Flat Friedman Robertson Walker Research Articles

Reconstruction in the Horndeski theory within the scope of the Bianchi I cosmology

In this paper, [R. K. Muharlyamov and T. N. Pankratyeva, Eur. Phys. J. Plus 136, 590 (2021)] we have proposed a reconstruction method for the kinetic gravity braiding theory in the framework of the flat Friedman–Robertson–Walker spacetime. Here, we develop this method in the Bianchi I spacetime model for a subclass of the Horndeski theory: [Formula: see text], [Formula: see text], [Formula: see text]. The Hubble parameter [Formula: see text] and the canonical kinetic term [Formula: see text] are set a priori. The choice of the function [Formula: see text] determines the anisotropic properties of the Universe. This makes it possible to provide believable anisotropy. The presented method allows for a realistic model of the Universe to simply reconstruct some scalar field theory. Reconstruction example is given for anisotropic model of a post-inflationary transition to the radiation-dominated phase. The model is investigated for the absence ghosts and Laplacian instabilities.

Reconstruction method in the kinetic gravity braiding theory with shift-symmetric

We present a reconstruction method for flat Friedman-Robertson-Walker (FRW) spacetime in a subclass of Horndeski theory -- specifically shiftsymmetric, the kinetic gravity braiding (KGB) theory with a non-vanishing conserved current. Choosing the form of the Hubble parameter and kinetic density $X$, we restore the functions $G_2$, $G_3$ of the KGB model. In order to determine whether the model is free of ghosts and Laplacian instabilities and thus cosmologically viable, two conditions related to scalar perturbations are checked. Initially, the Lagrangian does not include the term that describes, for example, the perfect fluid with the EoS parameter $w\neq -1$. This fluid can provide a dynamic solution $H(t)$, $X(t)$. In the presented method, dynamic solutions are provided by a nonzero scalar charge associated with the shift symmetry $\phi\rightarrow\phi+\phi_0$. Reconstruction examples are given for models: an perfect fluid, a unified description dark energy-dark matter, a post-inflationary transition to the radiation-dominated phase.

Qualitative Analysis of the Dynamics of a Two-Component Chiral Cosmological Model

We present a qualitative analysis of chiral cosmological model (CCM) dynamics with two scalar fields in the spatially flat Friedman–Robertson–Walker Universe. The asymptotic behavior of chiral models is investigated based on the characteristics of the critical points of the selfinteraction potential and zeros of the metric components of the chiral space. The classification of critical points of CCMs is proposed. The role of zeros of the metric components of the chiral space in the asymptotic dynamics is analysed. It is shown that such zeros lead to new critical points of the corresponding dynamical systems. Examples of models with different types of zeros of metric components are represented.

Reconstructing the k-essence and the dilation field models of the THDE in f(R, T) gravity

Inspired by the work of Chattopadhyay et al. (Eur Phys J C 74(9):3080, 2014. https://doi.org/10.1140/epjc/s10052-014-3080-3 ) and Yang et al. (Mod Phys Lett A 26:191, 2011. https://doi.org/10.1142/S0217732311034682 ), we examine the energy density explained via $$\rho _{\Lambda }=3\beta ^{2}M^{2}_{p}H^{-2\delta +4}$$ for the Tsallis holographic dark energy (THDE) model in the framework of f(R, T) gravity. In the structure of f(R, T) gravity, the correspondence between the scalar-field models of the k-essence and the dilation with the THDE is investigated by us. The correspondence among the Tsallis holographic density with the k-essence and the dilation densities permits the reconstruction of the dynamics and the potentials for the k-essence and the dilation field models, in a flat FRW (Friedman–Robertson–Walker) Universe. We have reconstructed the Tsallis holographic k-essence and the dilation fields models in the region $$\omega _{\Lambda } >-1$$ for the EoS parameter for the different Tsallis parameter $$\delta $$ . By investigation, we observe that for the THDE k-essence and the dilation models, the accelerated expansion can be obtained in the f(R, T) gravity if the related parameters satisfy some constraints.

Noether symmetries and boundary terms in extended Teleparallel gravity cosmology

We discuss an extended Teleparallel gravity models comprising functions of scalar invariants constructed by torsion, torsion Gauss–Bonnet and boundary terms. We adopt the Noether symmetry approach to select the functional forms, the first integrals and, eventually, the exact solutions of the dynamics in the context of flat Friedman–Robertson–Walker cosmology. Standard perfect fluid matter, minimally coupled to geometry, is considered. Several physically consistent models are derived with related exact solutions.

Thermodynamics of event horizon with modified Hawking temperature in scalar-tensor gravity

In recent past, Hawking temperature has been modified for the validity of thermodynamical laws at the event horizon in general relativity context. This lead to the introduction of modified Hawking temperature and it has been found that the modified Hawking temperature is more realistic on the event horizon. With this motivation, here we investigate the thermodynamical consistency of scalar-tensor gravity based models by examining the validity of the generalized second law of thermodynamics (GSLT) and thermodynamical equilibrium (TE) at the event horizon. In order to attain our goal, we consider a spatially flat Friedman–Robertson–Walker Universe filled with ordinary matter and the boundary of the Universe bounded by the event horizon that is in thermal equilibrium with modified Hawking temperature. Next, we calculate the general expressions for the GSLT and TE using modified Hawking temperature in the context of the more general action of scalar-tensor gravity where there is a non-minimally coupling between the scalar field and matter Lagrangian (as the chameleon field). From the general expression of GSLT, we find that the null energy condition must hold for a viable scalar-tensor model of the Universe dominated by a perfect fluid. Furthermore, in order to better understand these complicated general expressions of GSLT and TE, we explore the validity of the GSLT and TE for two viable models of scalar-tensor gravity namely Brans–Dicke gravity with a self-interacting potential and Chameleon gravity at the event horizon using special cosmological solutions. Finally, some graphical representation of the GSLT and TE have been presented. From the graphical analysis, we found that the power-law forms of the scale factor and scalar field is much favourable for the study of universal thermodynamics as compared to other choices of the scalar field and the analytic function.

Exact scalar–tensor cosmological models

Scalar–tensor gravitational theories are important extensions of standard general relativity, which can explain both the initial inflationary evolution, as well as the late accelerating expansion of the universe. In the present paper, we investigate the cosmological solution of a scalar–tensor gravitational theory, in which the scalar field [Formula: see text] couples to the geometry via an arbitrary function [Formula: see text]. The kinetic energy of the scalar field as well as its self-interaction potential [Formula: see text] are also included in the gravitational action. By using a standard mathematical procedure, the Lie group approach, and Noether symmetry techniques, we obtain several exact solutions of the gravitational field equations describing the time evolutions of a flat Friedman–Robertson–Walker universe in the framework of the scalar–tensor gravity. The obtained solutions can describe both accelerating and decelerating phases during the cosmological expansion of the universe.

Dirac Field as a Source of the Inflation in2+1Dimensional Teleparallel Gravity

In this paper, we study early-time inflation and late-time acceleration of the universe by nonminimally coupling the Dirac field with torsion in the spatially flat Friedman-Robertson-Walker (FRW) cosmological model background. The results obtained by the Noether symmetry approach with and without a gauge term are compared. Additionally, we compare these results with that of the3+1dimensional teleparallel gravity under Noether symmetry approach. And we see that the study explains early-time inflation and late-time acceleration of the universe.

Angular diameter distances reconsidered in the Newman and Penrose formalism

Using the Newman and Penrose spin coefficient (NP) formalism, we provide a derivation of the Dyer-Roeder equation for the angular diameter distance in cosmological space-times. We show that the geodesic deviation equation written in NP formalism is precisely the Dyer-Roeder equation for a general Friedman-Robertson-Walker (FRW) space-time, and then we examine the angular diameter distance to redshift relation in the case that a flat FRW metric is perturbed by a gravitational potential. We examine the perturbation in the case that the gravitational potential exhibits the properties of a thin gravitational lens, demonstrating how the weak lensing shear and convergence act as source terms for the perturbed Dyer-Roeder equation.

Five Dimensional Spherical Symmetric Universe in Creation Field Cosmology

The phenomenon of expanding universe, primordial nucleon-synthesis and the observed isotropy of cosmic microwave background radiation (CMBR) are the three very important observations in astronomy. These were successfully explained by big-bang cosmology based on Einstein’s field equations. Smoot et al. [2] revealed that the earlier prediction of the FriedmanRobertson-Walker type of models do not always exactly match with our expectations. Some puzzling results regarding the red shifts from the extra galactic objects continue to contradict the theoretical explanations given by the big-bang type model. Also, CMBR discovery did not prove it to be outcome of a big-bang theory. In fact, Narlikar et al. [3] have proved the possibility of non-relic interpretation of CMBR. To explain such phenomenon, many alternative theories have been proposed from time to time. Hoyle [4], Bondi and Gold [5] proposed steady state theory in which the universe does neither have singular beginning nor an end on the cosmic time scale. To overcome this difficulty Hoyle and Narlikar [6] adopted a field theoretic approach by introducing a mass-less and charge-less scalar field C in the Einstein-Hilbert action to account for the matter creation. In the Cfield theory introduced by Hoyle and Narlikar, there is no big-bang type of singularity as in the steady state theory of Bondi and Gold [5]. A solution of Einstein’s field equations admitting radiation with negative energy mass less scalar creation field C was obtained by Narlikar and Padmanabhan [1]. The study of Hoyle and Narlikar theory [6-8] of space-times with higher dimensions ____________________ mitasharma08@gmail.com was carried out by Chaterjee and Banarjee [9]. RajBali and Tikekar [10] studied C field Cosmology with variable G in the flat FriedmanRobertson-Walker model and with non flat FRW space time by Raj Bali and Kumawat [11]. The solutions of Einstien’s field equations in the presence of creation field have been obtained for different Binachi type universes by Singh and Chaubey [12]. In the present work, we have studied the Hoyle and Narlikar C-field cosmology in spherical symmetric space time. We have assumed that , = , that is, the creation field C is a function of time‘t’ only.

Corrected horizon of Kerr-Sen black hole as a series with terms involve powers of the inverse of the area

By means of the semiclassical approximations for the action, the horizon of Kerr-Sen black hole is studied. The corrected entropy of the Kerr-Sen black hole in a low-energy string theory is calculated. By assumption of a flat Friedman-Robertson-Walker (F.R.W.) geometries, we study horizon and present the semi-classic approximation affects of the thermodynamics properties. We discuss some physical consequences of this result and the properties of the Kerr-Sen black hole.

Generalizing the autonomous Kepler–Ermakov system in a Riemannian space

We generalize the two-dimensional autonomous Hamiltonian–Kepler–Ermakov dynamical system to three dimensions using the sl(2, R) invariance of Noether symmetries and determine all three-dimensional autonomous Hamiltonian–Kepler–Ermakov dynamical systems which are Liouville integrable via Noether symmetries. Subsequently, we generalize the autonomous Kepler–Ermakov system in a Riemannian space which admits a gradient homothetic vector by the requirements (a) that it admits a first integral (the Riemannian Ermakov invariant) and (b) it has sl(2, R) invariance. We consider both the non-Hamiltonian and the Hamiltonian systems. In each case, we compute the Riemannian–Ermakov invariant and the equations defining the dynamical system. We apply the results in general relativity and determine the autonomous Hamiltonian–Riemannian–Kepler–Ermakov system in the spatially flat Friedman–Robertson–Walker spacetime. We consider a locally rotational symmetric spacetime of class A and discuss two cosmological models. The first cosmological model consists of a scalar field with an exponential potential and a perfect fluid with a stiff equation of state. The second cosmological model is the f(R)-modified gravity model of ΛbcCDM. It is shown that in both applications the gravitational field equations reduce to those of the generalized autonomous Riemannian–Kepler–Ermakov dynamical system which is Liouville integrable via Noether integrals.

The IR-completion of gravity: what happens at Hubble scales?

We have recently proposed an ‘ultra-strong’ version of the equivalence principle (EP) that is not satisfied by standard semiclassical gravity. In the theory that we are conjecturing, the vacuum expectation value of the (bare) energy momentum tensor is exactly the same as in flat space: quartically divergent with the cut-off and with no spacetime-dependent (subleading) terms. The presence of such terms seems in fact related to some known difficulties, such as the black hole information loss and the cosmological constant problem. Since the terms that we want to get rid of are subleading in the high-momentum expansion, we attempt to explore the conjectured theory by ‘infrared (IR)-completing’ general relativity (GR). We consider a scalar field in a flat Friedman–Robertson–Walker (FRW) universe and isolate the first IR-correction to its Fourier modes operators that kills the quadratic (next to leading) time-dependent divergence of the stress energy tensor vacuum expectation value (VEV). Analogously to other modifications of field operators that have been proposed in the literature (typically in the UV), the present approach seems to suggest a breakdown (here, in the IR, at large distances) of the metric manifold description. We show that corrections to GR are in fact very tiny, become effective at distances comparable to the inverse curvature and do not contain any adjustable parameter. Finally, we derive some cosmological implications. By studying the consistency of the canonical commutation relations, we infer a correction to the distance between two co-moving observers, which grows as the scale factor only when small compared to the Hubble length, but gets relevant corrections otherwise. The corrections to cosmological distance measures are also calculable and, for a spatially flat matter dominated Universe, go in the direction of an effective positive acceleration.

Group velocity of gravitational waves in an expanding universe

The group velocity of gravitational waves in a flat Friedman–Robertson–Walker universe is investigated. For plane waves with wavelength well inside the horizon, and a universe filled with an ideal fluid with the pressure to density ratio less than 1/3, the group velocity is greater than the velocity of light. As a result, a planar pulse of gravitational waves propagating through the universe during the matter/dark energy dominated era arrives to the observer with the peak shifted towards the forefront. For gravitational waves emitted by inspiralling supermassive black holes at the edge of the observable universe, the typical shift that remains after the effects of nonplanarity are suppressed is of order of 10 ps.

The flat FRW model in LQC: self-adjointness

The flat Friedman–Robertson–Walker (FRW) model coupled to the massless scalar field according to the improved, background scale-independent version of Ashtekar, Pawłowski and Singh [1] is considered. The core of the theory is addressed directly: the APS construction of the quantum Hamiltonian is analyzed under the assumption that the cosmological constant Λ ⩽ 0. We prove the essential self-adjointness of the operator whose square-root defines in [1] the quantum Hamiltonian operator and therefore provide the explicit definition. If Λ < 0, then the spectrum is discrete. In the Λ = 0 case, the essential and absolutely continuous spectra of the operator are derived. The latter operator is related in the unitary way to the absolutely continuous part of the quantum mechanics operator (a, b > 0 being some constants) plus a trace class operator.

Fine-tuning free paradigm of two-measures theory:k-essence, absence of initial singularity of the curvature, and inflation with graceful exit to the zero cosmological constant state

The dilaton-gravity sector of the two-measures field theory (TMT) is explored in detail in the context of spatially flat Friedman-Robertson-Walker (FRW) cosmology. The model possesses scale invariance which is spontaneously broken due to the intrinsic features of the TMT dynamics. The dilaton $\ensuremath{\phi}$ dependence of the effective Lagrangian appears only as a result of the spontaneous breakdown of the scale invariance. If no fine-tuning is made, the effective $\ensuremath{\phi}$-Lagrangian $p(\ensuremath{\phi},X)$ depends quadratically upon the kinetic term $X$. Hence TMT represents an explicit example of the effective $k$-essence resulting from first principles without any exotic term in the underlying action intended for obtaining this result. Depending of the choice of regions in the parameter space (but without fine-tuning), TMT exhibits different possible outputs for cosmological dynamics: (a) Absence of initial singularity of the curvature while its time derivative is singular. This is a sort of sudden singularities studied by Barrow on purely kinematic grounds. (b) Power law inflation in the subsequent stage of evolution. Depending on the region in the parameter space the inflation ends with a graceful exit either into the state with zero cosmological constant (CC) or into the state driven by both a small CC and the field $\ensuremath{\phi}$ with a quintessencelike potential. (c) Possibility of resolution of the old CC problem. From the point of view of TMT, it becomes clear why the old CC problem cannot be solved (without fine-tuning) in conventional field theories. (d) TMT enables two ways for achieving small CC without fine-tuning of dimensionful parameters: either by a seesaw type mechanism or due to a correspondence principle between TMT and conventional field theories (i.e. theories with only the measure of integration $\sqrt{\ensuremath{-}g}$ in the action). (e) There is a wide range of the parameters such that in the late time universe: the equation of state $w=p/\ensuremath{\rho}&lt;\ensuremath{-}1$; $w$ asymptotically (as $t\ensuremath{\rightarrow}\ensuremath{\infty}$) approaches $\ensuremath{-}1$ from below; $\ensuremath{\rho}$ approaches a constant, the smallness of which does not require fine-tuning of dimensionful parameters.

EXACT SOLUTIONS FOR COSMOLOGICAL MODELS WITH A SCALAR FIELD

We consider the existence of a Noether symmetry in the scalar–tensor theory of gravity in flat Friedman–Robertson–Walker (FRW) cosmology. The forms of coupling function ω(ϕ) and generic potential V(ϕ) are obtained by requiring the existence of a Noether symmetry for such theory. We derive exact cosmological solutions of the field equations from a point-like Lagrangian.

Relativistic Self-Similar Flows

A mathematical framework analyzing a class of spherical self-similar hydrodynamical flows on a class of homothetic spherically symmetric background geometries is presented. The analysis covers relativistic flows propagating in the following class of spacetimes: (i) Minkowski spacetime, (ii) the homothetic Bondi–Tolman spacetime, (iii) the spatially flat Friedman–Robertson–Walker cosmologies. After the introduction of the mathematical framework, there follows a detailed investigation of special relativistic flows with the pressurePand densityρobeyingP=kρ,ka constant 0⩽k⩽1. An extensive analysis of the singular and critical points of the differential equations determining the flow is presented. By a combination of analytical and numerical techniques several classes of flows have been constructed. We have found flows describing an oscillation of the medium, as well as flows representing relativistic detonation waves propagating on a medium at rest. In addition, two classes of analytical closed form solutions are given. By invoking the relativistic Rankine–Hugoniot conditions we briefly discuss a way by which two self-similar solutions can be joined across an expanding (or contracting) shock wave.