Robertson Walker Space Research Articles

Noether symmetry in new extended modified f(R,G,T) theory of gravity

This study is dedicated to investigate the Noether symmetry approach in a newly introduced gravitational theory known as [Formula: see text] gravity, where [Formula: see text] is the function of Ricci scalar [Formula: see text], trace of energy–momentum tensor [Formula: see text], and the Gauss–Bonnet invariant term [Formula: see text]. The Noether symmetry approach plays a supportive role in generating models and then determining the exact solutions by using the conserved quantities. For this purpose, the flat Friedmann–Robertson–Walker space–time is selected to observe cosmic evolution. The set of partial differential equations is calculated in the background [Formula: see text] modified theory gravity. We further examine the four different [Formula: see text] gravity models and calculate the conserved quantities to investigate the exact solutions. The three models show the increasing behavior of the cosmic scale factor that supports the expansion of universe. In fourth model, we are able to get the corresponding conserved quantity only and it is anticipated that this model will also support the expansion of universe.

FLRW Transit Cosmological Model in f (R, T) Gravity

A Friedmann–Lemaitre–Robertson–Walker space–time model with all curvatures k=0, ±1 is explored in f(R,T) gravity, where R is the Ricci scalar, and T is the trace of the energy–momentum tensor. The solutions are obtained via the parametrization of the scale factor that leads to a model transiting from a decelerated universe to an accelerating one. The physical features of the model are discussed and analyzed in detail. The study shows that f(R,T) gravity can be a good alternative to the hypothetical candidates of dark energy to describe the present accelerating expansion of the universe.

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.

Stability Properties of Self-Similar Solutions in Symmetric Teleparallel f(Q)-Cosmology

Self-similar cosmological solutions correspond to spacetimes that admit a homothetic symmetry. The physical properties of self-similar solutions can describe important eras of the cosmological evolution. Recently, self-similar cosmological solutions were derived for symmetric teleparallel fQ-theory with different types of connections. In this work, we study the stability properties of the self-similar cosmological solutions in order to investigate the effects of the different connections on the stability properties of the cosmic history. For the background geometry, we consider the isotropic Friedmann–Lemaître–Robertson–Walker space and the anisotropic and homogeneous Bianchi I space, for which we investigate the stability properties of Kasner-like universes.

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.

Qualitative study of Lyra cosmologies with spatial curvature

We investigate the spatially curved Friedmann–Robertson–Walker space–time with Lyra geometry model. The cosmological solutions are studied by using dynamical system methodology to explore the universe evolution in the model. The constructed autonomous system has been explored to extract the physically viable cosmological solutions by studying the behavior of eigenvalues at the fixed points of the system. Late-time attractor solution corresponding to the accelerated expansion exist in the model and thus, the model may explain the late-time accelerating expansion of universe. The model is also composed of deceleration to acceleration transition with Λ cold dark matter evolution at late-times. The evolution of cosmological parameters like deceleration parameter , effective equation of state parameter, total matter density and role of energy conditions with scale factor have been studied along with statefinder diagnostic to explain the universe evolution in the model. By dynamical system analysis, it has been observed that the displacement field plays a dominant role during the early times and, the universe is dominated by stiff matter like component. Implications of bouncing behavior in the model with role of energy conditions and continuity equation have been discussed in detail along with their physical consequences. • Lyra geometry model with FRW metric having spatial curvature is investigated. • Dynamical system method has been used to extract the cosmic dynamics of model. • The model explains late-time accelerating evolution of universe. • Cosmological parameters are studied by integrating the dynamical variables. • We illustrate that the fixed point corresponding to radiation phase is absent.

Dynamics of tachyonic dark matter

Usually considered highly speculative, tachyons can be treated via straightforward Einsteinian dynamics. Kinetic theory and thermodynamics for a gas of “dark” tachyons are readily constructed. Such a gas exhibits density and pressure which, for the dominant constituent of a suitable Friedmann–Robertson–Walker space–time, can drive cosmic evolution with features both similar to and distinct from those of a standard dark-energy/dark-matter model. Hence, tachyons might bear further consideration as a cosmic dark-matter candidate.

Curvature conditions for spatial isotropy

In the context of mathematical cosmology, the study of necessary and sufficient conditions for a semi-Riemannian manifold to be a (generalized) Robertson-Walker space-time is important. In particular, it is a requirement for the development of initial data to reproduce or approximate the standard cosmological model. Usually these conditions involve the Einstein field equations, which change if one considers alternative theories of gravity or if the coupling matter fields change. Therefore, the derivation of conditions which do not depend on the field equations is an advantage. In this work we present a geometric derivation of such a condition. We require the existence of a unit vector field to distinguish at each point of space two (non-equal) sectional curvatures. This is equivalent for the Riemann tensor to adopt a specific form. Our geometrical approach yields a local isometry between the space and a Robertson-Walker space of the same dimension, curvature and metric tensor sign (the dimension of the largest subspace on which the metric tensor is negative definite). Remarkably, if the space is simply-connected, the isometry is global. Our result generalizes to a class of spaces of non-constant curvature the theorem that spaces of the same constant curvature, dimension and metric tensor sign must be locally isometric. Because we do not make any assumptions regarding field equations, matter fields or metric tensor sign, one can readily use this result to study cosmological models within alternative theories of gravity or with different matter fields.

Bouncing scenario of general relativistic hydrodynamics in extended gravity

In this paper, we have framed bouncing cosmological model of the Universe in the presence of general relativistic hydrodynamics in an extended theory of gravity. The metric assumed here is the flat Friedmann–Robertson–Walker space–time and the stress energy tensor is of perfect fluid. Since general relativity (GR) has certain issues with late time cosmic speed up phenomena, here we have introduced an additional matter geometry coupling that described the extended gravity to GR. The dynamical parameters are derived and analyzed. The dynamical behavior of the equation of state parameter has been analyzed. We have observed that the bouncing behavior is mostly controlled by the coupling parameter.

Codimension Two Spacelike Submanifolds Through a Null Hypersurface in a Lorentzian Manifold

Most important examples of null hypersurfaces in a Lorentzian manifold admit an integrable screen distribution, which determines a spacelike foliation of the null hypersurface. In this paper, we obtain conditions for a codimension two spacelike submanifold contained in a null hypersurface to be a leaf of the (integrable) screen distribution. For this, we use the rigging technique to endow the null hypersurface with a Riemannian metric, which allows us to apply the classical Eschenburg maximum principle. We apply the obtained results to classical examples as generalized Robertson–Walker spaces and Kruskal space.

Global dynamics for a charged and colliding plasma in presence of a massive scalar field on the Robertson–Walker spacetime

We consider the coupled Einstein–Maxwell–Boltzmann system with cosmological constant in presence of a massive scalar field. The background metric is that of Friedman–Lemaitre–Robertson–Walker space time in the spatially homogeneous case where the unknown functions only depend on time and not on the space variables $$(x^i)$$ , $$i=1,2,3$$ . By combining the energy estimates method with that of characteristics we derive under suitable conditions on the collision kernel [see (2.20)], a local (in time) solution of the coupled system. Further, under the hypotheses that the data are small in some appropriate norms and that the cosmological constant satisfies $$\Lambda > -4\pi m^2\Phi _0^2$$ , we derive a unique global (in time) solution (Theorem 6.1).

Curvature and thermal corrections in tree-level CPT-Violating Leptogenesis

In a model for leptogenesis based on spontaneous breaking of Lorentz and mathcal {CPT} symmetry [1–3], we examine the consistency of using the approximation of plane-wave solutions for a free spin-frac{1}{2} Dirac (or Majorana) fermion field propagating in a Friedmann–Lemahat{mathrm{i}}tre–Robertson–Walker space time augmented with a cosmic time-dependent (or, equivalently, a temperature-dependent) Kalb–Ramond (KR) background. For the range of parameters relevant for leptogenesis, our analysis fully justifies the use of plane-wave solutions in our study of leptogenesis with Boltzmann equations; any corrections induced by space-time-curvature are negligible. We also elaborate further on how the lepton asymmetry is communicated to the Baryon sector. We demonstrate that the KR background (KRB) does not contribute to the anomaly equations that determine the baryon asymmetry (a) through an explicit evaluation of a triangle Feynman graph and (b) indirectly, on topological grounds, by identifying the KRB as torsion (in the effective string-inspired low energy gravitational field theory).

Isoperimetric problems for spacelike domains in generalized Robertson–Walker spaces

We use a locally constrained mean curvature flow to prove the isoperimetric inequality for spacelike domains in generalized Robertson-Walker spaces satisfying the null convergence condition.

Solution of Einstein’s Equations for a Closed Null String with Axial Symmetry that Is Radially Increasing Its Size

A solution to the Einstein equations for a closed null string with axial symmetry that is radially increases its size is found. The possibility of choosing the ideal gas of null strings as a dominant source of gravity is confirmed in the study of the null string inflation mechanism in Friedmann–Robertson–Walker spaces. The absence of a limit transition between the solution that is found and the solution for a closed circular null string that is radially changing its size is shown. This indicates the stability of the configuration of a closed circular null string during its motion in an external gravitational field. It is noted that part of the characteristics of the null string gas, such as the ability to form a domain structure and existence of stable polarized states (multi-string systems), are independent of the shape of null string, but the dynamics of the test null string in a field of such multi-string system has singularities.

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.

Investigating cosmology with equation of state

The aim of this paper is to investigate the field equations of modified [Formula: see text] theory of gravity, where R and [Formula: see text] represent the Ricci scalar and scalar potential, respectively. We consider the Friedmann–Robertson–Walker space–time for finding some exact solutions by using different values of equation of state parameter. In this regard, different possibilities of the exact solutions have been discussed for dust universe, radiation universe, ultra-relativistic universe, sub-relativistic universe, stiff universe, and dark energy universe. Mainly power law and exponential forms of the scale factor are chosen for the analysis.

On null submanifolds of generalized Robertson–Walker space forms

We investigate totally umbilical $r$-null submanifolds of generalized Robertson-Walker space forms. Using generalized Newton transformations, we obtain new geometric configurations for the mean curvature functions which generalize many well-known results on null geometry.

A cosmological basis for E = mc2

The Universe has a gravitational horizon with a radius [Formula: see text] coincident with that of the Hubble sphere. This surface separates null geodesics approaching us from those receding, and as free-falling observers within the Friedmann–Lemaître–Robertson–Walker space–time, we see it retreating at proper speed [Formula: see text], giving rise to the eponymously named cosmological model [Formula: see text]. As of today, this cosmology has passed over 20 observational tests, often better than [Formula: see text]CDM. The gravitational radius [Formula: see text] therefore appears to be highly relevant to cosmological theory, and in this paper we begin to explore its impact on fundamental physics. We calculate the binding energy of a mass [Formula: see text] within the horizon and demonstrate that it is equal to [Formula: see text]. This energy is stored when the particle is at rest near the observer, transitioning to a purely kinetic form equal to the particle’s escape energy when it approaches [Formula: see text]. In other words, a particle’s gravitational coupling to that portion of the Universe with which it is causally connected appears to be the origin of rest-mass energy.

Influence of Linear Plus Quadratic Interactions Between Dark Components of the Universe on Thermodynamics

We work with the holographic model of interacting dark sector (dark energy plus dark matter) of the universe. The generalized Chaplygin gas model is taken as a Dark Energy (DE) candidate, and it interacts with Cold Dark Matter (CDM) in the framework of linear plus quadratic equation of state (EoS) parameter. We study the effect of interaction on the thermodynamics of the universe. Three interaction parameters of DE-CDM are considered: ΓρDE, ΓρDM, and Γ(ρDE + ρDM). We derive the corresponding effective equation of states for these different interaction parameters and analyze the behaviors of the derivative of entropies for DE, CDM and the apparent horizon, which is considered as a boundary of the universe. For this purpose the Generalized Second Law (GSL) of thermodynamics is used in the Friedman- Robertson-Walker (FRW) space to analyze the effect of quadratic terms on the thermodynamics of the universe, and the results are analyzed and compared with the solution for the linear form given in the literature.

Correction to: New Properties on Normalized Null Hypersurfaces

There is a mistake in the last subsection (5.3 Totally geodesic null hypersurfaces in Robertson–Walker spaces) of the paper [1]