Friedmann-Robertson-Walker Research Articles

Primordial dust universe in the Hořava–Lifshitz theory

In this paper, we apply quantum cosmology to investigate the early moments of a Friedmann–Lemaître–Robertson–Walker (FLRW) cosmological model, using Hořava–Lifshitz (HL) as the gravitational theory. The matter content of the model is a dust perfect fluid. We start studying the classical model. Then, we write the total Hamiltonian of the model, quantize it and find the appropriate Wheeler–DeWitt equation. In order to avoid factor ordering ambiguities, in the Wheeler–DeWitt equation, we introduce a canonical transformation. We solve that equation using the Wentzel–Kramers–Brillouin (WKB) approximation and compute the tunneling probabilities for the birth of that universe ([Formula: see text]). Since the WKB wave function depends on the dust energy and the free coupling constants coming from the HL theory, we compute the behavior of [Formula: see text] as a function of all these quantities.

Barrow entropic cosmology with exponential potential field

In this paper, we consider an exponential potential [Formula: see text] in the framework of Barrow entropy under the constant-roll inflation and check their viability in the light of observable Planck 2020 data. By applying the first law of thermodynamics to the apparent horizon of the Universe, a modification of the Friedmann–Robertson–Walker (FRW) metric is derived in the context of Barrow entropy. We consider the early inflationary period of the universe to consist phenomenologically of a single inflationary state, that is, a state of the costant-roll inflation in which inflation is driven by an exponential potential field function. By fitting the constant-roll inflationary models to the observations, we examined the effect of the Barrow parameter [Formula: see text] on the inflation mechanism with the constant-roll parameter [Formula: see text]. As a result, we concluded that for a viable inflation, the observation limits of the inflation parameters determine that the constant-roll parameter is in the range [Formula: see text].

Euclidean quantum wormholes

We study wormhole as the solution of the Wheeler–DeWitt (WdW) equation satisfying Hawking–Page wormhole boundary conditions in Friedmann–Robertson–Walker (FRW) cosmology. The quantum wormholes are formulated with arbitrary factor ordering of the Hamiltonian constraint operators with perfect fluid matter sources as well as minimally coupled scalar fields.

Two Fluids in [formula omitted] Gravity with Observational Constraints

A locally rotationally symmetric Bianchi type-I model has been studied with two fluids within the framework of the f(T) theory of gravity. Bianchi type-I is an immediate generalization of the Friedmann–Lemaître–Robertson–Walker (FLRW) metric. We have derived the exact field equations in f(T) gravity by considering the Bianchi type-I metric and applying the action for f(T) theory of gravity. We have utilized the torsion scalar T and the Lagrangian for matter. The field equations are obtained by taking the variation of the action with respect to the vierbein, leading to a set of equations that includes the energy–momentum tensor for two fluid sources: matter and radiation. We fit the H(z) curve using 57 data points and the R2-test, achieving an R2 value of 0.9321, indicating a strong fit with the Observational Hubble Dataset (OHD). Cosmological parameters like energy density, pressure, and state finder diagnostics are also discussed.

Global Anisotropies of ΩΛ

An analysis of the cosmological constant ΩΛ fitted to subsamples of the Pantheon+ Type Ia supernova sample spanning 2π steradians for a grid of 432 pole positions covering the whole sky reveals two large-scale asymmetries. One of them is closely aligned with the Galactic north–south direction and the other points approximately toward R.A. ∼ 217.°5, decl. ∼ −26.°4, ∼50.°9 from the cosmic microwave background dipole Apex. The signal-to-noise ratio (S/N) of the multiple ΩΛ measurements in these directions is 3.2 ≲ S/N ≲ 8.4. The first asymmetry is puzzling, and would indicate a systematic effect related with the distribution of Pantheon+ supernovae on the sky and, probably, how the correction for reddening in the Galaxy is calculated. The second one, which entails a 2.8-σ tension between ΩΛ measured in opposite directions, bears strong implications on our interpretation of ΩΛ as dark energy: it is consistent with the prediction for tilted observers located in a Friedmann–Robertson–Walker universe who could measure an acceleration or a deceleration with a dipolar asymmetry, irrespective of what the universe as a whole is doing. In this case, ΩΛ would not be a physical entity, a real dark energy, but an apparent effect associated with the relativistic frame of reference transformation.

On the Fractional Density Gradient Blow-Up Conjecture of Rendall

On exponentially expanding Friedmann–Lemaître–Robertson–Walker (FLRW) spacetimes, there is a distinguished family of spatially homogeneous and isotropic solutions to the relativistic Euler equations with a linear equation of state of the form p=σρ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p=\\sigma \\rho $$\\end{document}, where σ∈[0,1]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma \\in [0,1]$$\\end{document} is the square of the sound speed. Restricting these solutions to a constant time hypersurface yields initial data that uniquely generates them. In this article, we show, for sound speeds satisfying 13<σ<k+13k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{1}{3}<\\sigma <\\frac{k+1}{3k}$$\\end{document} with k∈Z>32\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k\\in {\\mathbb {Z}}{}_{>\\frac{3}{2}}$$\\end{document}, that T2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {T}}{}^2$$\\end{document}-symmetric initial data that is chosen sufficiently close to spatially homogeneous and isotropic data uniquely generates a T2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {T}}{}^2$$\\end{document}-symmetric solution of the relativistic Euler equations that exists globally to the future. Moreover, provided k∈Z>52\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k\\in {\\mathbb {Z}}{}_{>\\frac{5}{2}}$$\\end{document}, we show that there exist open sets of T2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {T}}{}^2$$\\end{document}-symmetric initial data for which the fractional density gradient becomes unbounded at timelike infinity. This rigorously confirms, in the restricted setting of relativistic fluids on exponentially expanding FLRW spacetimes, the fractional density gradient blow-up scenario conjectured by Rendall (Ann Henri Poincaré 5(6):1041–1064, 2004).

Impact of particle creation in Rastall gravity

In this paper, we investigate the Friedmann–Lemaitre–Robertson–Walker cosmological models within the framework of Rastall gravity incorporating particle creation. The modified field equations for Rastall gravity are derived and exact solutions are obtained under various assumptions of the scale factor. The qualitative behavior of our solutions depends on the Rastall coupling parameter [Formula: see text]. Following Akarsu et al. [Ö. Akarsu et al., Rastall gravity extension of the standard [Formula: see text] CDM model: Theoretical features and observational constraints, Eur. Phys. J. C 80 (2020) 1050], we have restricted the Rastall coupling parameter [Formula: see text] to the range [Formula: see text] at 68% CL from CMB+BAO data. Further, we have discussed the distinct physical behavior of the derived models in detail.

Constraints on the parameters of modified Chaplygin–Jacobi and modified Chaplygin–Abel gases in f(T) gravity

In this work, we explore the parameter constraints of two dark energy models, namely the Modified Chaplygin–Jacobi gas (MCJG) and Modified Chaplygin–Abel gas (MCAG), within the context of [Formula: see text] gravity model in a non-flat Friedmann–Lemaître–Robertson–Walker (FLRW) universe. Our investigation involves comparing the equation of state for the MCJG and MCAG dark energy models with the equation of state derived from the [Formula: see text] gravity model. To derive constraints for the dark energy and [Formula: see text] gravity models, we use recent astronomical datasets, including [Formula: see text] data, type Ia supernovae observations, Gamma Ray Bursts data, quasar data, and Baryon Acoustic Oscillation (BAO) measurements. We present the reduced Hubble parameter in terms of observable parameters such as [Formula: see text] (density parameter of radiation), [Formula: see text] (density parameter of dark matter), [Formula: see text] (density parameter associated with spatial curvature), [Formula: see text] (density parameter of Modified Chaplygin–Jacobi gas), [Formula: see text] (density parameter of Modified Chaplygin–Abel gas), and [Formula: see text] (present value of the Hubble parameter). We explore the cosmological evolution through various cosmic diagnostic parameters, including the deceleration parameter, [Formula: see text] diagnostic, and statefinder diagnostic pair [Formula: see text]. These diagnostic parameters offer valuable insights into the expansion dynamics and the nature of dark energy in the universe. We have also assessed the viability of the models using the information criteria. Our aim is to shed light on the nature of dark energy and its connection to the [Formula: see text] gravity model, and ultimately gain a deeper understanding of the underlying mechanisms driving the accelerated expansion of our universe.

Observational constraints on FLRW, Bianchi type I and V brane models

This study explores the compatibility of Covariant Extrinsic Gravity (CEG), a braneworld scenario with an arbitrary number of non-compact extra dimensions, with current cosmological observations. We employ the chi-square statistic and Markov Chain Monte Carlo (MCMC) methods to fit the Friedmann–Lemaître–Robertson–Walker (FLRW) and Bianchi type-I and V brane models to the latest datasets, including Hubble, Pantheon+ Supernova samples, Big Bang Nucleosynthesis (BBN), Baryon Acoustic Oscillations (BAO), and the structure growth rate, fσ8(z). Parameters for FLRW universe consist Ω0(b),Ω0(cd),Ω0(k),H0,γ,σ8, while for the Bianchi model are Ω0(b),Ω0(cd),Ω0(β),H0,γ,Ω0(θ),σ8. By comparing our models to observational data, we determine the best values for cosmological parameters. For the FLRW model, these values depend on the sign of γ (which gives the time variation of gravitational constant in Hubble time unit): γ>0 yields γ=0.00008−0.00011+0.00015, and Ω0(k)=0.014−0.022+0.024 and γ<0 leads to γ=−0.0226−0.0062+0.0054, and Ω0(k)=0.023−0.041+0.039. It should be noted that in both cases Ω0(k)>0, which represents a closed universe. Similarly, for the Bianchi type-V brane model, the parameter values vary with the sign of γ, resulting in γ=0.00084−0.00021+0.00019, Ω0(β)=0.0258−0.0063+0.0052, and Ω0θ(×10−5)=4.19−0.75+0.67 (as with the density parameter of stiff matter) for γ>0, and γ=−0.00107−0.00020+0.00019, Ω0(β)=0.0259−0.0062+0.0050, and Ω0θ(×10−5)=4.17−0.98+0.91 for γ<0. In both cases Ω0(β)>0, which represents the Bianchi type-V, because in the Bianchi type-I, β=0. Subsequently, utilizing these obtained best values, we analyze the behavior of key cosmological parameters such as the Hubble parameter, deceleration parameter, distance modulus, equation of state, and density parameters that characterize both matter and the geometric component of dark energy, as functions of redshift. Our results notably show that the FLRW model with γ<0 is more compatible with observational data than the Bianchi model, based on various statistical criteria.

Cosmology in R2-gravity: Effects of a higher derivative scalar condensate background

A well known extension of Einstein's General Relativity is the addition of an R2-term, which is free of ghost excitations and in the linearized framework, reduces to the conventional spin-2 graviton and an additional higher derivative scalar. According to Chakraborty and Ghosh (2022), the above scalar sector can sustain a Time Crystal-like minimum energy state, with non-trivial time dependence. Exploiting previous result that the scalar can sustain modes with periodic time dependence in its lowest energy, we consider this condensate as a source and study the Friedmann-Lemaître-Robertson-Walker (FLRW) cosmology in this background. The effect of the R2-term is interpreted as a back reaction. A remarkable consequence of the condensate is that, irrespective of open or close geometry of the Universe, for an appropriate choice of parameter window, the condensate can induce a decelerating phase before the accelerated expansion starts and again, in some cases, it can help to avoid the singularity in the deceleration parameter (that is present in conventional FLRW Cosmology).

Quintessential f(G) gravity with statistically fitting of H(z)

Inspired by high-energy physics and by considering standard gravity theory as the low-energy limit of quantum theory, the modification of general relativity as [Formula: see text] has been proposed. This paper is dedicated to investigating the cosmological model of modified Gauss–Bonnet gravity in four dimensions. General field equations for the four-dimensional Friedmann– Robertson–Walker metric are given in detail. Also, it is well known that Hubble parameter [Formula: see text] measurements are helpful for the inference of cosmological model parameters. We try to explain the MCMC statistical approach used to calculate Hubble’s parameter. The resulting form of [Formula: see text] was limited using Cosmic Chronometric data, Standard Candles SN Ia from Pantheon, and Baryon Acoustic Oscillations to obtain the best match values by using the regression equation. Finally, to examine the late-time dynamics of our Universe, the behavior of physical and kinematic variables like the deceleration parameter [Formula: see text], State-finder parameters [Formula: see text], diagnostic parameter ([Formula: see text]), equation of state parameter as well as the behavior of energy conditions versus redshift with the parameter values are presented.

Reconsidering bulk viscosity in Brans–Dicke theory

In this paper, we reconsider the concept of bulk viscosity in Brans–Dicke theory to study accelerated expansion of the universe in a flat Friedmann–Robertson–Walker metric. In recent works on bulk viscosity in Brans–Dicke theory, the power-law form of Brans–Dicke scalar field has been taken to explain recent phase transition of the universe, however, power-law form confronts constant deceleration parameter problem. Therefore, we consider recently proposed well-motivated logarithmic form of Brans–Dicke scalar field to discuss bulk viscous model in Brans–Dicke theory. We obtain the values of deceleration parameter and equation of state parameter for the model, and plot their graphs against the redshift parameter z. The plots show that the model is able to explain the recent phase transition of the universe and equation of state parameter shows the behavior of dark energy. Further, we apply two important analysis, namely, [Formula: see text] analysis and thermodynamic analysis to examine our model. The [Formula: see text] analysis shows that our model belong to thawing region and shows similarities with quintessence model. All the trajectories start from the point [Formula: see text] with different negative values of w having quintessence behavior. The thermodynamic analysis shows that the model satisfies generalized second law of thermodynamics.

Warm inflation in a Universe with a Weylian boundary

We investigate the influence of boundary terms in the warm inflationary scenario, by considering that in the Einstein–Hilbert action the boundary can be described in terms of a Weyl-type geometry. The gravitational action, as well as the field equations, are thus extended to include new geometrical terms, coming from the non-metric nature of the boundary, and depending on the Weyl vector, and its covariant derivatives. We investigate the effects of these new boundary terms by considering the warm inflationary scenario of the early evolution of the Universe, in the presence of a scalar field. We obtain the generalized Friedmann equations in the Universe with a Weylian boundary by considering the Friedmann–Lemaitre–Robertson–Walker metric. We consider the simultaneous decay of the scalar field, and of the creation of radiation, by appropriately splitting the general conservation equation through the introduction of the dissipation coefficient, which can depend on both the scalar field, and the Weyl vector. We consider three distinct warm inflationary models, in which the dissipation coefficients are chosen as different functions of the scalar field and of the Weyl vector. The numerical solutions of the cosmological evolution equations show that the radiation is created during the very early phases of expansion, and, after the radiation reaches its maximum value, the transition from an accelerating inflationary phase to a decelerating one takes place. Moreover, it turns out that the Weyl vector, describing the boundary effects on the cosmological evolution, plays a significant role during the process of radiation creation.

Late-time constraints on barotropic fluid cosmology

We investigate the cosmological implications of the Friedmann-Robertson-Walker (FRW) model having a flat-spatial section with barotropic fluid. We examine the resulting cosmological scenario obtained by solving the continuity equation. The model may yield the accelerating universe expansion from the transition of decelerated phase, subjected to the best fit values. We confront the cosmological model with the recent observational data, namely the Observational Hubble Data (OHD) and Supernovae type Ia (SN Ia) data. The model exhibits good agreement with these observational data sets. For the best fit values of the model parameters, the universe approaches to the Λ cold dark matter (ΛCDM) model in the distant future. Energy conditions except strong energy conditions are satisfied in the model. Analysis of the equation of state (EoS) parameter and statefinder diagnostic highlight that the phantom scenario does not arise for the best fit values. The universe is free from the finite-time future singularities in the model.

Significance of a quadratically varying deceleration parameter in scalar field-dominated model and cosmic acceleration

In this study, we explore the enigma of late-time cosmic acceleration in the framework of a general scalar field playing the role of dark energy. Our investigation yields an exact solution to Einstein’s field equations, achieved through a parametrization of the deceleration parameter [Formula: see text] in quadratic form in the homogeneous and isotropic background geometry represented by Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime. This parametrization unveils a seamless transition from a decelerated to an accelerated phase in the cosmic evolution. Furthermore, we leverage this parametrization to reconstruct cosmological parameters with respect to redshift z, elucidating their dependency on certain model parameters that govern the universe’s evolutionary trajectory. The model parameters are subsequently constrained using diverse observational datasets. We provide a comprehensive analysis of the evolution of geometrical and physical parameters, complete with the numerically constrained values. To gain deeper insights into the nature of dark energy, we employ Statefinder diagnostics, conducting a thorough examination. Our findings shed light on the intricate interplay between cosmic acceleration, quintessential dark energy and the parametrization of deceleration parameter, offering valuable insights into the fundamental dynamics of the universe.

On direct estimation of density parameters and Hubble constant for ΛCDM universe using Hubble measurements

The set of cosmological density parameters ( Ω0mh02 , Ω0kh02 , Ω0Λh02 ) and Hubble constant ( hˆ0 ) are useful for fundamental understanding of the Universe from many perspectives. In this article, we propose a new procedure to estimate these parameters for Λ cold dark matter (ΛCDM) universe in the Friedmann-Robertson-Walker (FRW) background. We generalize the two-point statistics first proposed by Sahni et al (2008) to the three point case and estimate the parameters using currently available Hubble parameter (H(z)) values in the redshift range 0.07 ≤ z ≤ 2.36 measured by differential age (DA) and baryon acoustic oscillation (BAO) techniques. All the parameters are estimated assuming the general case of non-flat universe. Using both DA and BAO data we obtain Ω0mh02=0.1485±0.0065 , Ω0kh02=−0.0137±0.017 , Ω0Λh02=0.3126±0.0145 and hˆ0=0.6689±0.0021 . These results are in satisfactory agreement with the Planck results. An important advantage of our method is that to estimate the value of any one of the independent cosmological parameters one does not need to use the values for the rest of them. Each parameter is obtained solely from the measured values of Hubble parameters at different redshifts without any need to use values of other parameters. Such a method is expected to be less susceptible to the undesired effects of degeneracy issues between cosmological parameters during their estimations. Moreover, there is no requirement of assuming spatial flatness in our method.

Domain wall and holographic dark energy in f(Q) theory of gravity

In this paper, we have studied the flat Friedmann–Robertson–Walker (FRW) space time with domain wall and holographic dark energy in the context of [Formula: see text] theory of gravity. The exact solutions of the field equations are obtained using two different forms of varying deceleration parameters: (i) [Formula: see text] and (ii) [Formula: see text]. It is observed that the universe is accelerating and expanding. Furthermore, we have also discussed some physical parameters of the investigated model.

FRW Universe with a Parameterization of the EoS Parameter in f(Q) Gravity

FRW Universe with a Parameterization of the EoS Parameter in f(Q) Gravity

Cosmology from string T-duality and zero-point length

Inspired by string T-duality and taking into account the zero-point length correction, l0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$l_0$$\\end{document}, to the gravitational potential, we construct modified Friedmann equations by applying the first law of thermodynamics on the apparent horizon of the Friedmann–Robertson–Walker (FRW) Universe. The cosmological viability of this extended scenario is investigated by studying influences on the evolution of the early Universe and performing cosmographic analysis. Furthermore, we explore the inflationary paradigm under the slow-roll condition. By testing the model against observational data, the zero-point length is constrained around the Planck scale, in compliance with the original assumption from string T-duality. We also study the growth of density perturbations in the linear regime. It is shown that the zero-point length stands out as an alternative characterization for the broken-power-law spectrum, providing a better fit for the experimental measurements than the simple power-law potential. Finally, we focus on implications for the primordial gravitational wave (PGW) spectrum. Should the zero-point length be running over energy scales, as is the case for all parameters and coupling constants in quantum gravity under renormalization group considerations, deviations from general relativity (GR) might be potentially tested through upcoming PGW observatories.

Investigation of generalised uncertainty principle effects on FRW cosmology

Based on the entropy-area relation from Nouicer's generalised uncertainty principle (GUP), we derive the GUP modified Friedmann equations from the first law of thermodynamics at apparent horizon. We find a minimum apparent horizon due to the minimal length notion of GUP. We show that the energy density of universe has a maximum and finite value at the minimum apparent horizon. Both minimum apparent horizon and maximum energy density imply the absence of the Big Bang singularity. Moreover, we investigate the GUP effects on the deceleration parameter for flat case. Finally, we examine the validity of generalised second law (GSL) of thermodynamics. We show that GSL always holds in a region enclosed by apparent horizon for the GUP effects. We also investigate the GSL in ΛCDM cosmology and find that the total entropy change of universe has a maximum value in the presence of GUP effects. To better grasp the effects of Nouicer's GUP on cosmology, we compare our results with those obtained from quadratic GUP (QGUP).