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Showing papers on "Friedmann–Lemaître–Robertson–Walker metric published in 2020"


Journal ArticleDOI
TL;DR: In this paper, conditions for islands to appear in general spacetimes, with or without black holes, were studied, and the boundary of an island must satisfy Bekenstein's area bound and several other information-theoretic inequalities.
Abstract: A quantum extremal island suggests that a region of spacetime is encoded in the quantum state of another system, like the encoding of the black hole interior in Hawking radiation. We study conditions for islands to appear in general spacetimes, with or without black holes. They must violate Bekenstein’s area bound in a precise sense, and the boundary of an island must satisfy several other information-theoretic inequalities. These conditions combine to impose very strong restrictions, which we apply to cosmological models. We find several examples of islands in crunching universes. In particular, in the four-dimensional FRW cosmology with radiation and a negative cosmological constant, there is an island near the turning point when the geometry begins to recollapse. In a two-dimensional model of JT gravity in de Sitter spacetime, there are islands inside crunches that are encoded at future infinity or inside bubbles of Minkowski spacetime. Finally, we discuss simple tensor network toy models for islands in cosmology and black holes.

182 citations


Journal ArticleDOI
TL;DR: In this paper, the authors study the non-relativistic expansion of general relativity coupled to matter, which is done by expanding the metric and matter fields analytically in powers of 1/c2 where c is the speed of light.
Abstract: We study the non-relativistic expansion of general relativity coupled to matter. This is done by expanding the metric and matter fields analytically in powers of 1/c2 where c is the speed of light. In order to perform this expansion it is shown to be very convenient to rewrite general relativity in terms of a timelike vielbein and a spatial metric. This expansion can be performed covariantly and off shell. We study the expansion of the Einstein-Hilbert action up to next-to-next-to-leading order. We couple this to different forms of matter: point particles, perfect fluids, scalar fields (including an off-shell derivation of the Schrodinger-Newton equation) and electrodynamics (both its electric and magnetic limits). We find that the role of matter is crucial in order to understand the properties of the Newton-Cartan geometry that emerges from the expansion of the metric. It turns out to be the matter that decides what type of clock form is allowed, i.e. whether we have absolute time or a global foliation of constant time hypersurfaces. We end by studying a variety of solutions of non-relativistic gravity coupled to perfect fluids. This includes the Schwarzschild geometry, the Tolman-Oppenheimer-Volkoff solution for a fluid star, the FLRW cosmological solutions and anti-de Sitter spacetimes.

75 citations


Journal ArticleDOI
TL;DR: In this paper, the authors study the non-relativistic expansion of general relativity coupled to matter, which is done by expanding the metric and matter fields analytically in powers of $1/c^2$ where $c$ is the speed of light.
Abstract: We study the non-relativistic expansion of general relativity coupled to matter. This is done by expanding the metric and matter fields analytically in powers of $1/c^2$ where $c$ is the speed of light. In order to perform this expansion it is shown to be very convenient to rewrite general relativity in terms of a timelike vielbein and a spatial metric. This expansion can be performed covariantly and off shell. We study the expansion of the Einstein-Hilbert action up to next-to-next-to-leading order. We couple this to different forms of matter: point particles, perfect fluids, scalar fields (including an off-shell derivation of the Schr\"odinger-Newton equation) and electrodynamics (both its electric and magnetic limits). We find that the role of matter is crucial in order to understand the properties of the Newton-Cartan geometry that emerges from the expansion of the metric. It turns out to be the matter that decides what type of clock form is allowed, i.e. whether we have absolute time or a global foliation of constant time hypersurfaces. We end by studying a variety of solutions of non-relativistic gravity coupled to perfect fluids. This includes the Schwarzschild geometry, the Tolman-Oppenheimer-Volkoff solution for a fluid star, the FLRW cosmological solutions and anti-de Sitter spacetimes.

50 citations


Journal ArticleDOI
TL;DR: In this paper, a model for cosmological hyperfluid fluids with intrinsic hypermomentum that induce spacetime torsion and non-metricity is presented.
Abstract: We develop a novel model for cosmological hyperfluids, that is fluids with intrinsic hypermomentum that induce spacetime torsion and non-metricity. Imposing the cosmological principle to metric-affine spaces, we present the most general covariant form of the hypermomentum tensor in an FLRW Universe along with its conservation laws and therefore construct a novel hyperfluid model for cosmological purposes. Extending the previous model of the unconstrained hyperfluid in a cosmological setting we establish the conservation laws for energy–momentum and hypermomentum and therefore provide the complete cosmological setup to study non-Riemannian effects in Cosmology. With the help of this we find the forms of torsion and non-metricity that were earlier reported in the literature and also obtain the most general form of the Friedmann equations with torsion and non-metricity. We also discuss some applications of our model, make contact with the known results in the literature and point to future directions.

47 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that the combination of cubic invariants defining five-dimensional quasitopological gravity, when written in four dimensions, reduce to the version of four-dimensional Einsteinian gravity recently proposed by Arciniega, Edelstein & Jaime, that produces second order equations of motion in a FLRW ansatz, with a purely geometrical inflationary period.

43 citations


Journal ArticleDOI
TL;DR: In this article, a non-interacting model of Barrow holographic dark energy (BHDE) using Barrow entropy in a spatially flat FLRW Universe considering the IR cutoff as the Hubble horizon was proposed.
Abstract: In this work, we propose a non-interacting model of Barrow holographic dark energy (BHDE) using Barrow entropy in a spatially flat FLRW Universe considering the IR cutoff as the Hubble horizon. We study the evolutionary history of important cosmological parameters, in particular, EoS $(\omega_{B})$, deceleration parameter and, the BHDE and matter density parameter and also observe satisfactory behaviours in the BHDE the model. In addition, to describe the accelerated expansion of the Universe the correspondence of the BHDE model with the quintessence scalar field has been reconstructed.

42 citations


Journal ArticleDOI
TL;DR: The quasi-topological electromagnetism as mentioned in this paper is defined to be the squared norm of the topological 4-form F ∧ F, and it can thus provide a model for dark energy.
Abstract: We introduce the quasi-topological electromagnetism which is defined to be the squared norm of the topological 4-form F ∧ F. A salient property is that its energy-momentum tensor is of the isotropic perfect fluid with the pressure being precisely the opposite to its energy density. It can thus provide a model for dark energy. We study its application in both black hole physics and cosmology. The quasi-topological term has no effect on the purely electric or magnetic Reissner-Nordstrom black holes, the dyonic solution is however completely modified. We find that the dyonic black holes can have four real horizons. For suitable parameters, the black hole can admit as many as three photon spheres, with one being stable. Another intriguing property is that although the quasi-topological term breaks the electromagnetic duality, the symmetry emerges in the on-shell action in the Wheeler-DeWitt patch. In cosmology, we demonstrate that the quasi-topological term alone is equivalent to a cosmological constant, but the model provides a mechanism for the dark energy to couple with other types of matter. We present a concrete example of the quasi-topological electromagnetism coupled to a scalar field that admits the standard FLRW cosmological solutions.

40 citations


Journal ArticleDOI
TL;DR: In this article, the authors compute the circuit complexity of scalar curvature perturbations on FLRW cosmological backgrounds with fixed equation of state $w$ using the language of squeezed vacuum states and uncover a bound on the growth of complexity for both expanding and contracting backgrounds.
Abstract: We compute the circuit complexity of scalar curvature perturbations on FLRW cosmological backgrounds with fixed equation of state $w$ using the language of squeezed vacuum states. Backgrounds that are accelerating and expanding, or decelerating and contracting, exhibit features consistent with chaotic behavior, including linearly growing complexity. Remarkably, we uncover a bound on the growth of complexity for both expanding and contracting backgrounds $\lambda \leq \sqrt{2} \ |H|$, similar to other bounds proposed independently in the literature. The bound is saturated for expanding backgrounds with an equation of state more negative than $w = -5/3$, and for contracting backgrounds with an equation of state larger than $w = 1$. For expanding backgrounds that preserve the null energy condition, de Sitter space has the largest rate of growth of complexity (identified as the Lyapunov exponent), and we find a scrambling time that is similar to other estimates up to order one factors.

38 citations


Journal ArticleDOI
TL;DR: In this article, a comprehensive discussion on lattice techniques for the simulation of scalar and gauge field dynamics in an expanding universe is presented, including the case of self-consistent expansion.
Abstract: We present a comprehensive discussion on lattice techniques for the simulation of scalar and gauge field dynamics in an expanding universe After reviewing the continuum formulation of scalar and gauge field interactions in Minkowski and FLRW backgrounds, we introduce basic tools for the discretization of field theories, including lattice gauge invariant techniques Following, we discuss and classify numerical algorithms, ranging from methods of $O(dt^2)$ accuracy like $staggered~leapfrog$ and $Verlet$ integration, to $Runge-Kutta$ methods up to $O(dt^4)$ accuracy, and the $Yoshida$ and $Gauss-Legendre$ higher-order integrators, accurate up to $O(dt^{10})$ We adapt these methods for their use in classical lattice simulations of the non-linear dynamics of scalar and gauge fields in an expanding grid in $3+1$ dimensions, including the case of `self-consistent' expansion sourced by the volume average of the fields' energy and pressure densities We present lattice formulations of canonical cases of: $i)$ Interacting scalar fields, $ii)$ Abelian $U(1)$ gauge theories, and $iii)$ Non-Abelian $SU(2)$ gauge theories In all three cases we provide symplectic integrators, with accuracy ranging from $O(dt^2)$ up to $O(dt^{10})$ For each algorithm we provide the form of relevant observables, such as energy density components, field spectra and the Hubble constraint Remarkably, all our algorithms for gauge theories respect the Gauss constraint to machine precision, including when `self-consistent' expansion is considered As a numerical example we analyze the post-inflationary dynamics of an oscillating inflaton charged under $SU(2)\times U(1)$ The present manuscript is meant as part of the theoretical basis for $CosmoLattice$, a modern C++ MPI-based package for simulating the non-linear dynamics of scalar-gauge field theories in an expanding universe, publicly available at this http URL

34 citations


Journal ArticleDOI
TL;DR: In this paper, the curvature tension in a Friedmann-lema-tre-Robertson-Walker (FLRW) spacetime can be resolved from the point of view of general relativity.
Abstract: Recently it has been noted by Di Valentino, Melchiorri and Silk (2019) that the enhanced lensing signal relative to that expected in the spatially flat $\Lambda$CDM model poses a possible crisis for the Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) class of models usually used to interpret cosmological data. The `crisis' amounts to inconsistencies between cosmological datasets arising when the FLRW curvature parameter $\Omega_{k0}$ is determined from the data rather than constrained to be zero a priori. Moreover, the already substantial discrepancy between the Hubble parameter as determined by Planck and local observations increases to the level of $5\sigma$. While such inconsistencies might arise from systematic effects of astrophysical origin affecting the Planck Cosmic Microwave Background (CMB) power spectra at small angular scales, it is an option that the inconsistencies are due to the failure of the FLRW assumption. In this paper we recall how the FLRW curvature ansatz is expected to be violated for generic relativistic spacetimes. We explain how the FLRW conservation equation for volume-averaged spatial curvature is modified through structure formation, and we illustrate in a simple framework how the curvature tension in a FLRW spacetime can be resolved---and is even expected to occur---from the point of view of general relativity. Requiring early-time convergence towards a Friedmannian model with a spatial curvature parameter $\Omega_{k0}$ equal to that preferred from the Planck power spectra resolves the Hubble tension within our dark energy-free model.

34 citations


Journal ArticleDOI
TL;DR: In this article, the cosmological phase space of the generalized hybrid metric-Palatini gravity theory is studied using a dynamical system approach, where the propagation equations of the suitable dimensionless variables that describe FLRW universes as an autonomous system are formulated.
Abstract: Using a dynamical system approach we study the cosmological phase space of the generalized hybrid metric-Palatini gravity theory, characterized by the function $f(R,\mathcal{R})$, where $R$ is the metric scalar curvature and $\mathcal{R}$ the Palatini scalar curvature of the spacetime. We formulate the propagation equations of the suitable dimensionless variables that describe FLRW universes as an autonomous system. The fixed points are obtained for four different forms of the function $f(R,\mathcal{R})$, and the behavior of the cosmic scale factor $a(t)$ is computed. We show that due to the structure of the system, no global attractors can be present and also that two different classes of solutions for the scale factor $a(t)$ exist. Numerical integrations of the dynamical system equations are performed with initial conditions consistent with the observations of the cosmological parameters of the present state of the Universe. In addition, using a redefinition of the dynamic variables, we are able to compute interesting solutions for static universes.

Journal ArticleDOI
TL;DR: In this paper, the role of dust reference fields on cosmological perturbations around a classical spatially flat Friedmann-Lema-tre-Robertson-Walker (FLRW) universe is investigated.
Abstract: The aim of this article is to understand the role of dust reference fields, often also called clocks, on cosmological perturbations around a classical spatially flat Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) universe. We derive the Mukhanov-Sasaki equation for the Brown-Kucha\ifmmode \check{r}\else \v{r}\fi{} and Gaussian dust models, which both consider four dust fields as reference fields. The reduced phase space of Dirac observables, that is the gauge-invariant part of the theory, is constructed by means of an observable map applied to all elementary phase space variables of the coupled system, consisting of gravity, a massive scalar field and the dust degrees of freedom and automatically yields the set of independent physical variables. The evolution of these observables is governed by a so called physical Hamiltonian which can be derived once the set of reference fields are chosen and differs for each model. First, the reduced phase space for full general relativity as well as the corresponding equations of motion are derived for full general relativity. Then from this, the gauge-invariant versions of the equations of motion for the background are derived which contain a fingerprint of the dust reference fields. Afterwards we study linear cosmological perturbations around a FLRW metric using the scalar-vector-tensor decomposition and derive the equation of motion for the Mukhanov-Sasaki variable in this formalism for a chosen set of variables on the reduced phase space and expressed in terms of Dirac observables. The Mukhanov-Sasaki equation involves additional contributions that can be understood as back reactions from the dust reference fields. These additional dust contributions to the Mukhanov-Sasaki equation were absent if the dust energy and momentum density as well as their perturbations are vanishing. The nature of the correction terms suggests that Brown-Kucha\ifmmode \check{r}\else \v{r}\fi{} and Gaussian dust reference fields contribute differently. We numerically study the behavior of the dust contributions to the Mukhanov-Sasaki equation during inflation.

Journal ArticleDOI
TL;DR: In this article, conditions for islands to appear in general spacetimes, with or without black holes, were studied, and the boundary of an island must satisfy several other information-theoretic inequalities.
Abstract: A quantum extremal island suggests that a region of spacetime is encoded in the quantum state of another system, like the encoding of the black hole interior in Hawking radiation. We study conditions for islands to appear in general spacetimes, with or without black holes. They must violate Bekenstein's area bound in a precise sense, and the boundary of an island must satisfy several other information-theoretic inequalities. These conditions combine to impose very strong restrictions, which we apply to cosmological models. We find several examples of islands in crunching universes. In particular, in the four-dimensional FRW cosmology with radiation and a negative cosmological constant, there is an island near the turning point when the geometry begins to recollapse. In a two-dimensional model of JT gravity in de Sitter spacetime, there are islands inside crunches that are encoded at future infinity or inside bubbles of Minkowski spacetime. Finally, we discuss simple tensor network toy models for islands in cosmology and black holes.

Journal ArticleDOI
TL;DR: In this paper, the authors presented the luminosity distance series expansion to third order in redshift for a general space-time with no assumption on the metric tensor or the field equations prescribing it.
Abstract: We present the luminosity distance series expansion to third order in redshift for a general space-time with no assumption on the metric tensor or the field equations prescribing it. It turns out that the coefficients of this general 'Hubble law' can be expressed in terms of a finite number of physically interpretable multipole coefficients. The multipole terms can be combined into effective direction dependent parameters replacing the Hubble constant, deceleration parameter, curvature parameter, and 'jerk' parameter of the Friedmann-Lema\^itre-Robertson-Walker (FLRW) class of metrics. Due to the finite number of multipole coefficients, the exact anisotropic Hubble law is given by 9, 25, 61 degrees of freedom in the $\mathcal{O}(z)$, $\mathcal{O}(z^2)$, $\mathcal{O}(z^3)$ vicinity of the observer respectively, where $z\!:=\,$redshift. This makes possible model independent determination of dynamical degrees of freedom of the cosmic neighbourhood of the observer and direct testing of the FLRW ansatz. We argue that the derived multipole representation of the general Hubble law provides a new framework with broad applications in observational cosmology.

Journal ArticleDOI
TL;DR: In this article, the authors investigated the complexity growth rate of a conformal field theory in a Friedman-Lema-tre-Roberstson-Walker (FLRW) universe.
Abstract: We investigate the holographic complexity growth rate of a conformal field theory in a Friedman-Lema\^{\i}tre-Roberstson-Walker (FLRW) universe. We consider two ways to realize an FLRW spacetime from an anti--de Sitter Schwarzschild geometry. The first one is obtained by introducing a new foliation of the Schwarzschild geometry such that the conformal boundary takes the FLRW form. The other one is to consider a brane universe moving in the Schwarzschild background. For each case, we compute the complexity growth rate in a closed universe and a flat universe by using both the complexity-volume and complexity-action dualities. We find that there are two kinds of contributions to the growth rate: one is from the interaction among the degrees of freedom, while the other one from the change of the spatial volume of the universe. The behaviors of the growth rate depend on the details to realize the FLRW universe as well as the holographic conjecture for the complexity. For the realization of the FLRW universe on the asymptotic boundary, the leading divergent term for the complexity growth rate obeys a volume law which is natural from the field theory viewpoint. For the brane universe scenario, the complexity-volume and complexity-action conjectures give different results for the closed universe case. A possible explanation of the inconsistency when the brane crosses the black hole horizon is given based on the Lloyd bound.

Journal ArticleDOI
TL;DR: In this paper, the exact form of generic functions present in different torsion-based modified gravitational frameworks using reconstruction technique was investigated, and it was concluded that all these parameters support accelerating cosmic expansion in later time and a stable state of cosmos.
Abstract: The present paper investigates the exact form of generic functions present in different torsion-based modified gravitational frameworks using reconstruction technique. For this purpose, we consider flat FRW geometry filled with the matter contents as perfect fluid. For the reconstruction paradigm, we take the Tsallis holographic dark energy model into account and explore the forms of generic functions present in the torsional frameworks of f(T) theory, non-minimally interacted torsion matter coupling, f(T, G) theory with G as Gauss–Bonnet term and $$f(T,{\mathcal {T}})$$ gravity, where $${\mathcal {T}}$$ denotes the energy–momentum tensor trace. We also computed the reconstructed form of generic functions by taking Tsallis holographic dark energy with power law and logarithmic corrections for all these cases. To check the cosmological viability and stability of the reconstructed models, we discuss some interesting cosmic parameters like dark energy EoS, deceleration parameter and the speed of sound graphically. It is concluded that all these parameters support accelerating cosmic expansion in later time and a stable state of cosmos (except few cases) which is also compatible with the recent observations.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the theoretical bounds on the coupling parameters of the interaction rate in order that the energy densities of the dark sector remain positive throughout the evolution of the universe and asymptotically converge to zero at very late times.
Abstract: Nongravitational interaction between dark matter and dark energy has been considered in a spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. The interaction rate is assumed to be linear in the energy densities of dark matter and dark energy and it is also proportional to the Hubble rate of the FLRW universe. This kind of interaction model leads to an autonomous linear dynamical system, and depending on the coupling parameters, could be solved analytically by calculating the exponential of the matrix, defining the system. We show here that such interaction rate has a very deep connection with some well-known cosmological theories. We then investigate the theoretical bounds on the coupling parameters of the interaction rate in order that the energy densities of the dark sector remain positive throughout the evolution of the universe and asymptotically converge to zero at very late times. Our analyses also point out that such linear interacting model may encounter with finite time future singularities depending on the coupling parameters as well as the dark energy state parameter.

Journal ArticleDOI
TL;DR: In this paper, a flat FLRW (Friedmann-Lemaitre-Robertson-Walker) cosmological model with perfect fluid comprising of variable Chaplygin gas (VCG) was studied in the context of f(R, T) gravity with particle creation.

Journal ArticleDOI
TL;DR: In this article, some holographic dark energy models including Tsallis, Renyi and Sharma-Mittal models are reconstructed in the context of extended teleparallel gravity theory with Gauss-Bonnet term.

Journal ArticleDOI
TL;DR: In this paper, the Friedmann-Robertson-Walker (FRW) model was investigated in viable f(R, T) gravity with f(r, t) function proposed as f (R, T ) = R + ξ T 1 / 2, where R is the scalar curvature and T is the trace of stress energy tensor.

Journal ArticleDOI
Abstract: Observations are studied in toy-models constituting exact cosmological solutions to the Einstein equation which are statistically homogeneous but locally inhomogeneous, without an a priori introduced FLRW background and with "structures" evolving fairly slowly. The mean redshift-distance relation and redshift drift along 500 light rays in each of two models are compared to relations based on spatial averages. The relations based on spatial averages give a good reproduction of the mean redshift-distance relation, although most convincingly in the model where the kinematical backreaction is subpercent. In both models, the mean redshift drift clearly differs from the drift of the mean redshift. This indicates that redshift drift could be an important tool for testing the backreaction conjecture as redshift drift appears to distinguish between local and global effects. The method presented for computing the redshift drift is straightforward to generalize and can thus be utilized to fairly easily compute this quantity in a general spacetime.

Journal ArticleDOI
TL;DR: In this article, a model for Cosmological Hyperfluids with intrinsic hypermomentum that induce spacetime torsion and non-metricity is presented, which is the most general covariant form of the hypermomentsum tensor in an FLRW universe along with its conservation laws.
Abstract: We develop a novel model for Cosmological Hyperfluids, that is fluids with intrinsic hypermomentum that induce spacetime torsion and non-metricity. Imposing the Cosmological Principle to Metric-Affine Spaces, we present the most general covariant form of the hypermomentum tensor in an FLRW Universe along with its conservation laws and therefore construct a novel hyperfluid model for Cosmological purposes. Extending the previous model of the unconstrained hyperfluid in a Cosmological setting we establish the conservation laws for energy-momentum and hypermomentum and therefore provide the complete Cosmological setup to study non-Riemannian effects in Cosmology. With the help of this we find the forms of torsion and non-metricity that were earlier reported in the literature and also obtain the most general form of the Friedmann equations with torsion and non-metricity. We also discuss some applications of our model, make contact with the known results in the literature and point to future directions.

Journal ArticleDOI
TL;DR: In this paper, a modified version of the Friedmann-Robertson-Walker (FRW) theory was proposed to explore some viable cosmological models and the Noether equations of this modified theory were solved for two types of models and obtained the symmetry generators as well as corresponding conserved quantities.
Abstract: In this paper, we investigate the newly developed $f(R,\mathbf{T}^2)$ theory ($R$ is the Ricci scalar and $\mathbf{T}^2=T_{\alpha\beta}T^{\alpha\beta},~T _{\alpha\beta}$ demonstrates the energy-momentum tensor) to explore some viable cosmological models. For this purpose, we use the Noether symmetry approach in the context of flat Friedmann-Robertson-Walker (FRW) universe. We solve the Noether equations of this modified theory for two types of models and obtain the symmetry generators as well as corresponding conserved quantities. We also evaluate exact solutions and investigate their physical behavior via different cosmological parameters. For the prospective models, the graphical behavior of these parameters indicate consistency with recent observations representing accelerated expansion of the universe. In the first case, we take a special model of this theory and obtain new class of exact solutions with the help of conserved quantities. Secondly, we consider minimal and non-minimal coupling models of $f(R,\mathbf{T} ^{2})$ gravity. We conclude that conserved quantities are very useful to derive the exact solutions that are used to study the cosmic accelerated expansion.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the consequences of different regularizations and ambiguities in loop cosmological models on the predictions in the scalar and tensor primordial spectrum of the cosmic microwave background using the dressed metric approach.
Abstract: We investigate the consequences of different regularizations and ambiguities in loop cosmological models on the predictions in the scalar and tensor primordial spectrum of the cosmic microwave background using the dressed metric approach. Three models, standard loop quantum cosmology (LQC), and two modified loop quantum cosmologies (mLQC-I and mLQC-II) arising from different regularizations of the Lorentzian term in the classical Hamiltonian constraint are explored for chaotic inflation in spatially flat Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) universe. In each model, two different treatments of the conjugate momentum of the scale factor are considered. The first one corresponds to the conventional treatment in dressed metric approach, and the second one is inspired from the hybrid approach which uses the effective Hamiltonian constraint. For these two choices, we find the power spectrum to be scale-invariant in the ultraviolet regime for all three models, but there is at least a 10% relative difference in amplitude in the infrared and intermediate regimes. All three models result in significant differences in the latter regimes. In mLQC-I, the magnitude of the power spectrum in the infra-red regime is of the order of Planck scale irrespective of the ambiguity in conjugate momentum of the scale factor. The relative difference in the amplitude of the power spectrum between LQC and mLQC-II can be as large as 50% throughout the infrared and intermediate regimes. Differences in amplitude due to regularizations and ambiguities turn out to be small in the ultraviolet regime.

Journal ArticleDOI
TL;DR: In this article, a cosmological model in which dark energy identified with the vacuum energy which is running and decaying is investigated, and different evolutional scenarios admissible for all initial conditions are obtained.
Abstract: We investigate a cosmological model in which dark energy identified with the vacuum energy which is running and decaying. In this model vacuum is metastable and decays into a bare (true) vacuum. This decaying process has a quantum nature and is described by tools of the quantum decay theory of unstable systems. We have found formulas for an asymptotic behavior of the energy density of dark energy in the form of a series of inverse powers of the cosmological time. We investigate the dynamics of FRW models using dynamical system methods as well as searching for exact solutions. From dynamical analysis we obtain different evolutional scenarios admissible for all initial conditions. For the interpretation of the dynamical evolution caused by the decay of the quantum vacuum we study the thermodynamics of the apparent horizon of the model as well as the evolution of the temperature. For the early Universe, we found that the quantum effects modified the evolution of the temperature of the Universe. In our model the adiabatic approximation is valid and the quantum vacuum decay occurs with an adequate unknown particle which constitutes quantum vacuum. We argue that the late-time evolution of metastable energy is the holographic dark energy.

Journal ArticleDOI
TL;DR: In this paper, the FRW model is used to study the cosmological implications of the universe with respect to redshift, and the age of universe is predicted in f(R) gravity.
Abstract: Nojiri and Odintsov (Phys Rev D 68:123512, 2003) and Hu and Sawicki (Phys Rev D 76:064004, 2007) have studied nonlinear functions in modified gravity that explain the cosmic acceleration without cosmological constant, fulfill the conditions of local gravity and stability and pass the solar system tests. In this paper, FRW model, a best fitted and fruitful mathematical model of the physical universe (Astrophys J 82:248, 1935; Proc Natl Acad Sci 15:168, 1929; Phys Rev D 73:80, 1948; Astrophys J 142:419, 1965), is studied in the context of these nonlinear functions. The cosmological implications such as Hubble parameter, deceleration parameter, jerk parameter, matter density and the effective equation of state parameter of the universe are plotted with respect to redshift. Subsequently, the age of the universe is predicted in f(R) gravity. All are found to represent the features of present phase of the universe.

Journal ArticleDOI
TL;DR: In this article, the Tsallis holographic quintessence model of dark energy in gravity with the Hubble horizon as IR cut-off is reconstructed in a flat FRW background.
Abstract: In the present work, we construct the Tsallis holographic quintessence model of dark energy in $f(R, T)$ gravity with Hubble horizon as IR cut-off. In a flat FRW background, the correspondence among the energy density of the quintessence model with the Tsallis holographic density permits the reconstruction of the dynamics and the potentials for the quintessence field. The suggested Hubble horizon infrared cut-off for the THDE density acts for two specific cases: (i) THDE 1 and (ii) THDE 2. We have reconstructed the Tsallis holographic quintessence model in the region $\omega_{\Lambda} > -1$ for the EoS parameter for both the cases. In addition, the quintessence phase of the THDE models is analyzed with swampland conjecture to describe the accelerated expansion of the Universe.

Journal ArticleDOI
TL;DR: In this paper, the authors studied the future of the singular dark universe where thermal effects due to the Hawking radiation on the apparent horizon of the FRW universe are taken in the consideration, and showed that the dark universe which ends up as finite-time Type I and Type III singularity or the infinite-time Little Rip singularity transits to the finite time Type II singularity thanks to account of the thermal effects.

Journal ArticleDOI
TL;DR: In this paper, the authors proposed the minimally extended VSL (meVSL) model and derived cosmological observables of meVSL and obtained the constraints on the variation of the speed of light by using the current observations.
Abstract: Even though there have been the various varying speed of light (VSL) cosmology models, they remain out of the mainstream because of their possible violation of physics laws built into fundamental physics. In order to be the VSL as a viable theory, it should inherit the success of special relativity including Maxwell equations and thermodynamics at least. Thus, we adopt that the speed of light, $\tilde c$ varies for the cosmic time not for the local time, i.e., $\tilde c[z]$ where $z$ is the cosmological redshift. When one describes the background FLRW universe, one can define the constant-time hypersurface by using physical quantities such as temperature, density, and $\tilde c$. It is because they evolve in time, and the homogeneity of the Universe demands that they must equal at the equal cosmic time. The variation of $\tilde c$ accompanies the joint variations of all related physical constants in order to satisfy the Lorentz invariance, thermodynamics, and Bianchi identity. We call this VSL model as a "minimally extended VSL (meVSL)". We derive cosmological observables of meVSL and obtain the constraints on the variation of $\tilde c$ by using the current observations. Interestingly, $z$ and all geometrical distances except the luminosity distance of meVSL are the same as those of general relativity. However, the Hubble parameter of meVSL is rescaled as $H = (1+z)^{-b/4} H^{(\rm GR)}$ which might be used as a solution for the tension of the Hubble parameter measurements. In this manuscript, we provide the main effects of meVSL on various cosmological observations including BBN, CMB, SZE, BAO, SNe, GWs, H, SL, and $\Delta \alpha$.

Journal ArticleDOI
TL;DR: In this paper, the analysis of Tsallis holographic dark energy for a particular choice of positive non-additivity parameter δ in modified f (T, B) gravity with the validity of thermodynamics and energy conditions for a homogeneous and isotropic FLRW Universe has been studied.
Abstract: In this article, the analysis of Tsallis holographic dark energy (which turns into holographic dark energy for a particular choice of positive non-additivity parameter δ) in modified f (T, B) gravity with the validity of thermodynamics and energy conditions for a homogeneous and isotropic FLRW Universe has been studied. The enlightenment of the field equation towards , made possible by the fact that the model is purely accelerating, corresponds to q = −0.54 (Mamon and Das 2017 Eur. Phys. J. C 77 49). The generalized second law of thermodynamics is valid not only for the same temperature inside the horizon, but also for the apparent horizon for a change in temperature. The essential inspiration driving this article is to exhibit the applicability that the holographic dark energy achieved from standard Tsallis holographic dark energy and the components acquired from f(T, B) gravity are identical for the specific bounty of constants. The analysis of energy conditions confirms that the weak energy condition and the null energy condition are fulfilled throughout the expansion, while violation of the strong energy condition validates the accelerated expansion of the Universe. With the expansion, the model becomes a quintessence dominated model. The dominant energy condition is not observed initially when the model is filled with genuine baryonic matter, whereas it appears when the model is in the quintessence dominated era.