Friedmann-Robertson-Walker Research Articles

Comparison of energy conditions in general relativity and modified theories of gravity

To make a comparison of energy conditions in the theory of general relativity and in the modified theories, we have considered [Formula: see text], [Formula: see text] and [Formula: see text] theories (where [Formula: see text] and [Formula: see text] are the Ricci scalar and trace of the energy–momentum tensor, respectively, while [Formula: see text]) to test the validity of all the four energy conditions. These energy conditions had been derived to check the viability of cosmological as well as astrophysical models. In this paper, we consider the standard Friedmann–Robertson–Walker spacetime representing the homogeneous and isotropic universe, and investigate the available literature on testing energy conditions as well as calculate these conditions ourselves. In order to provide the comparative results, we test these conditions analytically as well as graphically and present how energy bounds in modified theories depend on the values of the involved parameters and its validity within certain limits. We discuss here, that which of the modified theories comply with certain energy conditions, and hence provide a supporting argument on the existence of modified theories.

Quartic Horndeski-Cartan theories in a FLRW universe

Quartic Horndeski-Cartan theories in a FLRW universe

First law of thermodynamics and entropy of FLRW universe in modified gravity

We investigate the first law of thermodynamics and entropy associated to the apparent horizon of (non-flat) FLRW space–time in different theories of modified gravity and in the presence of a perfect fluid of matter. We pose our attention on those theories which lead to second order differential field equations on FLRW background. In this way, we observe that one may obtain a formula for entropy in terms of the radius of the apparent horizon only. Thus, when considering a modification to the area law of General Relativity, it is possible to reconstruct the gravitational lagrangian consistent with the corresponding first law.

Effect of [formula omitted]-curvature tensor in spacetimes and [formula omitted]-gravity

First, we prove that a Lorentzian manifold is of constant curvature if and only if W2-curvature tensor vanishes. We investigate W2-flat perfect fluid spacetime as a solution of fG-gravity theory and we obtain a relation among deceleration, jerk, and snap parameters in a W2-flat spacetime using Friedmann–Robertson–Walker metric. Several energy conditions in terms of Ricci scalar are investigated with the models fG=a1Gn+b1a2Gn+b2 and fG=log(αGn+βe−Gα). For these models, the weak, null and dominant energy conditions are satisfied, while the strong energy condition is violated, which is good agreement with the recent observational studies and this reveals that the current Universe is in accelerating phase.

Accretion of modified Chaplygin–Jacobi gas and modified Chaplygin–Abel gas onto Schwarzschild black hole

Herein, we have discussed about the accretion of two extremely interesting forms of dark energies, namely “Modified Chaplygin–Jacobi Gas” (MCJG) and “Modified Chaplygin–Abel Gas” (MCAG) onto a Schwarzschild black hole of dimension 4. First, considering the above-mentioned dark energies, we have deduced the rate of change of mass and then evolved the required mass from it in terms of the redshift [Formula: see text]. We have also plotted the mass versus redshift graphs for different values of the elliptic modulus [Formula: see text] in the case of MCJG and different values of [Formula: see text] in the case of MCAG, respectively. Also, mass versus redshift graphs have been portrayed in the different stages of the FRW universe. We have found that in the case of both MCJG and MCAG accretion, the mass of the black holes follow an increasing pattern. But as expected in the case of the phantom energy-filled universe, the mass of the black hole shows decreasing nature. Again in the case of the [Formula: see text]CDM stage of the universe, accretion of MCAG primarily leads to an increase in mass, and then it gradually diminishes.

F(R) gravity for a FLRW universe in a deformed phase space

Modify gravity theories have received huge attention in the last decade. In this work, we find the Wheeler-DeWitt (WDW) equation in the Quantum Cosmology (QC) scenario for a Friedmann-Lemaitre-Robertson-Walker (FLRW) model using the deformed phase space in f(R) gravity. In addition to the already stated, we consider a function fΛ(R) that provides the Λ-Cold Dark Matter (ΛCDM) model as an immediate consideration.

Warm inflation in [formula omitted] gravity

In this work, we explored warm inflation in the background of f(R,T) gravity in the strong dissipation regime. Considering scalar field for FLRW universe, we derived modified field equations. We then deduced slow-roll parameters under slow-roll approximations followed by power spectrum for scalar and tensor perturbations and their corresponding spectral indices. We have considered Chaotic and Natural potentials and estimated scalar spectral index and tensor-to-scalar ratio for constant as well as variable dissipation factor Γ. We found that both the rejected potentials can be revived under the context of f(R,T) gravity with suitable choice of the model parameters. Further, it is seen that within the warm inflationary scenario both the potentials can yield result consistent with Planck 2018 and BICEP/Keck bounds at the Planckian and sub-Planckian energy scales.

A crystal plasticity model of low cycle fatigue damage considering dislocation density, stress triaxiality and Lode parameter

To capture the mechanical behavior and low cycle fatigue damage of metals, a crystal plasticity model combined with isotropic continuum damage mechanics model of low cycle fatigue is developed. In this constitutive model, the Lemaitre model of low cycle fatigue damage is modified accounting for the effect of stress triaxiality and Lode parameter, the slip strength is associated with the evolution of the density of statistically stored forest dislocations and debris dislocations, and a non-linear kinematic hardening rule is employed to capture the cyclic response. Simulation is implemented by applying this developed constitutive model to the Voronoi polycrystalline aggregation of 7075 aluminum alloy. The studied results show that the grains with low Schmid factor generally suffer more severe damage compared to those with high Schmid factor. In addition, due to the orientation mismatch of adjacent grains, localized stress concentrations and the resulting severe damage generate near the grain boundaries, especially near the grain boundaries with high misorientation angles. The proposed constitutive model manifests the capacity for the determination of damage evolution of the polycrystalline metals.

An [formula omitted] gravity based FLRW model and observational constraints

We attempt to construct a Friedmann–Lemaitre–Robertson–Walker (FLRW) cosmological model in f(R,T) gravity which exhibits a phase transition from deceleration to acceleration at present. We take f(R,T)=R+2λT, λ being an arbitrary constant. In our model, the λ parameter develops a negative pressure in the universe whose Equation of state is parameterized. The present values of model parameters such as density, Hubble, deceleration, Equation of state, and λ are estimated statistically by using the Chi-Square test. For this, we have used three different types of observational data sets: the 46 Hubble parameter data set, the SNeIa 715 data sets of distance modulus, and the 66 Pantheon data set (the latest compilation of SNeIa 40 bined plus 26 high red shift apparent magnitude mb data set in the red shift ranges from 0.014≤z≤2.26). We have calculated the transitional red shift and time. The estimated results for the present values of various model parameters are found as per expectations and surveys. Interestingly, we get the present value of the density ρ0, ≃1.5ρc. The critical density is estimated as ρc≃1.88h0210−29gm/cm3 in the literature. The higher value of the present density is attributed to the presence of some additional energies in the universe apart from baryon energy. We have examined the behavior of the pressure in our model. It is negative and produces acceleration in the universe. Its present value is obtained as p0≃−0.7ρ0.

BEHAVIOR OF q-DEFORMED QUANTUM PARTICLE STATISTICS ON THE HOLOGRAPHIC SCREEN

In this study, we propose an approach to investigate the relationship between MOND theory and the holographic principle by incorporating q-deformed theory. We first present a brief overview of Verlinde's entropic gravity assumption, which suggests that gravity can be interpreted as an entropic force arising from the statistical mechanics of quantum fields. Some thermo-statistical properties of q-deformed fermion gas model in two spatial dimensions are introduced. At the low-temperature limit, we derive the q-deformed thermal energy and analyze the impacts of fermionic q-deformation on MOND theory. Specifically, we consider the q-deformed Fermi-Dirac statistics of the bits on the holographic screen and examine MOND theory depending on q-deformed acceleration scale. Deformed Friedmann equation is studied by taking into account Friedmann–Robertson–Walker (FRW) universe. This equation shows a modified identification of the evolution of the universe that is compatible with both MOND theory and the holographic principle

Gravitational lensing: dark energy models in non-flat FRW Universe

In a non-flat FRW model, we have considered our Universe to be filled with non-interacting dark energy and dark matter. For the dark energy models, we have assumed Tachyonic Field (TF), Generalized Cosmic Chaplygin Gas (GCCG), New Variable Modified Chaplygin Gas (NVMCG), Modified Chaplygin–Jacobi Gas (MCJG), and Modified Chaplygin–Abel Gas (MCAG). We then analyzed these dark energy models with varying cosmological parameters in their optical depth behaviour and presented our result graphically. Later on, a comparison of our findings of the corresponding models in flat and non-flat Universe with the Lambda CDM model has also been presented.

Observational Constraining Study of New Deceleration Parameters in FRW Universe

AbstractIn the current paper, a dark energy (DE) model reconstructed from the well‐motivated deceleration parameter (DP) is analyzed. A flat FRW Universe filled with radiation, dark matter (DM), and dark energy fluids is considered. The free parameters are constrained using measurements from Supernovae, Hubble, Gamma Ray Bursts, Quasars, and Baryon acoustic Oscillations. The model under study is found to be very supported by observation with respect to ΛCDM since . Besides, a cosmographic analysis is performed showing that the reconstructed model behaves similarly as ΛCDM does. Finally, a diagnostic analysis is performed reporting that the studied model behaves quintessence type at a late time.

Dark energy nature in logarithmic f(R,T) cosmology

This research paper is an investigation of dark energy nature of logarithmic [Formula: see text]-gravity cosmology in a flat FLRW space–time universe. We have derived modified Einstein’s field equations for the function [Formula: see text] where [Formula: see text] is the Ricci scalar curvature, [Formula: see text] is the trace of the stress energy momentum tensor, and [Formula: see text] is a model parameter. We have solved field equations in the form of two fluid scenarios as perfect fluid and dark fluid, where dark fluid term is derived in the form of perfect fluid source. We have made an observational constraint on the cosmological parameters [Formula: see text] and [Formula: see text] using [Formula: see text] test with observational datasets like Pantheon sample of SNe Ia and [Formula: see text]. With these constraints, we have discussed our model with deceleration parameter [Formula: see text], energy parameters [Formula: see text], EoS parameter [Formula: see text], etc. Also, we have done Om diagnostic analysis. The derived [Formula: see text] model shows a quintessence dark energy model [Formula: see text] and late-time universe approaches to [Formula: see text] CDM model.

Little Rip, Pseudo Rip and bounce cosmology from generalized equation of state in the universe with spatial curvature

We consider the Little Rip (LR), Pseudo Rip (PR) and bounce cosmological models in the Friedmann–Robertson–Walker (FRW) metric with nonzero spatial curvature. We describe the evolution of the universe using a generalized equation of state (EoS) in the presence of a viscous fluid. The conditions of the occurrence of the LR, PR and bounce were obtained from the point of view of the parameters of the generalized EoS for the cosmic dark fluid, taking into account the spatial curvature. The analytical expressions for the spatial curvature were obtained. Asymptotic cases of the early and late universe are considered. A method of Darboux transformation (DT) was proposed in the case of models of an accelerating universe with viscosity.

New emergent observational constraints in f(Q,T) gravity model

In the current study, we inspect the late-time acceleration of the universe in f(Q,T) gravity. In this theory, Q represents the non-metricity term and with Tμν the energy-momentum tensor, with T its trace. To explore the solutions in the theory for the Friedmann-Lemaitre-Robertson-Walker (FLRW) model, we propose a new scale factor called the emergent scale factor, which yields the Hubble parameter, H(z), having the form H(z)=nb(−B+1(A(z+1))1b) with a new relation a(t)=11+z). By using the SNIa from Pantheon, BAO from (6dFGS, BOSS-LOWZ, SDSS DR7 MGS, BOSS-DR12, BOSS-CMASS, WiggleZ and Lya), CMB from Planck 2018, and the 36 data points from Hubble datasets using the Monte-Carlo Markov Chain (MCMC) approach, we estimate the parameters of the model. The variation in time of the deceleration parameter in the model shows that a phase of deceleration transits to a phase of acceleration. Further, we examine the behaviour of the jerk parameter and carry out a statefinder analysis. In order to complete the current study, we consider two forms for f(Q,T), specifically, f(Q,T)=a1Qm+a2T and f(Q,T)=γQ2+ηQ+λT where a1, a2, m, γ, η, and λ are the model's parameters that need to satisfy observations. Finally, we present an appraisal of our current analysis.

Cosmic implications of generalized HDE model in FRW universe

In this study, we investigate a generalized holographic dark energy model within the framework of dynamical Chern–Simons modified gravity theory. By incorporating the Hubble parameter H and its higher order derivatives, we explore the equation of state and its implications for the expansion of the known universe using the Friedmann–Robertson–Walker metric. Our analysis reveals three distinct cases arising from the solutions to the Chern–Simons field equations, which depend on the chosen parameters. In the first two cases, we observe confirmation of the accelerated expansion of the universe, consistent with the predicted range of −1<ω<0. However, in the third case, the depicted behavior exhibits a phantom-like nature. It is important to note that irrespective of the case, the generalized holographic dark energy model supports the transition from deceleration to acceleration, aligning well with observational data. Furthermore, our findings establish that the generalized holographic dark energy model endorses the universe’s accelerated expansion within the framework of dynamical Chern–Simons modified gravity theory.

Electromagnetic Waves in Cosmological Spacetime

We consider the propagation of electromagnetic waves in the Friedmann–Lemaître–Robertson–Walker metric. The exact solutions for plane and spherical wave are written down. The corresponding redshift, amplitude change, and dispersion are discussed. We also speculate about the connection of the electromagnetic wave equation to the Proca equation and its significance for the early Universe.

Dynamical stability in presence of non-minimal derivative dependent coupling of k-essence field with a relativistic fluid

In this paper we investigate a non-minimal, space-time derivative dependent, coupling between the k-essence field and a relativistic fluid using a variational approach. The derivative coupling term couples the space-time derivative of the k-essence field with the fluid 4-velocity via an inner product. The inner product has a coefficient whose form specifies the various models of interaction. By introducing a coupling term at the Lagrangian level and using the variational technique we obtain the k-essence field equation and the Friedmann equations in the background of a spatially flat Friedmann–Lemaitre–Robertson–Walker (FLRW) metric. Explicitly using the dynamical analysis approach we analyze the dynamics of this coupled scenario in the context of two kinds of interaction models. The models are distinguished by the form of the coefficient multiplying the derivative coupling term. In the simplest approach we work with an inverse square law potential of the k-essence field. Both of the models are not only capable of producing a stable accelerating solution, they can also explain different phases of the evolutionary universe.

A constrained cosmological model in [formula omitted] gravity

In this article, we study the expanding nature of the universe in the context of f(R,Lm) gravity theory, here R represents the Ricci scalar and Lm is the matter Lagrangian density. With a specific form of f(R,Lm), we obtain the field equations for flat FLRW metric. We parametrize the deceleration parameter in terms of the Hubble parameter and from here we find four free parameters, which are constraints and estimated by using H(z), Pantheon, and their joint data sets. Further, we investigate the evolution of the deceleration parameter which depicts a transition from the deceleration to acceleration phases of the universe. The evolutionary behaviour of energy density, pressure, and EoS parameter shows that the present model is an accelerated quintessence dark energy model. To compare our model with the ΛCDM model we use some of the diagnostic techniques. Thus, we find that our model in f(R,Lm) gravity supports the recent standard observational studies and delineates the late-time cosmic acceleration.

Scale-invariant inflation

We examine a scalar-tensor model of gravity that is globally scale-invariant. When adapted to a spatially flat Robertson-Walker metric, the equations of motion describe a dynamical system that flows from an unstable de Sitter space to a stable one. We show that during this transition inflation can occur. Moreover, at the final fixed point, a mass scale naturally emerges that can be identified with the Planck mass. We compute the inflationary spectral indices and the tensor perturbation and we compare them with observations. We also study the possibility that primordial magnetic fields are generated during inflation.