Friedmann Lemaitre Robertson Walker Spacetime Research Articles

A Scale-Dependent Distance Functional between Past Light Cones in Cosmology

We discuss a rigorous procedure for quantifying the difference between our past light cone and the past light cone of the fiducial Friedmann–Lemaitre–Robertson–Walker spacetime, modeling the large-scale descriptions of cosmological data in the standard ΛCDM scenario. This result is made possible by exploiting the scale-dependent distance functional between past light cones recently introduced by us. We express this harmonic map-type functional in terms of the physical quantities that characterize the actual measurements along our past light cone, namely the area distance and the lensing distortion, also addressing the very delicate problem of the presence of light cone caustics. This analysis works beautifully and seems to remove several of the difficulties encountered in comparing the actual geometry of our past light cone with the geometry of the fiducial FLRW light cone of choice. We also discuss how, from the point of view of the FLRW geometry, this distance functional may be interpreted as a scale-dependent effective field, the pre-homogeneity field, which may be of relevance in selecting the FLRW model that best fits the observational data.

Circuit Complexity from Cosmological Islands

Recently, in various theoretical works, path-breaking progress has been made in recovering the well-known page curve of an evaporating black hole with quantum extremal islands, proposed to solve the long-standing black hole information loss problem related to the unitarity issue. Motivated by this concept, in this paper, we study cosmological circuit complexity in the presence (or absence) of quantum extremal islands in negative (or positive) cosmological constant with radiation in the background of Friedmann-Lemai^tre-Robertson-Walker (FLRW) space-time, i.e., the presence and absence of islands in anti de Sitter and the de Sitter space-time having SO(2, 3) and SO(1, 4) isometries, respectively. Without using any explicit details of any gravity model, we study the behavior of the circuit complexity function with respect to the dynamical cosmological solution for the scale factors for the above mentioned two situations in FLRW space-time using squeezed state formalism. By studying the cosmological circuit complexity, out-of-time ordered correlators, and entanglement entropy of the modes of the squeezed state, in different parameter space, we conclude the non-universality of these measures. Their remarkably different features in the different parameter space suggests their dependence on the parameters of the model under consideration.

Propagation of quantum gravity-modified gravitational waves on a classical FLRW spacetime

The linearized Einstein field equations provide a low-energy wave equation for the propagation of gravitational fields which may originate from a high energy source. Motivated by loop quantum gravity, we propose the polymer quantization scheme to derive the effective propagation of such waves on a classical Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime. To overcome the challenge of polymer quantizing a time-dependent Hamiltonian, we rewrite such a Hamiltonian in a time-independent manner in the extended phase space, polymerize it, and then transform it back to the usual phase space. In this way we obtain a time-dependent polymer Hamiltonian for the gravitational waves. We then derive the effective equations of motion and show that (i) the form of the waves is modified, (ii) the speed of the waves depends on their frequencies, and (iii) quantum effects become more apparent as waves traverse longer distances.

Off-Shell Noether Currents and Potentials for First-Order General Relativity

We report off-shell Noether currents obtained from off-shell Noether potentials for first-order general relativity described by n-dimensional Palatini and Holst Lagrangians including the cosmological constant. These off-shell currents and potentials are achieved by using the corresponding Lagrangian and the off-shell Noether identities satisfied by diffeomorphisms generated by arbitrary vector fields, local SO(n) or SO(n−1,1) transformations, ‘improved diffeomorphisms’, and the ‘generalization of local translations’ of the orthonormal frame and the connection. A remarkable aspect of our approach is that we do not use Noether’s theorem in its direct form. By construction, the currents are off-shell conserved and lead naturally to the definition of off-shell Noether charges. We also study what we call the ‘half off-shell’ case for both Palatini and Holst Lagrangians. In particular, we find that the resulting diffeomorphism and local SO(3,1) or SO(4) off-shell Noether currents and potentials for the Holst Lagrangian generically depend on the Immirzi parameter, which holds even in the ‘half off-shell’ and on-shell cases. We also study Killing vector fields in the ‘half off-shell’ and on-shell cases. The current theoretical framework is illustrated for the ‘half off-shell’ case in static spherically symmetric and Friedmann–Lemaitre–Robertson–Walker spacetimes in four dimensions.

The null and force-free electromagnetic field

This paper describes the electrodynamics of a null and force-free field in completely geometric terms. As was previously established in Menon (2020 Class. Quantum Grav. 37 245006), solutions to force-free electrodynamics are governed by the existence of certain special types of foliations of spacetime. Here the nature of the foliations in a coordinate-free formalism in the null case is prescribed. All of the general results are illustrated by constructing a new null, force-free electrodynamic field in a Friedmann–Lemaitre–Robertson–Walker spacetime.

Polar modes of gravitational waves in Rastall cosmology

In this article, we discuss propagation expressions for polar gravitational waves in the spatially flat Friedmann–Lemaitre–Robertson–Walker spacetime dominated by a perfect fluid in the Rastall theory. We perturb the spatially flat spacetime description by making use of Regge–Wheeler perturbations inducing the polar gravitational waves and formulate the corresponding field equations for both unperturbed and perturbed cases. Then, we focus on these field equations simultaneously to find out the unknown perturbation functions. We attain that the assumed perturbations affect the background matter distribution as well as the four-velocity components. We also investigate the impact of model parameters on the amplitude of the polar gravitational waves.

Bianchi-I cosmology within f(T): Reconstruction method and dynamical study

This paper is fundamentally devoted to the cosmological reconstruction and dynamic studying in homogeneous BIANCHI-I space-time under the [Formula: see text] background. Its content is supported by the fact that in the General Relativity description of the standard cosmological paradigm, the evolution from an anisotropic universe into an Friedmann–Lemaitre–Robertson–Walker (FLRW) one can be achieved by a period of inflationary expansion. Nowadays, modified gravity theories like [Formula: see text] are widely accepted to provide a real description of some universe evolution phases like inflation era, matter-dominated era, etc. So, we aim to examine here what [Formula: see text] gravity model can accommodate with an anisotropic universe, an expanding universe and even the transition between both evolutions. To reach this goal, we use a reconstruction method based on dynamic equations in Bianchi-I space-time by assuming a particular form for the metric anisotropy and by specifying some time functions describing average scale factor. Most of the obtained models are consistent with certain known results in the literature but other add new results in this work. In the second part of this work, the dynamical behaviors of the Bianchi-I space-time are addressed through the reconstruction of an autonomous dynamical system. For an aleatory choice of anisotropic fluid, the numerical analysis of the system shows that the metric anisotropy decreases with expansion. Then, an attractor point is reached and becomes unstable by the end of inflation. Such interesting properties found in this work on Bianchi-I space-time are often interpreted as graceful exit from inflation which doesn’t occur in ordinary FLRW space-time.

How Extra Symmetries Affect Solutions in General Relativity

To get exact solutions to Einstein’s field equations in general relativity, one has to impose some symmetry requirements. Otherwise, the equations are too difficult to solve. However, sometimes, the imposition of too much extra symmetry can cause the problem to become somewhat trivial. As a typical example to illustrate this, the effects of conharmonic flatness are studied and applied to Friedmann–Lemaitre–Robertson–Walker spacetime. Hence, we need to impose some symmetry to make the problem tractable, but not too much so as to make it too simple.

Klein Gordon Field in FLRW Space-Time

As a continuation of solving the equations governing the perturbation of the Friedmann-Lemaitre-Robertson- Walker (FLRW) space-time in Newman-Penrose formalism, the behaviour of the massive Klein-Gordon (KG) field coupled to the FLRW has been investigated. The Equation of Motion has been written and solved separately for radial and temporal parts. The former solution has come to be in terms of the Gegenbauer polynomials and spherical harmonics and the latter being in the WKB approximation. The particle current, energy momentum tensor and potential have also been obtained.

Uniformly accelerated traveler in an FLRW universe

This paper provides an analytical treatment of accelerated and geodesic motion within the framework of the Friedmann -Lemaitre-Robertson-Walker (FLRW) spacetime. By employing conformal time transformations we manage to convert second order differential equations of motion in FLRW spacetime to first order equations in the conformally transformed spacetime. This allows us to derive a general analytical solution in closed-form for accelerated motion in spatially curved FLRW spacetime. We provide few examples of this general solution for the spatially flat cases. The last part of our work focuses on the return journey for a traveler exploring a FLRW universe. We derive certain condition for de Sitter universe that must be satisfied in order to have an actual return journey.

Global dynamics of the Hořava–Lifshitz cosmological system

Using the qualitative theory of the differential equations we describe the global dynamics of the cosmological model based on Hořava–Lifshitz gravity in a Friedmann–Lemaitre–Robertson–Walker space time with zero curvature and without the cosmological constant term.

Stable singularity-free cosmological solutions in nonprojectable Hořava-Lifshitz gravity

We find stable singularity-free cosmological solutions in non-flat Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) spacetime in the context of Ho\v{r}ava-Lifshitz (HL) theory. Although we encounter the negative squared effective masses of the scalar perturbations in the original HL theory, the behaviors can be remedied by relaxing the projectability condition. In our analysis, the effects from the background dynamics are taken into account as well as the sign of the coefficients in the quadratic action for perturbations. More specifically, we give further classification of the gradient stability/instability into five types. These types are defined in terms of the effective squared masses of perturbations $\mathcal{M}^2$, the effective friction coefficients in perturbation equations $\mathcal{H}$ and these magnitude relations $|\mathcal{M}^2|/\mathcal{H}^2$. Furthermore, we indicate that oscillating solutions possibly show a kind of resonance especially in open FLRW spacetime. We find that the higher order spatial curvature terms with Lifshitz scaling $z=3$ are significant to suppress the instabilities due to the background dynamics.

Holographic approach for dark energy–dark matter interaction in curved FLRW spacetime

In this work we explore under a holographic approach, the dark energy–dark matter interaction in a non-flat Friedmann–Lemaitre–Robertson–Walker spacetime, with a cut-off for the dark energy component given in terms of the Hubble scale. Based on results coming from the use of observational data, we consider a positive interaction Q-term together with a Chevallier–Polarsky–Linder type parametrization for the coincidence parameter, we realize that the model admits a Type III future singularity, in this singular universe we have that for a null value of the curvature parameter its scale factor is a constant value. With the use of some cosmological parameters constrained with observational data, we obtain that the crossing of the phantom divide is possible. Once the singular nature is obtained for the model, its Statefinder diagnosis reveals a behavior that is far from the Λ-CDM model.

Exact geodesic distances in FLRW spacetimes

Geodesics are used in a wide array of applications in cosmology and astrophysics. However, it is not a trivial task to efficiently calculate exact geodesic distances in an arbitrary spacetime. We show that in spatially flat (3+1)-dimensional Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetimes, it is possible to integrate the second-order geodesic differential equations, and derive a general method for finding both timelike and spacelike distances given initial-value or boundary-value constraints. In flat spacetimes with either dark energy or matter, whether dust, radiation, or a stiff fluid, we find an exact closed-form solution for geodesic distances. In spacetimes with a mixture of dark energy and matter, including spacetimes used to model our physical universe, there exists no closed-form solution, but we provide a fast numerical method to compute geodesics. A general method is also described for determining the geodesic connectedness of an FLRW manifold, provided only its scale factor.

Toroidal marginally outer trapped surfaces in closed Friedmann-Lemaître-Robertson-Walker spacetimes: Stability and isoperimetric inequalities

We investigate toroidal Marginally Outer Trapped Surfaces (MOTS) and Marginally Outer Trapped Tubes (MOTT) in closed Friedmann-Lemaitre-Robertson-Walker (FLRW) geometries. They are constructed by embedding Constant Mean Curvature (CMC) Clifford tori in a FLRW spacetime. This construction is used to assess the quality of certain isoperimetric inequalities, recently proved in axial symmetry. Similarly to spherically symmetric MOTS existing in FLRW spacetimes, the toroidal ones are also unstable.

Stability of singularity-free cosmological solutions in Hořava-Lifshitz gravity

We study stability of singularity-free cosmological solutions with positive cosmological constant based on projectable Ho\v{r}ava-Lifshitz (HL) theory. In HL theory, the isotropic and homogeneous cosmological solutions with bounce can be realized if spacial curvature is non-zero. By performing perturbation analysis around non-flat Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime, we derive a quadratic action and discuss the stability, i.e, ghost and tachyon-free conditions. Although the squared effective mass of scalar perturbation must be negative in infrared regime, we can avoid tachyon instability by considering strong Hubble friction. Additionally, we estimate the backreaction from the perturbations on background geometry, especially, against anisotropic perturbation in closed FLRW spacetime. It turns out that certain types of bouncing solution may be spoiled even if all perturbation modes are stable.

Cosmological models in alternative theory of gravity with bilinear deceleration parameter

In this paper we have studied the exact solution of modified EFE (Einstein’s field equations) within the scope of spatially homogeneous and isotropic FLRW (Friedmann-Lemaitre-Robertson-Walker) space-time in scalar-tensor BD (Brans-Dicke) theory of gravity. For the purpose we have proposed DP (Deceleration Parameter) $q$ as a bilinear function of proper cosmic time $t$ as $q = \frac{\alpha (1-t)}{1+t}$ and $q = -\frac{\alpha t}{1+t}$ , here $\alpha $ is a non-negative constant. As per requirement we have already addressed the various aspects of cosmological models. Physical and geometric properties of the models have been also presented.

Cosmological evolution with the cubic order field derivative coupling

We investigate cosmological evolution in the scalar–tensor theory with the field derivative coupling to the double-dual of the Riemann tensor (the cubic-type theory). The theory can be seen as the straightforward extension of the scalar–tensor with the quadratic order field derivative coupling to the Einstein tensor (the quadratic-type theory). Both the field derivative couplings to the Einstein tensor and the double-dual of the Riemann tensor have been argued in terms of the successful realization of the self-tuning of the cosmological constant within the Horndeski theory. Assuming the constant potential given by the sum of the cosmological constant and the quantum vacuum energy, the shift symmetry for the scalar field and no matter fields, in the spatially-flat Friedmann–Lemaitre–Robertson–Walker spacetime, we can reduce the set of the field equations to the first-order ordinary nonlinear differential equation for the Hubble parameter, showing the existence of the self-tuned and runaway de Sitter solutions, in addition to the standard de Sitter solutions in general relativity and the finite Hubble singularities which can be reached within the finite time. We then argue the possible cosmological evolution in terms of the values of the effective cosmological constant, the kinetic coupling constants and the initial Hubble parameter. Although the behavior of the universe around each of the de Sitter solutions as well as the finite time singularities is very similar in both theories, we find that the crucial difference appears in terms of no bounce or turnaround behavior across the vanishing Hubble parameter as well as no limitation for the range of the Hubble parameter in the cubic-type theory.

Lindquist-Wheeler formulation of lattice universes

This paper examines the properties of `lattice universes' wherein point masses are arranged in a regular lattice on space-like hypersurfaces; open, flat, and closed universes are considered. The universes are modelled using the Lindquist-Wheeler (LW) approximation scheme, which approximates the space-time in each lattice cell by Schwarz\-schild geometry. Extending Lindquist and Wheeler's work, we derive cosmological scale factors describing the evolution of all three types of universes, and we use these scale factors to show that the universes' dynamics strongly resemble those of Friedmann-Lema\^itre-Robertson-Walker (FLRW) universes. In particular, we use the scale factors to make more salient the resemblance between Clifton and Ferreira's Friedmann-like equations for the LW models and the actual Friedmann equations of FLRW space-times. Cosmological redshifts for such universes are then determined numerically, using a modification of Clifton and Ferreira's approach; the redshifts are found to closely resemble their FLRW counterparts, though with certain differences attributable to the `lumpiness' in the underlying matter content. Most notably, the LW redshifts can differ from their FLRW counterparts by as much as 30\%, even though they increase linearly with FLRW redshifts, and they exhibit a non-zero integrated Sachs-Wolfe effect, something which would not be possible in matter-dominated FLRW universes without a cosmological constant.

Multiple field modified gravity and localized energy in teleparallel framework

This work is devoted to drive an energy-momentum complex (due to matter and fields including gravity) in the realm of modified teleparallel gravity. For this purpose, the Lagrangian of teleparallel theory is extended to a more general form by replacing the torsion scalar with an arbitrary function of it. Furthermore, considering cosmological perturbations, we explicitly calculate energy distribution associated with the Friedmann–Lemaitre–Robertson–Walker spacetime. Finally, we discuss also the coupling case between matter and gravity in the context of teleparallel modified theory.