Robertson-Walker Spacetimes Research Articles

Noether symmetry approach in scalar-torsion f(T,phi ) gravity

The Noether Symmetry approach is applied to study an extended teleparallel f(T,phi ) gravity that contains the torsion scalar T and the scalar field phi in the context of an Friedmann–Lemaître–Robertson–Walker space-time. We investigate the Noether symmetry approach in f(T,phi ) gravity formalism with the specific form of f(T,phi ) and analyze how to demonstrate a nontrivial Noether vector. The Noether symmetry method is a helpful resource for generating models and finding out the exact solution of the Lagrangian. In this article, we go through how the Noether symmetry approach enables us to define the form of the function f(T,phi ) and obtain exact cosmological solutions. We also find the analytical cosmological solutions to the field equations, that is consistent with the Noether symmetry. Our results demonstrate that the obtained solutions enable an accelerated expansion of the Universe. We have also obtained the present value of the Hubble parameter, deceleration parameter, and effective equation of state parameter, which is fit in the range of current cosmological observations.

Correction to Lagrangian for bouncing cosmologies in f(Q) gravity

Symmetric teleparallel gravity offers to reformulate the gravitational formalism without the presence of curvature and torsion with the help of non-metricity tensors. Interestingly, Symmetric teleparallel gravity can be formulated equivalently to teleparallel gravity or general relativity for an appropriate setup. In this study, our aim lies in exploring the bouncing cosmologies as an alternative to the initial singularity of the Universe in the background of modified symmetric teleparallel gravity. To explore this, we adopt the reconstruction technique to present the possible reconstructed Lagrangian for various cosmological bouncing solutions in a flat Friedmann–Lemaître–Robertson–Walker spacetime with a perfect fluid matter distribution. We study the reconstructed gravitational Lagrangians, which are capable of reproducing analytical or semianalytical solutions for symmetric bounce, super-bounce, oscillatory bounce, matter bounce, and exponential bouncing model settings. Further, we examine the dark energy profiles of the models using reconstructed Lagrangians. In addition, we found that an additional term arises in each reconstructed Lagrangian compared to general relativity (GR). That extra term corrected the background GR to present bouncing cosmology in modified gravity. These newly motivated cosmological models may have an effect on gravitational phenomena at other cosmological scales.

The classical and quantum implications of the Raychaudhuri equation in f(T)-gravity

The present work deals with the classical and quantum aspects of the Raychaudhuri equation (RE) in the framework of f(T)-gravity theory. In the background of homogeneous and isotropic Friedmann–Lemaître–Robertson–Walker space-time, the RE has been formulated and used to examine the focusing theorem and convergence condition for different choices of f(T). Finally in quantum cosmology, the wave function of the Universe has been shown to be the energy eigen function of the time-independent Schrödinger equation of a particle. Also probability measure on the minisuperspace has been examined at zero volume for singularity analysis in the quantum regime. Lastly, the Bohmian trajectory for the present quantum system has been explicitly determined for some particular choices.

On sequential warped product manifolds admitting gradient Ricci-harmonic solitons

We consider sequential warped product manifolds admitting gradient Ricci-harmonic solitons. We give the main relations for a gradient Ricci-harmonic soliton on sequential warped product manifolds. As physical applications, we consider gradient Ricci-harmonic solitons on sequential generalized Robertson-Walker space-times and sequential standard static space-times.

Global bifurcation of positive solutions of a quasilinear indefinite Neumann problem in some FLRW spacetimes

We are concerned with the global structure of the radial positive solution set of the radially symmetric prescribed curvature problem with the Neumann boundary condition in some Friedmann–Lemaître–Robertson–Walker spacetimes. The proof of our main result is based on bifurcation techniques.

Reconstruction of [formula omitted]CDM Universe from Noether symmetries in Chameleon gravity

We apply the Noether symmetries to constrain the unknown functions of chameleon gravity in the cosmological scenario of a spatially flat Friedmann–Lemaître–Robertson–Walker space–time with an ideal gas. For this gravitational model the field equations admit a point-like Lagrangian with as unknown functions the scalar field potential and the coupling function which is responsible for the chameleon mechanism. Noether’s first theorem provides us with four sets of closed-form functional forms for which variational symmetries exist. We construct the corresponding conservation laws and we use them in order to determine new analytic solutions in chameleon gravity. From the analysis of the physical properties of the new solution it follows that in the late universe they can reproduce the ΛCDM model without having to assume the presence of a pressureless fluid in the cosmological fluid.

Dynamical Analysis in Chameleon Dark Energy

AbstractA detailed analysis of the phase‐space for the field equations in scalar field cosmology with a chameleon cosmology in a spatially flat Friedmann–Lemaître–Robertson–Walker spacetime is presented. For the matter source it is assumed that it is an ideal gas with a constant equation of state parameter, while for the scalar field potential and the coupling function of the chameleon mechanism it is considered that four different sets which provide four different models. The H‐normalization approach and the field equations with the help of dimensionless variables written is considered. The asymptotic solutions are determined from where the theory can describe the main eras of cosmological history and evolution that are found. Future attractors which describe acceleration exist; however, acceleration solutions related to the inflationary era is found in past, as also the radiation epoch and the matter dominated eras are provided by the dynamics. The Chameleon dark energy model can be used as a unified model for the elements which contribute to the dark sector of the universe that are concluded.

On Calabi–Bernstein’s Problem for Uniqueness of Complete Spacelike Hypersurfaces in Weighted Generalized Robertson–Walker Spacetimes

In this paper, we study Calabi–Bernstein’s problem for the uniqueness of complete constant weighted mean curvature spacelike hypersurfaces Σn in weighted generalized Robertson–Walker spacetimes −I×ρMfn. Under appropriate geometric assumptions, we confirm that Σn is a spacelike slice.

A new approach to the study of spacelike submanifolds in a spherical Friedmann–Lemaître–Robertson–Walker spacetime: characterization of the stationary spacelike submanifolds as an application

A natural codimension one isometric embedding of each -dimensional spherical Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime in the -dimensional Lorentz–Minkowski spacetime permits to contemplate as a rotation Lorentzian hypersurface in . After a detailed study of such Lorentzian hypersurfaces, any k-dimensional spacelike submanifold of such an FLRW spacetime can be contemplated as a spacelike submanifold of . Then, we use that situation to study k-dimensional stationary (i.e. of zero mean curvature vector field) spacelike submanifolds of the FLRW spacetime. In particular, we prove a wide extension of the Lorentzian version of the classical Takahashi theorem, giving a characterization of stationary spacelike submanifolds of when contemplating them as spacelike submanifolds of .

Ricci solitons on general relativistic spacetimes

The main aim of this manuscript is to characterize the general relativistic spacetimes with Ricci and gradient Ricci solitons. It is proven that if the metric of a general relativistic spacetime (M 4, ξ) admitting a special unit timelike vector field ξ is an almost Ricci soliton (g, ξ, λ), then (M 4, ξ) is a perfect fluid spacetime, and almost Ricci soliton (g, ξ, λ) on (M 4, ξ) becomes shrinking Ricci soliton. We prove that a general relativistic perfect fluid spacetime equipped with a special unit timelike vector field together with a Ricci soliton is an Einstein spacetime. In this sequel, we also prove that the Ricci soliton is shrinking, soliton vector field is Killing and the scalar curvature of the perfect fluid spacetime is constant. It is proven that a general relativistic perfect fluid spacetime together with a Ricci soliton is a generalized Robertson-Walker (GRW) spacetime. The existence of gradient Ricci solitons on general relativistic spacetimes are established. We also construct a non-trivial example of general relativistic spacetime equipped with a special unit timelike vector field, and verify some of our theorems.

Characterizations of a Spacetime of Quasi‐Constant Sectional Curvature and F(R)$\mathcal {F}(\mathcal {R})$‐Gravity

AbstractThe main aim of this article is to investigate a spacetime of quasi‐constant sectional curvature. At first, the existence of such a spacetime is established by several examples. We have shown that a spacetime of quasi‐constant sectional curvature agrees with the present state of the universe and it represents a Robertson Walker spacetime. Moreover, if the spacetime is Ricci semi‐symmetric or Ricci symmetric, then either the spacetime represents a spacetime of constant sectional curvature, or the spacetime represents phantom era. Also, we prove that a Ricci symmetric spacetime of quasi‐constant sectional curvature represents a static spacetime and the spacetime under consideration is of Petrov type I, D or O. Finally, we concentrate on a quasi‐constant sectional curvature spacetime solution in ‐gravity. As a result, various energy conditions are studied and analyzed our obtained outcomes in terms of a ‐gravity model.

Relativistic spacetimes admitting almost Schouten solitons

In this paper, we investigate almost Schouten solitons and almost gradient Schouten solitons in spacetimes of general relativity. At first, it is proven that if a generalized Robertson–Walker spacetime permits an almost Schouten soliton, then it becomes a perfect fluid spacetime as well as the spacetime represents a dark matter era. Besides this, we investigate almost gradient Schouten solitons in generalized Robertson–Walker spacetimes. Moreover, a spacetime obeying almost Schouten solitons whose potential vector field is a non-homothetic conformal vector field is of Petrov type [Formula: see text] or [Formula: see text].

F(Q, T) gravity, its covariant formulation, energy conservation and phase-space analysis

In the present article we analyze the matter-geometry coupled f(Q, T) theory of gravity. We offer the fully covariant formulation of the theory, with which we construct the correct energy balance equation and employ it to conduct a dynamical system analysis in a spatially flat Friedmann–Lemaître–Robertson–Walker spacetime. We consider three different functional forms of the f(Q, T) function, specifically, f(Q,T)=alpha Q+ beta T, f(Q,T)=alpha Q+ beta T^2, and f(Q,T)=Q+ alpha Q^2+ beta T. We attempt to investigate the physical capabilities of these models to describe various cosmological epochs. We calculate Friedmann-like equations in each case and introduce some phase space variables to simplify the equations in more concise forms. We observe that the linear model f(Q,T)=alpha Q+ beta T with beta =0 is completely equivalent to the GR case without cosmological constant Lambda . Further, we find that the model f(Q,T)=alpha Q+ beta T^2 with beta ne 0 successfully depicts the observed transition from decelerated phase to an accelerated phase of the universe. Lastly, we find that the model f(Q,T)= Q+ alpha Q^2+ beta T with alpha ne 0 represents an accelerated de-Sitter epoch for the constraints beta < -1 or beta ge 0.

Phase-Space Analysis of an Einstein–Gauss–Bonnet Scalar Field Cosmology

We perform a detailed study of the phase-space of the field equations of an Einstein–Gauss–Bonnet scalar field cosmology for a spatially flat Friedmann–Lemaître–Robertson–Walker spacetime. For the scalar field potential, we consider the exponential function. In contrast, we assume two cases for the coupling function of the scalar field with the Gauss–Bonnet term: the exponential function and the power–law function. We write the field equations in dimensionless variables and study the equilibrium points using normalized and compactified variables. We recover previous results, but also find new asymptotic solutions not previously studied. Finally, these couplings provide a rich cosmological phenomenology.

On the bifurcation of spacelike hypersurfaces with constant mean curvature in spacetimes

In a time-oriented Lorentzian manifold M‾n+1, we use equivariant bifurcation theory in order to establish sufficient conditions that allow us to guarantee the existence of bifurcation instants or the local rigidity of family {Ωτ} of open sets of M‾n+1 whose boundaries ∂Ωτ are closed (compact without boundary) spacelike H-hypersurfaces, this is, closed spacelike hypersurfaces with constant mean curvature H. In particular, we do this study for a certain family of open sets in a spatially closed generalized Robertson-Walker spacetime, namely, Lorentz warped products (−I×fMn,−dt2+f2〈,〉M) with 1-dimensional negative definite base (I,−dt2), closed Riemannian fiber (Mn,〈,〉M) and warping function f:I→(0,+∞). In this case, the results are obtained considering some appropriate hypotheses that depend of f and of the behavior of the eigenvalues of Laplacian operator of Mn. Applications to such families in some spacetimes, like the de Sitter space, are also given.

Some physical properties of generalized quasi-Einstein spacetimes under Gray’s decomposition

In this study, we analyze generalized quasi-Einstein spacetimes endowed with Gray’s decomposition, as well as generalized Robertson–Walker spacetimes. It is shown that the Ricci tensor of a generalized quasi-Einstein spacetime assumes the form of a perfect fluid in all Gray’s subspaces under certain restrictions. Finally, it is established that a generalized quasi-Einstein generalized Robertson–Walker spacetime is a perfect fluid spacetime.

Matter bounce scenario in extended symmetric teleparallel gravity

In this paper, we have shown the matter bounce scenario of the Universe in an extended symmetric teleparallel gravity, the f(Q) gravity. Motivated from the bouncing scenario and loop quantum cosmology (LQC), the form of the function f(Q) has been obtained at the backdrop of Friedmann–Lema{hat{i}}tre–Robertson Walker (FLRW) space time. Considering the background cosmology dominated by dust fluid, the e-folding parameter has been expressed, which contains the nonmetricity term. Since the slow roll criterion in the bouncing context is not valid, we used a conformal equivalence between f(Q) and scalar-tensor model to apply the bottom-up reconstruction technique in the bouncing model. The dynamics of the model has been studied through the phase space analysis, where both the stable and unstable nodes are obtained. Also, the stability analysis has been performed with the first order scalar perturbation of the Hubble parameter and matter energy density to verify the stability of the model.

Characterizations of -flat curvature tensor on spacetimes and -gravity

The prime goal of this article is to characterize spacetimes endowed with -flat curvature tensor. It is demonstrated that a 4-dimensional -flat perfect fluid spacetime is either a de-Sitter spacetime or locally isometric to Minkowski spacetime under certain energy condition. Moreover, it is established that a Ricci simple -flat spacetime becomes a Robertson-Walker spacetime. In addition, we shown that a Ricci simple spacetime with harmonic -curvature tensor is a generalized Robertson-Walker spacetime. Also, we explain several conclusions based on -flat generalized Robertson-Walker spacetimes. Finally, we investigate -flat spacetimes that satisfy the -gravity and -gravity.

Hyperbolic Ricci soliton on warped product manifolds

In this paper, we investigate hyperbolic Ricci soliton as the special solution of hyperbolic geometric flow on warped product manifolds. Then, especially, we study these manifolds admitting either a conformal vector field or a concurrent vector field. Also, the question that:? whether or not a hyperbolic soliton reduces to an Einstein manifold?? is considered and answered. Finally, we obtain some necessary conditions for generalized Robertson-Walker space-time to be a hyperbolic Ricci soliton.

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.