Flat Friedmann Lemaitre Robertson Walker Research Articles

A comprehensive data-driven odyssey to explore the equation of state of dark energy

For the first time, we reconstruct the dark energy equation of the state parameter w from the combination of background and perturbation observations, specifically combining the Hubble parameter data from cosmic chronometer observations and the logarithmic growth rate data from the growth rate observations. We do this analysis using posterior Gaussian process regression without considering any specific cosmological model or parametrization. However there are three main assumptions: (I) a flat Friedmann–Lemaître–Robertson–Walker (FLRW) metric is considered for the cosmological background, (II) there is no interaction between dark energy and matter sectors, and (III) for the growth of inhomogeneity, sub-Hubble approximation and linear perturbations are considered. This study is unique in the sense that the reconstruction of w is independent of any derived parameters such as the present values of the matter-energy density parameter and Hubble parameter. From the reconstruction, we look at how the dark energy equation of state evolves between redshifts 0 and 1.5, finding a slight hint of dynamical behavior in dark energy. However, the evidence is not significant. We also find a leaning towards non-phantom behavior over phantom behavior. We observe that the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varLambda $$\\end{document}CDM model (w=-1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(w=-1)$$\\end{document} nearly touches the lower boundary of the 1σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma $$\\end{document} confidence region in the redshift range 0.6≲z≲0.85.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0.6 \\lesssim z \\lesssim 0.85.$$\\end{document} However, it comfortably resides within the 2σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma $$\\end{document} confidence region in the whole redshift range under investigation, 0≤z≤1.5.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0\\le z \\le 1.5.$$\\end{document} Consequently, the non-parametric, model-independent reconstruction of dark energy provides no compelling evidence to deviate from the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varLambda $$\\end{document}CDM model when considering cosmic chronometer and growth rate observations.

Noether symmetry analysis in f(T,TG) gravity theory: A study of classical cosmology

This work deals with [Formula: see text] gravity in the background of homogeneous and isotropic flat Friedmann–Lemaître–Robertson–Walker (FLRW) space-time model. The main aim of this work is to examine whether the model supports the observational data or not. By using the Noether symmetry analysis, not only the symmetry vector is obtained, but also the coupling function [Formula: see text] in the Lagrangian has been determined. Also, the symmetry analysis identifies a transformation from [Formula: see text] to [Formula: see text] in such a way that one of the new variables become cyclic along the direction symmetry vector and as a result the field equations become solvable. Then the solution is analyzed from the observational point of view. Finally, quantum cosmology has been formulated for the present model and the wave function of the universe has been evaluated by solving the Wheeler–DeWitt equation with some assumptions.

Cosmic evolution in f(Q,T) gravity with observational constraints: A comparative analysis with ΛCDM

In this investigation, we explore the flat Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological model within the framework of the f(Q,T) modified gravitation theory. This theory was recently introduced to account for the late cosmic acceleration of our Universe. To address the modified field equations derived from the f(Q,T)=αQ+βQ2+kT form of the f(Q,T) function, we assume a redshift-dependent deceleration parameter. Our goal is to impose observational constraints on the model parameters, ensuring its viability and alignment with the observable Universe's characteristics. The observational constraints are derived from a diverse dataset, encompassing Cosmic Chronometers (CC), type Ia supernovae (SNIa), Baryon Acoustic Oscillation (BAO), Gamma Ray Burst (GRB), and Quasar (Q) measurements. Employing the Markov Chain Monte Carlo (MCMC) technique with the CC + BAO + SNIa + GRB + Q dataset, we conduct simulations to obtain constraints on the model parameters. In the subsequent segments of the study, we delve into the evolution of the constrained model from the past to the present. We utilize metrics such as deceleration and jerk parameters, statefinder pairs, the Om diagnostic, and various physical parameters of the model. This detailed analysis allows us to scrutinize the transition of the model from a decelerating phase in the past to the late accelerating phase, comparing its evolution with established dark energy models. To assess the model's goodness of fit, we employ statistical criteria, including the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), P-value, and L-statistic. Remarkably, these criteria consistently indicate that the ΛCDM model is slightly favored by the observational data compared to the proposed cosmological model.

Generalized ghost dark energy model in Brans–Dicke theory with logarithmic scalar field

We study generalized ghost dark energy model in Brans–Dicke theory within the framework of flat Friedmann–Lemaitre–Robertson–Walker Universe. We assume the well-motivated logarithmic form of Brans–Dicke scalar field in terms of the scale factor to find the observational parameters such as equation of state parameter [Formula: see text] and deceleration parameter q. It is observed that the equation of state parameter crosses the phantom divide line [Formula: see text] for a suitable range of model parameters. We observe that the deceleration parameter is time-dependent which shows the recent phase transition from decelerated to accelerated expansion of the Universe. Moreover, the model shows that the Universe will go through two future phase transitions, recent accelerated expansion to decelerated expansion and again decelerated expansion to accelerated expansion. We have also plotted the trajectories of the model in the [Formula: see text] plane for different values of parameters and explored the freezing and thawing regions. Further, we apply the sound squared speed method to check the stability of the model and found that the model is stable for suitable range of parameters.

Modified f(Q,C) gravity dark energy models with observational constraints

We investigate an isotropic and homogeneous flat dark energy model in [Formula: see text] gravity theory that is linear in non-metricity Q and quadratic in boundary term C as [Formula: see text], where [Formula: see text] is a model parameter. We have solved the field equations in flat Friedmann–Lemaitre–Robertson–Walker (FLRW) spacetime geometry and considered a relation in the form of Hubble function in total energy density parameters [Formula: see text], [Formula: see text], and Hubble constant [Formula: see text]. We have compared our results with two observational datasets [Formula: see text] and Pantheon SNe Ia datasets by using MCMC analysis and have obtained the best fit present values of parameters. We have used these best fit values throughout in result analysis and discussion. We have found the equation of state (EoS) parameter as [Formula: see text] over [Formula: see text]. We have also investigated the Om diagnostic function and present age of the universe for these two datasets.

Cosmological effects on f(R̄,T̄) gravity through a non-standard theory

This study aims to investigate the impact of dark energy in cosmological scenarios by exploiting [Formula: see text] gravity within the framework of a nonstandard theory, called K-essence theory, where [Formula: see text] represents the Ricci scalar and [Formula: see text] denotes the trace of the energy–momentum tensor associated with the K-essence geometry. The Dirac–Born–Infeld (DBI) nonstandard Lagrangian has been employed to generate the emergent gravity metric [Formula: see text] associated with the K-essence. This metric is distinct from the usual gravitational metric [Formula: see text]. It has been shown that under a flat Friedmann–Lemaître–Robertson–Walker (FLRW) background gravitational metric, the modified field equations and the Friedmann equations of the [Formula: see text] gravity are distinct from the usual ones. In order to get the equation of state (EoS) parameter [Formula: see text], we have solved the Friedmann equations by taking into account the function [Formula: see text], where [Formula: see text] represents a parameter within the model. We have found a relationship between [Formula: see text] and time for different kinds of [Formula: see text] by treating the kinetic energy of the K-essence scalar field ([Formula: see text]) as the dark energy density which fluctuates with time. Surprisingly, this result meets the condition of the restriction on [Formula: see text]. By presenting graphical representations of the EoS parameter with time, we show that our model is consistent with the data of SNIa[Formula: see text][Formula: see text][Formula: see text]BAO[Formula: see text][Formula: see text][Formula: see text][Formula: see text] within a certain temporal interval.

Late time cosmological solutions in f(R,T) gravity in a viscous universe

Considering the condition on conservation of energy–momentum tensor (EMT), we study late time cosmological solutions in the context of [Formula: see text] gravity (where [Formula: see text] and n are constants) in a flat Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime. The present model discusses the case of a barotropic perfect fluid as the matter content of the Universe, along with the case when dissipative effects are taken into account. Briefly, assuming a single perfect fluid, we find that the mentioned model is not capable of presenting an observationally consistent picture of the late time accelerated expansion of the Universe; nevertheless, the model leads to admissible solutions when the bulk viscosity is included. In this regard, a consistent setting is found considering the Eckart, Truncated and Full Israel–Stewart theories which determine the behavior of bulk viscosity. In the presence of bulk viscosity, the behavior of the deceleration parameter (DP) shows that the underlying model can describe an acceptable evolution even if the isotropic pressure of matter content of the Universe is negligible.

Observational constraint in f(R, ∇R) gravity model in power-law cosmology

In this paper, we have considered the flat Friedmann-Lemaître-Robertson-Walker (FRW) model in the framework of f( R, ∇ R) gravity. We have analyzed the significance of bulk viscosity in the f( R, ∇ R) gravity model to study the expansion of the universe. We have considered two bulk viscosity parameterizations and the use of power-law cosmology to constrain the model parameters H0 and q. Using the Bayesian analysis and likelihood function in conjunction with the Markov Chain Monte Carlo method, we obtained the model parameters [Formula: see text] and [Formula: see text]. The behaviors of energy density, bulk viscous pressure, and the effective equation of the state parameter with redshift are investigated in detail. These features demonstrate that the bulk viscosity is a valid candidate for acquiring the negative pressure needed to effectively drive the expansion of the universe. To check the validity of the f( R, ∇ R) model, we also analyze the behavior of energy conditions. The adiabatic squared speed of the sound is used to test the model’s stability. The Om( z) diagnostic is used in the model to identify the quintessence and phantom regions.

Cosmic dynamics of isotropic models with inhomogeneous EoS: A dynamical system perspective

We examine the homogeneous and isotropic models sourced by the fluid having an inhomogenous equation of state (EoS) using qualitative methods. The flat Friedmann–Lemaitre–Robertson–Walker (FLRW) model explains the accelerating universe expansion of the present era having past of decelerating era dominated by radiation and matter. The open FLRW model incorporates the radiation, matter and dark energy dominated era in order with the spatial curvature playing role just before the accelerated universe evolution. The dominating behaviors of radiation, matter and spatial curvature affect the evolution trajectories of the deceleration and effective EoS parameter, which are obtained by the numerical solutions of autonomous system. The model parameters affect the nature of dark energy and therefore the EoS parameter may also lie in the quintessence or phantom regions. The closed FLRW model having constant positive curvature may yield the bouncing and turnaround universe evolution with dark energy-dominated phase at late-times. The application of statefinder diagnostic in the cosmological dynamical systems highlights that the universe may approach the [Formula: see text] cold dark matter ([Formula: see text]CDM) universe as a particular case in the future.

Brans–Dicke cosmology with cosmological term [formula omitted

In this paper, we study the dynamics of a flat Friedmann–Lemaître–Robertson–Walker (FLRW) cosmological model by considering varying vacuum energy density (VED) in Brans–Dicke (BD) cosmology. For this purpose, we consider the well-motivated VED of the form Λ(H)=c0+3νH2, where c0 and ν are dimensionless constants. We first adopt a theoretical method to find the exact solutions for various cosmological parameters of two models, namely ΛRG1 and ΛRG2. In ΛRG1 model, the scale factor evolves as a power-law expansion which gives the deceleration parameter a constant value. Hence, this type of model does not show the transition phase. The second model ΛRG2 describes the transition phase from deceleration to acceleration. In the second part, we perform two joint likelihood analysis in order to find the constrain on the main free parameters of the ΛRG2 model using the latest observational data sets including SNe Pantheon, H(z) data, BAO/CMB data and local H0 by SH0ES. Performing the two different combination of datasets, we find that the model shows prior decelerated epoch followed by late time accelerated epoch. We also compare the decaying VED with traditional Λ cosmology, which help us to define the evolution of the VED model. The results show that varying VED model in BD theory is consistent with data and the cosmic evolutions are in good agreement with the concordance ΛCDM and BD with constant Λ models. The AIC and BIC selection criteria are also discussed.

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.

How Different Connections in Flat FLRW Geometry Impact Energy Conditions in f(Q)$f(Q)$ Theory?

AbstractIn this study of the modified theory of gravity in the spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime, all the affine connections compatible with the symmetric teleparallel structure are explored; three classes of such connections exist, each involving an unknown time‐varying parameter . Assuming ordinary barotropic fluid as the matter source, the Friedmann‐like pressure and energy equations are derived. Next constraints on the parameters of two separate models, and from the traditional energy conditions are imposed. Observational values of some prominent cosmological parameters are used for this purpose, yielding an effective equation of state .

Reconstruction and dynamical aspects of bouncing scenarios in f(T,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 [Formula: see text] modified theory is the competitive candidate of extended theories on the cosmological scale.

Explicit formulas and decay rates for the solution of the wave equation in cosmological spacetimes

We obtain explicit formulas for the solution of the wave equation in certain Friedmann–Lemaître–Robertson–Walker (FLRW) spacetimes. Our method, pioneered by Klainerman and Sarnak, consists in finding differential operators that map solutions of the wave equation in these FLRW spacetimes to solutions of the conformally invariant wave equation in simpler, ultra-static spacetimes, for which spherical mean formulas are available. In addition to recovering the formulas for the dust-filled flat and hyperbolic FLRW spacetimes originally derived by Klainerman and Sarnak and generalizing them to the spherical case, we obtain new formulas for the radiation-filled FLRW spacetimes and also for the de Sitter, anti-de Sitter, and Milne universes. We use these formulas to study the solutions with respect to the Huygens principle and the decay rates and to formulate conjectures about the general decay rates in flat and hyperbolic FLRW spacetimes. The positive resolution of the conjecture in the flat case is seen to follow from known results in the literature.

Holographic Ricci DE as running vacuum with nonlinear interaction

The holographic Ricci dark energy (HRDE) can be treated as a running vacuum due to its analogy in the energy density, which is a combination of H and [Formula: see text], the model can predict either eternal acceleration or eternal deceleration. In the earlier works, we have shown that the presence of additive constant in the energy density or by considering possible interaction between dark sectors through a phenomenological term, the model can predict a transition from a prior decelerated to a late accelerated epoch. This paper analyzes the cosmic evolution of HRDE as running vacuum with a nonlinear interaction (NLI) between dark sectors in a flat Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. We consider three possible NLI forms which give analytically feasible solutions. We have constrained the model using the Type1a Supernova(Pantheon) + CMB(Planck 2018) + BAO(SDSS) data and evaluated the best estimated values of all the model parameters. We have analyzed the evolution of the Hubble parameter and deceleration parameter of all three cases. We perform state finder analysis of the model, which implies the quintessence nature of the model and found that it is distinguishably different from the standard [Formula: see text]CDM model. The dynamical system analysis of all three cases confirms the evolution of the universe from an unstable prior matter-dominated era to a stable end de Sitter phase.

Statefinder hierarchy of Kaniadakis holographic dark energy with composite null diagnostic

We investigate Kaniadakis holographic dark energy (KHDE) model taking the apparent horizon as the IR cutoff in a flat Friedmann-Lemaître-Robertson-Walker (FLRW) universe. We apply variant dark energy (DE) diagnostic tool to study KHDE model in flat universe with different values of the constant [Formula: see text] and Kaniadakis entropy parameter [Formula: see text]. We use the tools statefinder hierarchy [Formula: see text], fractional growth parameter [Formula: see text] and composite null diagnostic (CND), which is blend of [Formula: see text] and [Formula: see text]. The evolution of trajectories of [Formula: see text] and [Formula: see text] depicts that there occur degeneracies in early time and also in the far future, whereas, in between these two extremes they are discriminated distinctly. The analysis of the present work shows that by the inclusion of fractional growth parameter [Formula: see text] with statefinder hierarchy (CND) degeneracy is removed reasonably, particularly more in the low redshift region.

Lorentzian vacuum transitions with a generalized uncertainty principle

The vacuum transition probabilities between to minima of a scalar field potential in the presence of gravity are studied using the Wentzel–Kramers–Brillouin approximation. First we propose a method to compute these transition probabilities by solving the Wheeler–DeWitt equation in a semi-classical approach for any model of superspace that contains terms of squared as well as linear momenta in the Hamiltonian constraint generalizing in this way previous results. Then we apply this method to compute the transition probabilities for a Friedmann–Lemaitre–Robertson–Walker (FLRW) metric with positive and null curvature and for the Bianchi III metric when the coordinates of minisuperspace obey a Standard Uncertainty Principle and when a Generalized Uncertainty Principle (GUP) is taken into account. In all cases we compare the results and found that the effect of considering a GUP is that the probability is enhanced at first but it decays faster so when the corresponding scale factor is big enough the probability is reduced. We also consider the effect of anisotropy and compare the result of the Bianchi III metric with the flat FLRW metric which corresponds to its isotropy limit and comment the differences with previous works.

Observational limits on the Nash theory of gravity with matter contents

We generalize the original Nash theory of gravity by adding the matter fields by specifying a proper form of the field equations on more general footings for space with matter contents. We first derive the equations of motion in the flat Friedmann–Lemaitre–Robertson–Walker (FLRW) spacetime and examine the behaviors of the solutions by invoking specific forms of the Hubble parameter. We also classify the physical behaviors of the solutions by employing the stability analysis. We check the consistency of the model by considering particular cosmological parameters. We use observational data from Supernovae Ia (SNeIa) and baryonic acoustic oscillations (BAO) to constrain the parameters of the model. Interestingly, we discover the best fit of our model with [Formula: see text] and [Formula: see text] for [Formula: see text] and [Formula: see text] assuming the Hubble parameter [Formula: see text].

Qualitative analysis for viscous cosmologies in a non linear regime of the Israel-Stewart formalism

We explore the dynamical properties of a cosmological model that includes viscous effects in the dark matter sector of the fluid equations in a flat Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime. The bulk viscous effects are described by a non linear extension of the full Israel-Stewart model, which is a fluid causal scheme. We allow the interchange of energy in the dark sector and describe this by means of the interaction term, namely Q. We establish the dynamical system corresponding to Friedmann and fluid set of equations associated to the model and study the linear stability of its critical points. From the exploration of the dynamical system, we show the appearance of a critical point characterizing a de Sitter universe within the non interacting and interacting dark sector. We focus our study to analyse the stability of this fixed point in a large region of parameter space and derive linearized solutions around it. These approximate and analytical solutions are potentially able to describe the expansion of the universe since they are close to a de Sitter stationary solution. Within this regime with Q ≠ 0, we realize the existence of regions in the space of parameters where this critical point is stable and describes the behavior of dark energy as quintessence, cosmological constant and phantom like fluids. We perform a comparison between numerical and linearized solutions nearby the critical points within the full non linear regimes and also contrast them against ΛCDM model as a fiducial model. We find that the fully non linear regime is favored by observations and closer to the concordance model due to the non-zero value of the parameter j, which controls the non linear effects of bulk viscosity. In fact, at low redshift values, the expansion rate associated to the full non linear regime is practically indistinguishable from the ΛCDM model. The deceleration parameter obtained in this regime exhibits a transition from decelerated to accelerated cosmic expansion.

On the cosmological constant of flat FLRW spacetime

We consider an exponentially expanding, flat, Friedmann–Lemaître–Robertson–Walker (FLRW) Universe filled with a free Schroedinger field. The probability fluid of the latter is used to mimic the cosmological fluid (baryonic plus dark matter), thus providing the matter density and pressure terms in the corresponding Friedmann–Lemaître equations. We first obtain the eigenfunctions of the Laplacian operator on flat FLRW space. A quantum operator qualifying as a cosmological constant is defined to act on the Schroedinger field. We then compute the matrix representing the cosmological constant in the basis of Laplacian eigenfunctions. For an estimate of the orders of magnitude involved it suffices to determine the expectation values of this operator. The expectation value that best fits the experimentally measured value of the cosmological constant allows us to identify the quantum state of the Schroedinger field that best represents the matter contents (baryonic and dark) of the current Universe. Finally, the operator inverse (modulo dimensional factors) to the one representing the cosmological constant provides a measure of the gravitational Boltzmann entropy of the Universe. We compute its matrix in the basis of Laplacian eigenfunctions and verify that the expectation values of this entropy operator comply with the upper bound set by the holographic principle.