Flat FLRW Spacetime Research Articles

A flat FLRW model with dynamical Λ as function of matter and geometry

We revisit the evolution of the scale factor in a flat FLRW spacetime with a new generalized decay rule for the dynamic Λ-term under modified theories of gravity. It analyzes certain cosmological parameters and examines their behaviours in this generalized setting which includes several decay laws in the literature. We have also obtained observational constraints on various model parameters and estimated the present values of cosmological parameters {Ωm0, ΩΛ0, q0,t0, ω0} and have discussed with various observational results. Finite time past and future singularities in this model are also discussed.

Holography and black holes in asymptotically flat FLRW spacetimes

In this paper, we extend the treatment of asymptotically decelerating spatially flat Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) spacetimes initiated in [M. E. Rojo and T. Heckelbacher, Phys. Rev. D 103, 064009 (2021).]. We show that a certain class of those metrics is ruled by the asymptotic algebra $\mathfrak{b}\mathfrak{m}{\mathfrak{s}}_{s}$, which belongs to a one-parameter family of deformations of $\mathfrak{b}\mathfrak{m}\mathfrak{s}$. Furthermore, we enlarge our ansatz to include $\text{Diff}({S}^{2})$ transformations whose asymptotic algebra $\mathfrak{g}\mathfrak{b}\mathfrak{m}{\mathfrak{s}}_{s}$ is a one-parameter deformation of $\mathfrak{g}\mathfrak{b}\mathfrak{m}\mathfrak{s}$. Therefore, the holographic algebras $\mathfrak{b}\mathfrak{m}{\mathfrak{s}}_{s}$ and $\mathfrak{g}\mathfrak{b}\mathfrak{m}{\mathfrak{s}}_{s}$ in FLRW can be related to their flat counterparts through a cosmological holographic flow. Finally, we introduce a logarithmic ansatz in order to account for cosmological black holes, which does not generally satisfy the peeling property but preserves the asymptotic algebra.

Dynamical system analysis of self-interacting three-form field cosmological model: stability and bifurcation

The present work deals with Cosmological model of a three-form field, minimally coupled to gravity and interacting with cold dark matter in the background of flat FLRW space-time. By suitable choice of the dimensionless variables, the evolution equations are converted to an autonomous system and cosmological study is done by dynamical system analysis. The critical points are determined and the stability of the (non-hyperbolic) equilibrium points are examined by center manifold Theory. Possible bifurcation scenarios have been examined by the Poincaré index theory to identify possible cosmological phase transition. Also stabilities of the critical points have been analyzed globally using geometric features.

On Nash theory of gravity with matter contents

One of the alternative theories to Einstein’s general theory, a divergence-free theory was proposed by J. Nash with Lagrangian density given by [Formula: see text]. Although it was proved that the Nash theory does not have classical Einstein limits, it has been proven to be formally divergent free and considered to be of interest in constructing theories of quantum gravity. The original Nash gravity without matter contents cannot explain the current acceleration expansion of the Universe. A possible extension of theory is by adding some matter contents to the model. In this work, we generalize Nash theory of gravity by adding the matter fields. In order to examine the effects of this generalization, we first derive the equations of motion in the flat FLRW space–time 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 and check the consistency of the model by considering particular cosmological parameters.

Time evolution of the free Dirac field in spatially flat FLRW space–times

The framework of the relativistic quantum mechanics on spatially flat FLRW space–times is considered for deriving the analytical solutions of the Dirac equation in different local charts of these manifolds. Systems of commuting conserved operators are used for determining the fundamental solutions as common eigenspinors giving thus physical meaning to the integration constants related to the eigenvalues of these operators. Since these systems, in general, are incomplete on the FLRW space–times there are integration constants that must be fixed by setting the vacuum either as the traditional adiabatic one or as the rest frame vacuum we proposed recently. All the known solutions of the Dirac equation on these manifolds are discussed in all details and a new type of spherical waves of given energy in the de Sitter expanding universe is reported here for the first time.

Quasilocal conservation laws in cosmology: A first look

Quasilocal definitions of stress-energy–momentum—that is, in the form of boundary densities (in lieu of local volume densities) — have proven generally very useful in formulating and applying conservation laws in general relativity. In this Essay, we take a basic look into applying these to cosmology, specifically using the Brown–York quasilocal stress-energy–momentum tensor for matter and gravity combined. We compute this tensor and present some simple results for a flat FLRW spacetime with a perfect fluid matter source. We emphasize the importance of the vacuum energy, which is almost universally underappreciated (and usually “subtracted”), and discuss the quasilocal interpretation of the cosmological constant.

Dynamical system analysis of three-form field dark energy model with baryonic matter

A cosmological model having matter field as (non) interacting dark energy (DE) and baryonic matter and minimally coupled to gravity is considered in the present work with flat FLRW space time. The DE is chosen in the form of a three-form field while radiation and dust (i.e; cold dark matter) are the baryonic part. The cosmic evolution is studied through dynamical system analysis of the autonomous system so formed from the evolution equations by suitable choice of the dimensionless variables. The stability of the non-hyperbolic critical points are examined by Center manifold theory and possible bifurcation scenarios have been examined.

Rest frame vacua of massive Klein\u2013Gordon fields on spatially flat FLRW spacetimes

We propose a method of projecting the quantum states from a state space of a given geometry into another state space generated by a different geometry, taking care of the correct normalization which is crucial in interpreting the quantum theory. Thanks to this method we can define on any spatially flat FLRW spacetime states in which genuine Minkowskian parameters are measured. We use these Minkowskian states for separating the frequencies in the rest frames of the massive scalar particles defining thus the scalar rest frame vacuum. We show that this vacuum is stable on the de Sitter expanding universe where the energy is conserved. In contrast, on a spatially flat FLRW spacetime with a Milne-type scale factor this vacuum is found to be dynamic, corresponding to a time-dependent rest energy interpreted as an effective mass. This dynamic vacuum gives rise to cosmological particle creation which is significant only in the early Milne-type universe considered here. Some interesting features of this new effect are pointed out in a brief analysis.

Non-zero torsion and late cosmology

In this work, we study some thermodynamical aspects associated with torsion in a flat FLRW spacetime cosmic evolution. By implementing two Ansatze for the torsion term, we find that the model admits a phantom regime or a quintessence behavior. This scheme differs from the Lambda CDM model at the thermodynamical level. The resulting cosmic expansion is not adiabatic, the fulfillment of the second law of thermodynamics requires a positive torsion term, and the temperature of the cosmic fluid is always positive. The entropy of the torsion phantom scenario is negative, but introducing chemical potential solves this issue. For a Dirac-Milne type Universe, the torsion leads to a growing behavior for the temperature of the fluid but has no incidence on the rate of expansion.

A new class of f(R)-gravity model with wormhole solutions and cosmological properties

A spherically symmetric wormhole family of solutions, with null red-shift, in the context of f(R)-gravity is presented. The model depends on two parameters: m and beta and meets all requirements to be an asymptotically and traversable wormhole. To solve the field equations, an EoS is imposed: p_{perp }=-rho . It is found that for m=1 the solution satisfies the null energy condition, although F(R)<0 everywhere. For m=0, the model satisfies the null energy condition away from the throat, where the function F(R) is everywhere positive and together with dF(R)/dR vanish at the throat of the wormhole. This fact is beyond the scope of the non-existence theorem. Furthermore, the cosmological viability of the model, to address the late – time accelerated epoch, is analyzed on the background of a flat FLRW space-time. The model satisfies consistency of local gravity tests, stability under cosmological perturbations, ghosts free and stability of the de Sitter point.

Higher derivative and mimetic models on non flat FLRW space–times

Abstract An effective Lagrangian approach, partly inspired by Quantum Loop Cosmology (QLC), is presented and formulated in a non flat FLRW space–times, making use of modified gravitational models. The models considered are non generic, and their choice is dictated by the necessity to have at least second order differential equations of motion in a non flat FLRW space–time. This is accomplished by a class of Lagrangian which are not analytic in the curvature invariants, or making use of a mimetic gravitational scalar field. In this paper we want to show that, for some effective models, although the associated generalized Friedmann equation may admit non singular metrics as solutions, the de Sitter space–time is present only for a restricted class, which includes General Relativity and Lovelock gravity. The other models admit pseudo de Sitter solutions, namely FLRW metrics, such that for vanishing spatial curvature looks like flat de Sitter patch, but for non vanishing spatial curvature are regular bounce metrics or, when the spatial curvature is negative, Big-Bang singular metrics.

Evolution of scalar and vector cosmological perturbations through a bounce in metric f(R) gravity in flat FLRW spacetime

In the present work we present the full treatment of scalar and vector cosmological perturbations in a non-singular bouncing universe in the context of metric f(R) cosmology. Scalar metric perturbations in f(R) cosmology were previously calculated in the Jordan frame, in the present paper we successfully use the Einstein frame to calculate the scalar metric perturbations where the cosmological bounce takes place in the Jordan frame. The Einstein frame picture presented corrects and completes a previous calculation of scalar perturbations and adds new information. Behavior of fluid velocity potential and the pure vector fluid velocity terms are elaborately calculated for the first time in f(R) cosmology for a bouncing universe in presence of exponential gravity. It is shown that the vector perturbations can remain bounded and almost constant during the non-singular bounce in f(R) gravity unlike general relativistic models where we expect the vector perturbations to be growing during the contracting phase and decaying during the expanding phase. The paper shows that the Einstein frame can be used for calculation of scalar and vector metric perturbations in a bouncing universe for most of the cases except the case of asymmetric non-singular bounces.

Scalar fields and the FLRW singularity

The dynamics of multiple scalar fields on a flat FLRW spacetime can be described entirely as a relational system in terms of the matter alone. The matter dynamics is an autonomous system from which the geometrical dynamics can be inferred, and this autonomous system remains deterministic at the point corresponding to the singularity of the cosmology. We show the continuation of this system corresponds to a parity inversion at the singularity, and that the singularity itself is a surface on which the space-time manifold becomes non-orientable.

A non-canonical scalar field cosmological model: Stability and bifurcation analysis

In this work, cosmological implications of a non-canonical scalar field model have been studied in the background of homogeneous and isotropic flat FLRW spacetime by using dynamical system analysis. By suitable change of variables, the field equations are transformed to an autonomous system and the stability of the system of critical points are examined. For hyperbolic critical points, the analysis of the system is done by using Hartman–Grobman theorem, while the center manifold theory is used to study non-hyperbolic critical points. It is found that the parameters in the autonomous system play a crucial role for phase transition of the Universe. Finally, possible bifurcation scenarios are discussed to identify the point of phase transition.

Quantum Cramer–Rao Bound for a Massless Scalar Field in de Sitter Space

How precisely can we estimate cosmological parameters by performing a quantum measurement on a cosmological quantum state? In quantum estimation theory, the variance of an unbiased parameter estimator is bounded from below by the inverse of measurement-dependent Fisher information and ultimately by quantum Fisher information, which is the maximization of the former over all positive operator-valued measurements. Such bound is known as the quantum Cramer –Rao bound. We consider the evolution of a massless scalar field with Bunch–Davies vacuum in a spatially flat FLRW spacetime, which results in a two-mode squeezed vacuum out-state for each field wave number mode. We obtain the expressions of the quantum Fisher information as well as the Fisher informations associated to occupation number measurement and power spectrum measurement, and show the specific results of their evolution for pure de Sitter expansion and de Sitter expansion followed by a radiation-dominated phase as examples. We will discuss these results from the point of view of the quantum-to-classical transition of cosmological perturbations and show quantitatively how this transition and the residual quantum correlations affect the bound on the precision.

Adiabatic regularization with a Yukawa interaction

We extend the adiabatic regularization method for an expanding universe to include the Yukawa interaction between quantized Dirac fermions and a homogeneous background scalar field. We give explicit expressions for the renormalized expectation values of the stress-energy tensor $\langle T_{\mu\nu} \rangle$ and the bilinear $\langle \bar\psi\psi\rangle$ in a spatially flat FLRW spacetime. These are basic ingredients in the semiclassical field equations of fermionic matter in curved spacetime interacting with a background scalar field. The ultraviolet subtracting terms of the adiabatic regularization can be naturally interpreted as coming from appropriate counterterms of the background fields. We fix the required covariant counterterms. To test our approach we determine the contribution of the Yukawa interaction to the conformal anomaly in the massless limit and show its consistency with the heat kernel method using the effective action.

Late-time behaviour of Israel particles in a FLRW spacetime with Λ > 0

In this paper we study the space-homogeneous Boltzmann equation in a spatially flat FLRW spacetime. We consider Israel particles, which are the relativistic counterpart of the Maxwellian particles, and obtain global-in-time existence and the asymptotic behaviour of solutions. The main argument of the paper is to use the energy method of Guo, and we observe that the method can be applied to study small solutions in a cosmological case. It is the first result of this type where a physically well-motivated scattering kernel is considered for the general relativistic Boltzmann equation.

Cosmological memory effect

The ``memory effect'' is the permanent change in the relative separation of test particles resulting from the passage of gravitational radiation. We investigate the memory effect for a general, spatially flat Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) cosmology by considering the radiation associated with emission events involving particle-like sources. We find that if the resulting perturbation is decomposed into scalar, vector, and tensor parts, only the tensor part contributes to memory. Furthermore, the tensor contribution to memory depends only on the cosmological scale factor at the source and observation events, not on the detailed expansion history of the universe. In particular, for sources at the same luminosity distance, the memory effect in a spatially flat FLRW spacetime is enhanced over the Minkowski case by a factor of ($1+z$).

Spin1/2field and regularization in a de Sitter and radiation dominated universe

We construct a simple algorithm to derive number density of spin 1/2 particles created in spatially flat FLRW spacetimes and resulting renormalized energy-momentum tensor within the framework of adiabatic regularization. Physical quantities thus found are in agreement with the known results. This formalism can be considered as an appropriate extension of the techniques originally introduced for scalar fields, applicable to fermions in curved space. We apply this formalism to compute the particle number density and the renormalized energy density and pressure analytically (wherever possible) and numerically, in two interesting cosmological scenarios: a de Sitter spacetime and a radiation dominated universe. Results prove the efficiency of the methodology presented here.

Intricacies of cosmological bounce in polynomial metric f(R) gravity for flat FLRW spacetime

In this paper we present the techniques for computing cosmological bounces in polynomial f(R) theories, whose order is more than two, for spatially flat FLRW spacetime. In these cases the conformally connected Einstein frame shows up multiple scalar potentials predicting various possibilities of cosmological evolution in the Jordan frame where the f(R) theory lives. We present a reasonable way in which one can associate the various possible potentials in the Einstein frame, for cubic f(R) gravity, to the cosmological development in the Jordan frame. The issue concerning the energy conditions in f(R) theories is presented. We also point out the very important relationships between the conformal transformations connecting the Jordan frame and the Einstein frame and the various instabilities of f(R) theory. All the calculations are done for cubic f(R) gravity but we hope the results are sufficiently general for higher order polynomial gravity.