Particle creation in FLRW higher dimensional universe with gravitational and cosmological constants

We study the mechanism of particle creation in the higher dimensional FLRW type cosmological models by using variable cosmological and gravitational constants. The solution of the corresponding field equations is obtained by assuming a linear function of the Hubble parameter (H), i.e., q = α + βH [Dixit et al., Pramana: 94, 25 (2020)] which gives a scale factor a(t) = exp({\frac{1}{\beta}\sqrt{2\beta t +k} }), where k and β are positive constants. Here we consider the time-dependent higher-dimensional (HD) field equations, including the general formulation of particle creation (PC) and entropy generation mechanisms (EGM). We also investigate few quantities such as the deceleration parameter (DP) q, particle creation rate \psi, the entropy S, the cosmological constant (CC) /Lambda, Newton's gravitational constant (GC) G, the energy density (ED) ρ and discuss their physical significance. We have observed that all quantities, except the gravitational constant (G) and the entropy (S), decrease with time in all dimensions characteristically. However, the entropy S and the gravitational constant G increase with time. Additionally, we have also discussed the look-back time, luminosity distance, distance modulus and age of the universe with redshift z and observed the role of particle formation in universe evolution in early and late times. For the derived model, we have calculated various physical parameters, which are in good agreement with the recent observations.

Bianchi type-V solutions with varying G and Λ: The general case

The homogeneous and anisotropic Bianchi type-V cosmological model with variable gravitational and cosmological “constants” with a general (nonstiff) perfect fluid is investigated. The Einstein field equations (EFEs) are numerically integrated with the fourth-order Runge–Kutta method for different values of [Formula: see text] and [Formula: see text] parameters of quantum fields in a curved and expanding background. Three realistic models, namely matter, radiation and phantom dark energy models are also discussed. In all these models, it was found that the cosmological “constant” decreases with time, whereas the gravitational “constant” increases over time. It is shown that the universe in these models becomes isotropic at late times.

Dark Matter as a Result of Field Oscillations in the Modified Theory of Induced Gravity

The paper studies the modified theory of induced gravity (MTIG). The solutions of the MTIG equations contain two branches (stages): Einstein (ES) and “restructuring” (RS). Previously, solutions were found that the values of such parameters as the “Hubble parameter”, gravitational and cosmological “constants” at the RS stage, fluctuate near monotonously developing mean values. This article gives MTIG equations with arbitrary potential. Solutions of the equations of geodesic curves are investigated for the case of centrally symmetric space and quadratic potential at the RS stage. The oscillatory nature of the solutions leads to the appearance of a gravitational potential containing a spectrum of minima, as well as to antigravity, which is expressed by acceleration directed from the center. Such solutions lead to the distribution of the potential of the gravitational field creating an additional mass effect at large distances and are well suited for modeling the effect of dark matter in galaxies. The solutions of the equation of geodesic lines are obtained and analyzed. We found that the transition from flat asymptotics to oscillatory asymptotics at large distances from the center with a combination of the presence of antigravity zones leads to a rich variety of shapes and dynamics of geodesic curves and to the formation of complex structures.

Oscillating Cosmological Solutions in the Modified Theory of Induced Gravity

This work is the extension of author’s research, where the modified theory of induced gravity (MTIG) is proposed. In the framework of the MTIG, the mechanism of phase transitions and the description of multiphase behavior of the cosmological scenario are proposed. The theory describes two systems (stages): Einstein (ES) and “restructuring” (RS). This process resembles the phenomenon of a phase transition, where different phases (Einstein’s gravitational systems, but with different constants) pass into each other. The hypothesis that such transitions are random and lead to stochastic behavior of cosmological parameters is considered. In our model, effective gravitational and cosmological “constants” arise, which are defined by the “mean square” of the scalar fields. These parameters can be compared with observations related to the phenomenon of dark energy. The aim of the work is to solve equations of MTIG for the case of a quadratic potential and compare them with observational cosmology data. The interaction of fundamental scalar fields and matter in the form of an ideal fluid is introduced and investigated. For the case of Friedmann-Robertson-Walker space-time, numerical solutions of nonlinear MTIG equations are obtained using the qualitative theory of dynamical systems and mathematical computer programs. For the case of a linear potential, examples joining of solutions, the ES and RS stages, of the evolution of the cosmological model are given. It is shown that the values of such parameters as “Hubble parameter” and gravitational and cosmological “constants” in the RS stage contain solutions oscillating near monotonically developing averages or have stochastic behavior due to random transitions to different stages (RS or ES). Such a stochastic behavior might be at the origin of the tension between CMB measurements of the value of the Hubble parameter today and its local measurements.

Bianchi Type VI Cosmological Model with Dynamical Cosmological Parameters G and ⩘ in the presence of Bulk Viscous Stress

In the present study, we have obtained Bianchi type VI anisotropic model of the universe filled with a bulk viscous stress in the presence of variable gravitational and cosmological constants. Here we have assumed the cosmological term in the form Λ∝H to discuss the effect of cosmological variables. It is found that the bulk viscosity coefficient (ξ) is a decreasing function of time. The expression for proper distance, luminosity distance, angular diameter distance, look back time and distance modulus curve have been analyzed and also the distance modulus curve of derived model nearly matches with Supernova Ia (SN Ia) observations.

The Ambiguity in the Definition and Behavior of the Gravitational and Cosmological `Coupling Constants’ in the Theory of Induced Gravity

This work is the extension of author`s research, where the modified theory of induced gravity (MTIG) is proposed. The theory describes two systems (stages): Einstein (ES) and “restructuring” (RS). We consider equations with quadratic potential that are symmetric with respect to scale transformations. The solutions of the equations obtained for the case of spaces defined by the Friedman-Robertson-Walker metric, as well as for a centrally symmetric space are investigated. In our model arise effective gravitational and cosmological “constants”, which are defined by the “mean square” of the scalar fields. In obtained solutions the values of such parameters as “Hubble parameter”, gravitational and cosmological “constants” in the RS stage fluctuate near monotonically evolving mean values. These parameters are matched with observational data, described as phenomena of dark energy and dark matter. The MTIG equations for the case of a centrally symmetric gravitational field, in addition to the Schwarzschild-de Sitter solutions, contain solutions that lead to the new physical effects at large distances from the center. The Schwarzschild-Sitter solution becomes unstable and enters the oscillatory regime. For distances greater than a certain critical value, the following effects can appear: deviation from General relativity and Newton’s law of gravitational interaction, antigravity.

A Generalized Solution of Bianchi Type-V Models with Time-Dependent G and Λ

We study the homogeneous but anisotropic Bianchi type-V cosmological model with time-dependent gravitational and cosmological “constants”. Exact solutions of the Einstein field equations (EFEs) are presented in terms of adjustable parameters of quantum field theory in a spatially curved and expanding background. It has been found that the general solution of the average scale factor a as a function of time involved the hypergeometric function. Two cosmological models are obtained from the general solution of the hypergeometric function and the Emden–Fowler equation. The analysis of the models shows that, for a particular choice of parameters in our first model, the cosmological “constant” decreases whereas the Newtonian gravitational “constant” increases with time, and for another choice of parameters, the opposite behaviour is observed. The models become isotropic at late times for all parameter choices of the first model. In the second model of the general solution, both the cosmological and gravitational “constants” decrease while the model becomes more anisotropic over time. The exact dynamical and kinematical quantities have been calculated analytically for each model.