated by a scalar field with a power law potential (i.e., the form of ϕn where ϕ is the scalar field under consideration). Actually without any matter inside of the horizon, the entropic cosmology leads to a de-Sitter spacetime, or equivalently, an eternal inflation with no exit. Thus in order to achieve a viable inflation, we consider a minimally coupled scalar field inside the horizon, and moreover, with the simplest quadratic potential. It is well known that the ϕ2 potential in standard scalar field cosmology is ruled out from inflationary perspective as it is not consistent with the recent Planck 2018 data; (here it may be mentioned that in the realm of “apparent horizon thermodynamics”, the standard scalar field cosmology is analogous to the case where the entropy of the apparent horizon is given by the Bekenstein–Hawking entropy). However, the story becomes different if the horizon entropy is of generalized entropic form, in which case, the effective energy density coming from the horizon entropy plays a significant role during the evolution of the universe. In particular, it turns out that in the context of generalized entropic cosmology, the ϕ2 potential indeed leads to a viable inflation (according to the Planck data) with a graceful exit, and thus the potential can be made back in the scene.

Euclidean Wormhole with k-essence field in the presence of Gauss–Bonnet term

In this paper, we present some analytical solutions of wormhole in four-dimensional Robertson–Walker Euclidean background considering Einstein–Gauss–Bonnet dilaton interaction with a [Formula: see text]-essence field for [Formula: see text]. The solutions are obtained assuming some restrictions on coupling function with a form of potential or with the ratio of kinetic to potential energy of the dilaton field. Euclidean wormhole, in one case, evolves through early transient inflationary era and after graceful exit from inflation, it asymptotically yields a radiation dominated era or a matter dominated era. In another solution, initial Euclidean wormhole is accompanied by oscillation of scale factor in Euclidean time at some late era which asymptotically yields exponential expansion. The violation of the null energy condition can be avoided asymptotically. The potential is also found to decay sharply.

Some aspects of an exponential f(R) modified gravity

In this paper, we consider an exponential form for f(R) modified gravity as , where α is a parameter with the dimension of (length)2. The theory is consistent with local tests which give a bound on the value of this parameter: α ≤ 2 × 10−6. We investigate the static solution of this model corresponding to the Schwarzschild-de Sitter space. We also study the Jordan and Einstein frames of the model and obtain the scalar field potential related to the Einstein frame. In this respect, the mass of the scalar field is calculated as a function of Ricci curvature. Furthermore, by performing a dynamical system approach, we investigate the dimensionless parameters in the model and study the stability of the critical points in the phase space. Finally, we study the realization of inflation in this model and its graceful exit.

A vacuum transition in the FSM with a possible new take on the horizon problem in cosmology

The framed standard model (FSM), constructed to explain the empirical mass and mixing patterns (including CP phases) of quarks and leptons, in which it has done quite well, gives otherwise the same result as the standard model (SM) in almost all areas in particle physics where the SM has been successfully applied, except for a few specified deviations such as the [Formula: see text] mass and the [Formula: see text] of muons, that is, just where experiment is showing departures from what SM predicts. It predicts further the existence of a hidden sector of particles some of which may function as dark matter. In this paper, we first note that the above results involve, surprisingly, the FSM undergoing a vacuum transition (VTR1) at a scale of around 17[Formula: see text]MeV, where the vacuum expectation values of the colour framons (framed vectors promoted into fields) which are all nonzero above that scale acquire some vanishing components below it. This implies that the metric pertaining to these vanishing components would vanish also. Important consequences should then ensue, but these occur mostly in the unknown hidden sector where empirical confirmation is hard at present to come by, but they give small reflections in the standard sector, some of which may have already been seen. However, one notes that if, going off at a tangent, one imagines colour to be embedded, Kaluza–Klein (KK) fashion, into a higher-dimensional space–time, then this VTR1 would cause 2 of the compactified dimensions to collapse. This might mean then that when the universe cooled to the corresponding temperature of [Formula: see text] K when it was about [Formula: see text] s old, this VTR1 collapse would cause the three spatial dimensions of the universe to expand to compensate. The resultant expansion is estimated, using FSM parameters previously determined from particle physics, to be capable, when extrapolated backwards in time, of bringing the present universe back inside the then horizon, solving thus formally the horizon problem. Besides, VTR1 being a global phenomenon in the FSM, it would switch on and off automatically and simultaneously over all space, thus requiring seemingly no additional strategy for a graceful exit. However, this scenario has not been checked for consistency with other properties of the universe and is to be taken thus not as a candidate solution of the horizon problem but only as an observation from particle physics which might be of interest to cosmologists and experts in the early universe. For particle physicists also, it might serve as an indicator for how relevant this VTR1 can be, even if the KK assumption is not made.

Understanding The Role of Psychological Characteristics in Retirement Planning Among Employees Working in Delhi NCR.

The transition towards retirement needs coping and adapting, both of which provide challenges to psychological health. Notably, the transition into retirement sheds light on the core definition of psychological ageing, which may be summed up as the capacity to adapt not only to internal biological changes but also to changes in the external environment, which can have an impact on psychological health. The ability to adapt not only to internal biological changes but also to changes in the external environment that can have an impact on psychological health is central to the concept of psychological ageing. Since people are becoming more conscious that having financial security in retirement is only one of many crucial factors, there has been a rise in interest in the psychological aspects of retirement. It is highly likely that retirees will struggle with at least some psychological disorders, the severity of which will vary. For instance, a married couple whose ages are widely different but who both work full-time could wonder if they should retire at the same time or wait until one of them reaches a certain milestone age. While one person worked, the other might retire and spend their time relaxing at home by themselves. When faced with such a situation, retirees are prone to have psychological issues, which, in order to achieve their highest possible level of life satisfaction, need to be addressed. The purpose of this study was to investigate how psychological factors influence the retirement planning behaviour of employees in the Delhi National Capital Region. This article examines the challenges that many leaders face when it comes time for them to step down from their positions. It analyses the physical and psychological aspects of ageing and discusses a number of the obstacles that stand in the way of a graceful exit, including financial, social, and psychological factors. In addition to this, it delves into a variety of mental processes that come into play during retirement.
 

Holographic realization from inflation to reheating in generalized entropic cosmology

The growing cosmological interest of different entropy functions (like the Tsallis entropy, the Rényi entropy, the Barrow entropy, the Sharma-Mittal entropy, the Kaniadakis entropy and the Loop Quantum gravity entropy) naturally raises an important question: ”Does there exist a generalized entropy that can bring all the known entropies proposed so far within a single umbrella?” In spirit of this, recently a four parameter generalized entropy has been formulated that reduces to different known entropies for suitable limits of the parameters. Based on such four parameter generalized entropy (symbolized by Sg), in the present paper, we examine the universe’s evolution during its early phase, particularly from inflation to reheating, in the context of entropic cosmology where the entropic energy density acts as the inflaton. It turns out that the entropic energy successfully drives an early inflationary phase with a graceful exit, and moreover, the theoretical expectations of the observable indices get consistent with the recent Planck data for suitable ranges of the entropic parameters. After the inflation ends, the universe enters to a reheating stage when the entropic energy decays to relativistic particles with a certain decay rate. Actually the presence of the entropic parameters in the Sg ensures a continuous evolution of the Hubble parameter from a quasi de-Sitter phase during the inflation to a power law phase during the reheating stage dominated by a constant EoS parameter. Consequently we investigate the reheating phenomenology, and scan the entropic parameters from both the inflation and reheating requirements. We further address the possibility of instantaneous reheating in the present context of generalized entropy.

Salvaging power-law inflation through warming

Power-law inflation with scale factor a propto t^m is investigated in the context of warm inflation. The treatment is performed in the weak and strong dissipation limits. In addition, we discuss the three common cases for the thermal dissipation coefficient varGamma (T). We compare the theoretical results of the power-law model within warm inflation with the observational constraints from Planck 2018 and BICEP/Keck 2018, as presented by the tensor-to-scalar ratio r and spectral index n_s. The model results agree largely with the observations for most of the varGamma (T) cases. Furthermore, in order to address the problem of exiting the inflationary epoch, we suggest a perturbed modification to the power-law definition so that it becomes affine, and find that this small change indicates a way for having an exit scenario with a suitable e-foldings number. Finally, we examine this perturbation ansatz within the context of cold inflation with exponential potential, and we find that it can accommodate the observational data with sufficient e-foldings. Our study suggests that the power-law inflation and the exponential potential, in both warm and cold inflation contexts, can in principle be made consistent with the observations and with a possible graceful exit.

Graceful exit from inflation and reheating with twin waterfall scalar fields

Graceful exit from inflation and reheating with twin waterfall scalar fields

Observational constraints and preheating in cuscuton inflation

We study cuscuton inflation for the models where the potential of the cuscuton takes quadratic and exponential forms. We find that for the quadratic potential, a scalar spectral index n_s is not affected by cuscuton at the leading order in the slow-roll inflation models. However, a tensor-to-scalar ratio r can be suppressed. For the exponential potential of cuscuton, we find the condition for which the inflation has a graceful exit. Under this condition, the observational predictions in this model differ by a few percent from those found in standard inflation. We also examine the particle production due to parametric resonances in both models. We find that in Minkowski space the stage of parametric resonances can be described by the Mathieu equation. For the case where the cuscuton has quadratic potential, the amplitude of the driving force in the Mathieu equation has a similar form as that in standard inflation. Nevertheless, in the case of exponential potential, the amplitude of the driving force decreases faster than that in the standard case. However, parametric resonances in our models can be sufficiently broad possible for the exponential growth of the number of particles. We briefly discuss the case in which the expansion of space is taken into account.

Aspects of cosmologies with complete scenario

We consider a flat Friedmann–Robertson–Walker (FRW) universe with expansion history based on a Hubble parameter. The Hubble parameter ansatz, by construction, yields de Sitter-like evolution at early and late-times. The phase transition from accelerated to decelerated era during early times and decelerated to accelerated era in the recent past provide the complete cosmological history of the universe in a natural way. In order to exhibit the dynamical evolution of universe, we explore the inflationary dynamics along with graceful exit, behaviors of cosmological parameters, energy conditions along with behavior in ω − ω ′ plane to identify the thawing and freezing regions. Statefinder diagnostic highlights that the universe will evolve to Λ cold dark matter model during late-times. We also find the scalar field description for the considered Hubble parameter ansatz. • The FRW model having expansion history based on the Hubble parameter is studied. • Cosmic parameters illustrate physically realistic cases of the universe evolution. • Model exhibits graceful exit from inflation during early era. • The model explains late-time accelerating evolution of the universe. • The model possess potential having polynomial form with field.

Studies on modified power law inflation

In this study, we evaluate power law inflation (PLI) with a monomial potential and obtain a novel exact solution. It is well known that the conventional PLI with an exponential potential is inconsistent with the Planck data. Unlike the standard PLI, the present model does not encounter the graceful exit problem, and the results agree fairly well with recent observations. In our analysis, we calculate the spectral index and the tensor-to-scalar ratio, both of which agree very well with recent observational data and are comparable with those of other modified inflationary models. The employed technique reveals that the large cosmological constant decreases with the expansion of the universe in the case of the PLI. The coupling of the inflaton with gravitation is the primary factor in this technique. The basic assumption here is that the two metric tensors in the gravitational and inflaton parts correspond to different conformal frames, which contradicts with the conventional PLI, where the inflaton is directly coupled with the background metric tensor. This fact has direct applications to different dark energy models and the assisted quintessence theory.

Pseudo-Nambu-Goldstone inflation with twin waterfalls

We propose a pseudo-Nambu-Goldstone inflation where twin waterfall fields coupled to the inflaton are responsible for the graceful exit from inflation by a waterfall transition. In this scenario, the Z2 symmetry for the waterfall fields and the inflaton protects the inflaton potential against dangerous quantum corrections coming from the waterfall couplings. We show that there is a wide range of natural model parameters and initial conditions for a successful inflation and discuss the reheating process by the perturbative decay of the waterfall field with a Z2 invariant Higgs portal. We also present a microscopic model for the inflaton couplings to the twin waterfall fields in the context of a dark QCD with light and heavy quarks.

The robustness of slow contraction and the shape of the scalar field potential

We use numerical relativity simulations to explore the conditions for a canonical scalar field ϕ minimally coupled to Einstein gravity to generate an extended phase of slow contraction that robustly smooths the universe for a wide range of initial conditions and then sets the conditions for a graceful exit stage. We show that to achieve robustness it suffices that the potential V(ϕ) is negative and M Pl|V, ϕ /V|≳5 during the smoothing phase. We also show that, to exit slow contraction, the potential must have a minimum. Beyond the minimum, we find no constraint on the uphill slope including the possibility of ending on a positive potential plateau or a local minimum with V min > 0.Our study establishes ultralocality, i.e., all spatial gradients quickly becoming negligible, for a wide range of potentials as a key both to robust smoothing and to graceful exit.

The quantum de Sitter root of quasi de Sitter observables

In inflationary cosmology the quasi de Sitter graceful exit allows us to measure the quantum features of the primordial dS phase, in particular, the lack of scale invariance parametrized by the spectral index ns. In this article we summarize previous work on how the underlying primordial scaling law is implemented in the dS quantum Fisher information of the dS planar ground state (dSQFI). At large scales the dSQFI unequivocally sets, without any qdS input, the value of ns to be 0.9672. This value is independent of the tensor to scalar ratio whose value requires model dependent input. In addition the dSQFI predicts, at large scales, a small running compatible with the current experimental results. Other phenomenological consequences of the dSQFI for small scales, will be discussed in a future publication.

Emergent universe from Energy–Momentum Squared Gravity

In order to bypass the big bang singularity, we develop an emergent universe scenario within a covariant extension of General Relativity known as “Energy–Momentum Squared Gravity”. The extra terms of the model emerge in the high energy regime. Considering dynamics in a Friedmann–Lemaître–Robertson–Walker background, critical points, representing stable Einstein static states of the phase space, result as solutions. It then turns out that as the equation of state parameter ω gradually declines from a constant value as t→−∞, eventually some of the static past eternal solutions find the chance to naturally enter into thermal history through a graceful exit mechanism. In this way, the successful realization of the emergent universe allows an expanding thermal history without the big bang singularity for the spatially flat universe free of cosmological constant.

Multiple fluid theory of cosmic evolution and its thermodynamic analysis

In this paper we have discussed the modified gravity and scalar field DE model specifically DBI essence model with the analysis of thermodynamics during cosmological evolution. We have used the modified gravity with the form f(R,T)=R+2\Lambda T in our calculations. The basic aim behind this paper is to discuss a theory that unifies modified gravity with DE models including the solutions of some cosmological problems like thermodynamics energy conditions violation problems, finite time future singularity problems, initial singularity problem, Cosmic inflation problem, decelerated expansion problem, graceful exit problem, reheating problem, bouncing nature problem, phase transformation-spontaneous symmetry breaking problem, negative heat capacity paradox problem and obviously the present day universe problems (Continuously decreasing temperature problem, present day DE dominated expansion problem). We have established the viscous effects (both positive and negative viscosity) in our calculation and discussed the negative-positive viscosity by introducing two special type of energy cycles. Finally, we have discussed the stability conditions for universe evolution through cosmic perturbation and resolved the instability problems. We have also shown the state finder trajectories for both with and without viscous fluid on the basis of our calculations to compare our research with the results of other independent DE models

Inflation with antisymmetric tensor field: new candidates

We study classes of inflation models driven by antisymmetric tensor field, with minimal and nonminimal couplings to gravity, that address the known issues of such models considered in the past. First, we show that with a different choice of the background structure of the antisymmetric tensor field, inflation is supported even for the minimal model with quadratic potential contrary to past results. We also include the nonminimal coupling to gravity and analyse perturbations to the antisymmetric tensor as well as the tensor modes of perturbed metric. The two models differ in terms of the behaviour of tensor modes, where the speed of the gravitational wave can be tuned to c in the latter model. The power spectrum and spectral index receive slight scale dependence. Finally, we consider a quartic potential motivated by the graceful exit to reheating phase, which requires a nonminimal coupling to support inflation. The two tensor modes of the perturbed metric are found to evolve differently in this model, and give rise to a highly scale-dependent power spectrum.

Noncommutativity, Sáez–Ballester Theory and Kinetic Inflation

This paper presents a noncommutative (NC) version of an extended Sáez–Ballester (SB) theory. Concretely, considering the spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) metric, we propose an appropriate dynamical deformation between the conjugate momenta and, applying the Hamiltonian formalism, obtain deformed equations of motion. In our model, the NC parameter appears linearly in the deformed Poisson bracket and the equations of the NC SB cosmology. When it goes to zero, we get the corresponding commutative counterparts. Even by restricting our attention to a particular case, where there is neither an ordinary matter nor a scalar potential, we show that the effects of the noncommutativity provide interesting results: applying numerical endeavors for very small values of the NC parameter, we show that (i) at the early times of the universe, there is an inflationary phase with a graceful exit, for which the relevant nominal condition is satisfied; (ii) for the late times, there is a zero acceleration epoch. By establishing an appropriate dynamical framework, we show that the results (i) and (ii) can be obtained for many sets of the initial conditions and the parameters of the model. Finally, we indicate that, at the level of the field equations, one may find a close resemblance between our NC model and the Starobinsky inflationary model.