Gravitational baryogenesis models comparison in f(R) gravity

We have studied the gravitational baryogenesis in $f\left(R\right)$ theory of gravity with an anisotropic Bianchi I space-time. The matter field is considered to be that of perfect fluid. Two models pertaining to specific form of Ricci scalar have been presented. The baryon-to-entropy ratio has been derived with some specific form of Ricci scalar in an an anisotropic background. The gravitational baryogenesis is examined and its behaviors are studied.     

Estimation of cosmological parameters,stability analysis and energy conditions in viable modified gravity

In the present paper, we have investigated the Friedmann-Robertson-Walker (FRW) model in viable f(R, T) gravity with f(R, T) function proposed as $f(R,T)=R+\xi T^{1/2},$ where ξ is an arbitrary constant, R is the scalar curvature and T is the trace of stress energy tensor. Defining the scale factor, the field equations are solved numerically and the energy conditions are analyzed. Further, determining Hubble parameter and deceleration parameter, their present values are estimated. Furthermore, 57 redshift data (42 redshift data from Supernova Cosmology project and 15 redshift data from Calán/ Tolono Supernova survey) are used to estimate the age of the universe and to find the best fit curves for luminosity distance and apparent magnitude.     

Modeling of anisotropic spheres in extended teleparallel theory with matter coupling

This work is devoted to investigate the structures of compact stars by using spherically static symmetric space-time in the background of $f(\tau ,T)$ gravity, where $\tau$ represents the torsion scalar and $T$ represents the trace of the energy momentum tensor. We develop the field equations by using the concept of quintessence to discuss the motion by using anisotropic fluid distribution with a spherically symmetric metric. We use the convention of junction conditions to evaluate the unknown parameters used in the study of the compact stars. In this study we use the available data of three different compact objects $4U1608-52,$ $CenX-3$ and $EXO1785-240$. We discuss the physical and analytical existence of compact stars by satisfying some standard properties of compact stars like the behavior of the energy density, quintessence density, radial and tangential pressures, anisotropy, to elaborate the anisotropic nature of the star. We discuss the sound speeds and casuality conditions to show the stability of the system. Equilibrium of the star is justified by the TOV equation. Red-shift function, compactness, and mass function states the physical existence of the star. It is examined that all these parameters show the viability and stability of the model used in the effects of $f(\tau ,T)$ gravity.     

Study of the q-Gaussian distribution with the scale index and calculating entropy by normalized inner scalogram

In this paper, we discuss a method based on wavelet analysis for the study of the q-index of the Gaussian distribution. We derive q-index from the scale index, $i_{\mathit{scale}}$, using the expression; $q\equiv 1+2i_{\mathit{scale}}$ where $i_{\mathit{scale}}$ is a wavelet based tool for measuring the degree of aperiodicity of a dynamical system in the range of $0\le i_{\mathit{scale}}\le 1$. We show that this expression gives consistent results with the numerical approach of q-Gaussian distribution which determines the degree of non-extensivity of a dynamical system in the range of $1<q<3$. We also suggest a new entropy calculation method based on the normalized inner scalogram for studying the chaotic characteristics of nonlinear dynamical systems.     

New findings for two new type sine hyperbolic potentials

We propose two new type sine hyperbolic potentials $V(x)=a^2{\sinh }^2?(x)?k{\tanh }^2?(x)$ and $V(x)=c^2{\sinh }^4?(x)?k{\tanh }^2?(x)$. They may become single- or double-well potentials depending on the potential parameters $a,c$ and k. We find that its exact solutions can be written as the confluent Heun functions $H_c(\alpha ,\beta ,\gamma ,\delta ,\eta ;z)$, in which the energy level E is involved inside the parameter η. The properties of the wave functions, which is strongly relevant for the potential parameters $a,c$ and k, are illustrated.