Flat Friedmann Lemaitre Robertson Walker Research Articles

Study of Particle Creation with Quadratic Equation of State in Higher Derivative Theory

We investigate the effect of particle creation in flat Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime under the higher derivative theory composition. The exact solution of the field equation in higher derivative theory is obtained by considering the quadratic equation of state, p = ωρ2 − ρ and different forms of deceleration parameter. The physical acceptance and stability of the models are explored by discussing energy conditions and squared sound speed. In addition to that, the statefinder diagnostic pair {r,s} is also scrutinized to measure the deviation of considered models from Λ cold dark matter (ΛCDM) model.

Tsallis holographic dark energy with hybrid expansion law

In this work, we explore the Tsallis holographic dark energy (THDE) model with IR cutoff as Granda–Oliveros horizon describing the Universe experiencing an accelerating expansion phase in the framework of flat Friedmann–Lemaître–Robertson–Walker (FLRW) Universe. The Universe evolution from earlier decelerated to the current accelerated phase is exhibited by the deceleration parameter acquired in the THDE model. By the value of the Tsallis parameter [Formula: see text], the equation of state (EoS) parameter for the THDE model represents the rich behavior of the Cosmos as, the quintessence era ([Formula: see text]), crossing the phantom divide line and phantom era ([Formula: see text]). The squared sound speed [Formula: see text] also suggests that the THDE model is classically stable at present. Also, the correspondence with the quintessence and phantom scalar field for the THDE model is analyzed to describe the accelerated expansion of the Universe.

Understanding the phenomenology of interacting dark energy scenarios and their theoretical bounds

Non-gravitational interaction between dark matter and dark energy has been considered in a spatially flat Friedmann-Lema\^{i}tre-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.

First order QED processes in a spatially flat FLRW space-time with a Milne-type scale factor

The quantum electrodynamics (QED) in a spatially flat (1+3)-dimensional Friedmann-Lemaître-Robertson-Walker (FLRW) space-time with a Milne-type scale factor is outlined focusing on the amplitudes of the allowed processes in the first order perturbations. The definition of the transition rates is reconsidered such that an appropriate angular behavior of the probability for creation of an electron-positron pair from a photon is obtained, which has a similar rate as the creation of a photon and an electron-positron pair from vacuum. It is shown that these processes are allowed only in the first order perturbations, since the photon emission or absorption by an electron or positron are forbidden.

Variable Chaplygin gas cosmologies in f(R, T) gravity with particle creation

A flat FLRW (Friedmann–Lemaitre–Robertson–Walker) cosmological model with perfect fluid comprising of variable Chaplygin gas (VCG) has been studied in the context of f(R, T) gravity with particle creation. The solutions of the modified field equations are obtained through three different considered form of scale factors. The effective pressure is negative throughout the evolution of universe, which leads to accelerated expansion of the universe. In addition to that we have also discussed the importance of particle creation pressure on the cosmological parameters, energy conditions and state-finder diagnostic parameters. It is noticed that the time evolution of source function yields almost constant particle production at late times.

Transit cosmological model with specific Hubble parameter in F(R, T) gravity

In this paper, we have investigated a flat FLRW (Friedmann Lemaitre Robertson Walker metric) cosmological model in f(R, T) gravity with specific Hubble parameter. We have considered f(R,T)=f(R)+2f(T) where f(R)=R+αR2,f(T)=λT and R is Ricci scalar, T the trace of energy momentum tensor. To obtain exact solutions of modified Einstein’s field equation, we have considered a specific Hubble parameter H(a)=l(a−n+k) which gives the scale factor a(t)=[ekln(t+m)−1k]1n where n > 0, k, l, m are arbitrary constants called model parameters. With this scale factor, we have obtained a transit phase cosmological model with variable deceleration parameter (DP). We have compared our results with observational constraints obtained from various observations by using the curve-fitting techniques and found that the derived model is a transit dark energy model quintessence (ω>−1) at present (ω0≈−0.7406) and approaches to cosmological constant value (ω=−1) at late time universe. The transition point is found as ztc≈0.676 which is in good agreement with the recent observations. Also, the derived model explains formation of different structures in the universe from past to present scenarios.

The Lambert W Function: A Newcomer in the Cosmology Class?

Abstract We propose a novel equation of state (EoS) which explains the evolutionary history of a flat Friedmann–Lemaitre–Robertson–Walker universe. The uniqueness of this EoS lies in the fact that it incorporates the Lambert W function in a special fashion. It is explicitly demonstrated that with observationally relevant values of the unknown parameters ϑ 1 and ϑ 2, all the evolutionary phases of the universe can be reproduced. Moreover, it also shows that the initial singularity is unavoidable and asserts that the late-time acceleration of the universe would continue forever.

Global existence of smooth solution to 2D relativistic membrane equation in asymptotically flat FLRW space‐time

This paper is concerned with the 2D relativistic membrane equation evolving in curved space‐time, whose metric is prescribed as a small perturbation to the flat Friedmann‐Lemaître‐Robertson‐Walker (FLRW) metric with time‐dependent coefficients. Thanks to the partial “null structure” of the membrane equation and the properties of the background metric, we could prove the global stability of a class of time‐dependent solutions by weighted energy estimate.

Decay of solutions of the wave equation in expanding cosmological spacetimes

We study the decay of solutions of the wave equation in some expanding cosmological spacetimes, namely flat Friedmann–Lemaître–Robertson–Walker (FLRW) models and the cosmological region of the Reissner–Nordström–de Sitter (RNdS) solution. By introducing a partial energy and using an iteration scheme, we find that, for initial data with finite higher order energies, the decay rate of the time derivative is faster than previously existing estimates. For models undergoing accelerated expansion, our decay rate appears to be (almost) sharp.

Propagators of the Dirac fermions on spatially flat FLRW space–times

The general formalism of the free Dirac fermions on spatially flat (1[Formula: see text]+[Formula: see text]3)-dimensional Friedmann-Lemaître–Robertson–Walker (FLRW) space–times is developed in momentum representation. The mode expansions in terms of the fundamental spinors satisfying the charge conjugation and normalization conditions are used for deriving the structure of the anticommutator matrix-functions and, implicitly, of the retarded, advanced, and Feynman fermion propagators. The principal result is that the new type of integral representation we proposed recently in the de Sitter case can be applied to the Dirac fermions in any spatially flat FLRW geometry. Moreover, the Dirac equation of the left-handed massless fermions can be analytically solved finding a general spinor solution and deriving the integral representations of the neutrino propagators. It is shown that in the Minkowski flat space–time our new integral representation is up to a change of variable just like the usual Fourier representation of the fermion propagators. The form of the Feynman propagator of the massive fermions on a spatially flat FLRW space–time with a scale factor of Milne-type is also outlined.

Gauge-ready formulation of cosmological perturbations in scalar-vector-tensor theories

In scalar-vector-tensor (SVT) theories with parity invariance, we perform a gauge-ready formulation of cosmological perturbations on the flat Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) background by taking into account a matter perfect fluid. We derive the second-order action of scalar perturbations and resulting linear perturbation equations of motion without fixing any gauge conditions. Depending on physical problems at hand, most convenient gauges can be chosen to study the development of inhomogeneities in the presence of scalar and vector fields coupled to gravity. This versatile framework, which encompasses Horndeski and generalized Proca theories as special cases, is applicable to a wide variety of cosmological phenomena including nonsingular cosmology, inflation, and dark energy. By deriving conditions for the absence of ghost and Laplacian instabilities in several different gauges, we show that, unlike Horndeski theories, it is possible to evade no-go arguments for the absence of stable nonsingular bouncing/genesis solutions in both generalized Proca and SVT theories. We also apply our framework to the case in which scalar and vector fields are responsible for dark energy and find that the separation of observables relevant to the evolution of matter perturbations into tensor, vector, and scalar sectors is transparent in the unitary gauge. Unlike the flat gauge chosen in the literature, this result is convenient to confront SVT theories with observations associated with the cosmic growth history.

Cosmological Bounce and Some Other Solutions in Exponential Gravity

In this work, we present some cosmologically relevant solutions using the spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime in metric f ( R ) gravity where the form of the gravitational Lagrangian is given by 1 α e α R . In the low curvature limit this theory reduces to ordinary Einstein-Hilbert Lagrangian together with a cosmological constant term. Precisely because of this cosmological constant term this theory of gravity is able to support nonsingular bouncing solutions in both matter and vacuum background. Since for this theory of gravity f ′ and f ″ is always positive, this is free of both ghost instability and tachyonic instability. Moreover, because of the existence of the cosmological constant term, this gravity theory also admits a de-Sitter solution. Lastly we hint towards the possibility of a new type of cosmological solution that is possible only in higher derivative theories of gravity like this one.

Stable Big Bang formation in near-FLRW solutions to the Einstein-scalar field and Einstein-stiff fluid systems

We prove a stable blowup result for solutions to the Einstein-scalar field and Einstein-stiff fluid systems. Our result applies to small perturbations of the spatially flat Friedmann–Lemaitre–Robertson–Walker (FLRW) solution with topology $$(0,\infty ) \times \mathbb {T}^3$$ . The FLRW solution models a spatially uniform scalar-field/stiff fluid evolving in a spacetime that expands towards the future and that has a “Big Bang” singularity at $$\lbrace 0 \rbrace \times \mathbb {T}^3$$ , where various curvature invariants blow up. We place “initial” data on a Cauchy hypersurface $$\Sigma _1'$$ that are close, as measured by a Sobolev norm, to the FLRW data induced on $$\lbrace 1 \rbrace \times \mathbb {T}^3$$ . We then study the asymptotic behavior of the perturbed solution in the collapsing direction and prove that its basic qualitative and quantitative features closely resemble those of the FLRW solution. In particular, for the perturbed solution, we construct constant mean curvature-transported spatial coordinates covering $$(t,x) \in (0,1] \times \mathbb {T}^3$$ and show that it also has a Big Bang at $$\lbrace 0 \rbrace \times \mathbb {T}^3$$ , where its curvature blows up. The blowup confirms Penrose’s Strong Cosmic Censorship hypothesis for the “past-half” of near-FLRW solutions. Furthermore, we show that the equations are dominated by kinetic (that is, time-derivative-involving) terms that induce approximately monotonic behavior near the Big Bang. As a consequence of the monotonicity, we also show that various time-rescaled components of the solution converge to regular functions of x as $$t \downarrow 0$$ . The most difficult aspect of the proof is showing that the solution exists for $$(t,x) \in (0,1] \times \mathbb {T}^3$$ , and to this end, we derive a hierarchy of energy estimates that allow for the possibility of mild energy blowup as $$t \downarrow 0$$ . To close these estimates, it is essential that we are able to rule out more singular energy blowup, a step that is in turn tied to the most important ingredient in our analysis: a collection of integral identities that, when combined in the right proportions, yield an $$L^2$$ -type approximate monotonicity inequality, a key point being that the error terms are controllable up to the singularity for near-FLRW solutions. In a companion article, we derived similar approximate monotonicity inequalities for linearized versions of the Einstein-scalar field equations and used them to prove linear stability results for a family of spatially homogeneous background solutions. The present article shows that the linear stability of the FLRW background solution can be upgraded to a full proof of the nonlinear stability of its singularity.

Note on bouncing backgrounds

The theory of inflation is one of the fundamental and revolutionary developments of modern cosmology that became able to explain many issues of early universe in the context of the standard cosmological model (SCM). However, the initial singularity of the universe, where physics is indefinite, is still obscure in the combined `SCM+inflation' scenario. An alternative to `SCM+inflation' without the initial singularity is thus always welcome, and bouncing cosmology is an attempt of that. The current work is thus motivated to investigate the bouncing solutions in modified gravity theories when the background universe is described by the spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) geometry. We show that the simplest way to obtain the bouncing cosmologies in such spacetime is to consider some kind of Lagrangians whose gravitational sector depends only on the square of the Hubble parameter of the FLRW universe. For these modified Lagrangians, the corresponding Friedmann equation, a constraint in the dynamics of the universe, depicts a curve in the phase space $(H,rho)$, where $H$ is the Hubble parameter and $rho$ being the energy density of the universe. As a consequence, a bouncing cosmology is obtained when this curve is closed and crosses the axis $H = 0$ at least twice, and whose simplest particular example is the ellipse depicting the well-known holonomy corrected Friedmann equation in Loop Quantum Cosmology (LQC). Sometimes, a crucial point in such theories is the appearance of the Ostrogradski instability at the perturbative level, however, fortunately enough, in the present work as long as the linear level of perturbations is concerned, this instability does not appear but such instability may appear at the higher-order of perturbations.

Statefinder diagnostic for modified Chaplygin gas cosmology in f(R,T) gravity with particle creation

In this paper, we have studied flat Friedmann–Lemaître–Robertson–Walker (FLRW) model with modified Chaplygin gas (MCG) having equation of state [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] is any positive constant in [Formula: see text] gravity with particle creation. We have considered a simple parametrization of the Hubble parameter [Formula: see text] in order to solve the field equations and discussed the time evolution of different cosmological parameters for some obtained models showing unique behavior of scale factor. We have also discussed the statefinder diagnostic pair [Formula: see text] that characterizes the evolution of obtained models and explore their stability. The physical consequences of the models and their kinematic behaviors have also been scrutinized here in some detail.

Cosmological Van Der Waals Model with Viscosity in an Inflationary Universe

The evolution of the Universe in the early (inflationary) stage of its development in the spatially flat Friedmann–Lemaitre–Robertson–Walker metric is considered. A theoretical model, described by a van der Waals fluid with the effect of bulk viscosity taken into account is investigated. A solution of the gravitation equation for the energy density is found and an analytical expression for the scale factor has been obtained. To verify the reliability of the cosmological model, the inflation parameters, the spectral index, and the scalartensor ratio were calculated. A comparison of these parameters with data obtained from observations of the Planck satellites is carried out. Conditions for the applicability of the van der Waals model with viscosity to the description of an inflationary Universe are obtained.

Exact solutions, finite time singularities and non-singular universe models from a variety of Λ(t) cosmologies

Cosmological models with time-dependent [Formula: see text] (read as [Formula: see text]) have been investigated widely in the literature. Models that solve background dynamics analytically are of special interest. Additionally, the allowance of past or future singularities at finite cosmic time in a specific model signals for a generic test on its viabilities with the current observations. Following these, in this work we consider a variety of [Formula: see text] models focusing on their evolutions and singular behavior. We found that a series of models in this class can be exactly solved when the background universe is described by a spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) line element. The solutions in terms of the scale factor of the FLRW universe offer different universe models, such as power-law expansion, oscillating, and the singularity free universe. However, we also noticed that a large number of the models in this series permit past or future cosmological singularities at finite cosmic time. At last we close the work with a note that the avoidance of future singularities is possible for certain models under some specific restrictions.

Dark energy survivals in massive gravity after GW170817: SO(3) invariant

The recent detection of the gravitational wave signal GW170817 together with an electromagnetic counterpart GRB 170817A from the merger of two neutron stars puts a stringent bound on the tensor propagation speed. This constraint can be automatically satisfied in the framework of massive gravity. In this work, we consider a general SO(3)-invariant massive gravity with five propagating degrees of freedom and derive the conditions for the absence of ghosts and Laplacian instabilities in the presence of a matter perfect fluid on the flat Friedmann-Lemaître-Robertson-Walker (FLRW) cosmological background. The graviton potential containing the dependence of three-dimensional metrics and a fiducial metric coupled to a temporal scalar field gives rise to a scenario of the late-time cosmic acceleration in which the dark energy equation of state wDE is equivalent to −1 or varies in time. We find that the deviation from the value wDE=−1 provides important contributions to the quantities associated with the stability conditions of tensor, vector, and scalar perturbations. In concrete models, we study the dynamics of dark energy arising from the graviton potential and show that there exist viable parameter spaces in which neither ghosts nor Laplacian instabilities are present for both wDE>−1 and wDE<−1. We also generally obtain the effective gravitational coupling Geff with non-relativistic matter as well as the gravitational slip parameter ηs associated with the observations of large-scale structures and weak lensing. We show that, apart from a specific case, the two quantities Geff and ηs are similar to those in general relativity for scalar perturbations deep inside the sound horizon.

Thermodynamics and cosmological reconstruction inf(T,B)gravity

Abstract Recently, it was formulated a teleparallel theory called f ( T , B ) gravity which connects both f ( T ) and f ( R ) under suitable limits. In this theory, the function in the action is assumed to depend on the torsion scalar T and also on a boundary term related with the divergence of torsion, B = 2 ∇ μ T μ . In this work, we study different features of a flat Friedmann–Lemaitre–Robertson–Walker (FLRW) cosmology in this theory. First, we show that the FLRW equations can be transformed to the form of Clausius relation T ˆ h S eff = − d E + W d V , where T ˆ h is the horizon temperature and S eff is the entropy which contains contributions both from horizon entropy and an additional entropy term introduced due to the non-equilibrium. We also formulate the constraint for the validity of the generalised second law of thermodynamics (GSLT). Additionally, using a cosmological reconstruction technique, we show that both f ( T , B ) and − T + F ( B ) gravity can mimic power-law, de-Sitter and Λ CDM models. Finally, we formulate the perturbed evolution equations and analyse the stability of some important cosmological solutions.

Universal features of quantum bounce in loop quantum cosmology

In this Letter, we study analytically the evolutions of the flat Friedmann–Lemaitre–Robertson–Walker (FLRW) universe and its linear perturbations in the framework of the dressed metric approach in loop quantum cosmology (LQC). Assuming that the evolution of the background is dominated by the kinetic energy of the inflaton at the quantum bounce, we find that both evolutions of the background and its perturbations are independent of the inflationary potentials during the pre-inflationary phase. During this period the effective potentials of the perturbations can be well approximated by a Pöschl–Teller (PT) potential, from which we find analytically the mode functions and then calculate the corresponding Bogoliubov coefficients at the onset of the slow-roll inflation, valid for any inflationary model with a single scalar field. Imposing the Bunch–Davies (BD) vacuum in the contracting phase prior to the bounce when the modes are all inside the Hubble horizon, we show that particles are generically created due to the pre-inflation dynamics. Matching them to those obtained in the slow-roll inflationary phase, we investigate the effects of the pre-inflation dynamics on the scalar and tensor power spectra and find features that can be tested by current and forthcoming observations. In particular, to be consistent with the Planck 2015 data, we find that the universe must have expanded at least 141 e-folds since the bounce.