Inflation in mimetic f(R,T) gravity

In this paper, we employ mimetic $f(R,T)$ gravity coupled with Lagrange multiplier and mimetic potential to yield viable inflationary cosmological solutions consistent with latest Planck and BICEP2/Keck Array data. We present here three viable inflationary solutions of the Hubble parameter ($H$) represented by $H\left(N\right)={(A\exp \beta N+B{\alpha }^N)}^{\gamma }$, $H\left(N\right)={(A{\alpha }^N+B\log N)}^{\gamma }$, and $H\left(N\right)={(A{e}^{\beta N}+B\log N)}^{\gamma }$, where $A$, $\beta$, $B$, $\alpha$, $\gamma$ are free parameters, and $N$ represents the number of e-foldings. We carry out the analysis with the simplest minimal $f(R,T)$ function of the form $f(R,T)=R+\chi T$, where $\chi$ is the model parameter. We report that for the chosen $f(R,T)$ gravity model, viable cosmologies are obtained compatible with observations by conveniently setting the Lagrange multiplier and the mimetic potential.     

First photometric study of two eclipsing binary star systems: V523 And and V543 And

Detailed photometric analysis of V523 And and V543 And from the Wide Angle Search for Planets survey is presented for the first time. It was found that while V523 And is a detached binary, V543 And is a semi-detached binary star system. The adopted masses and radii for the primary and secondary components are $M_1=0.77\pm 0.08$ M${}_{\odot }$, $R_1=0.87\pm 0.08$ R${}_{\odot }$ and $M_2=0.50\pm 0.12$ M${}_{\odot }$, $R_2=0.77\pm 0.17$ R${}_{\odot }$ for V523 And; and $M_1=1.59\pm 0.16$ M${}_{\odot }$, $R_1=1.46\pm 0.09$ R${}_{\odot }$ and $M_2=0.58\pm 0.17$ M${}_{\odot }$, $R_2=1.66\pm 0.22$ R${}_{\odot }$ for V543 And. Orbital period variations of the systems were analyzed using the O-C method. The O-C change of V523 And is discussed in terms of the magnetic activity cycle of one or both components and light travel time effect (LTTE) due to a third body in the system. Among these mechanisms, LTTE seems to be the most appropriate mechanism to explain the O-C variation of the system since the quadrupole moments of the primary and secondary components ($\Delta Q$) were found to be in the order of $10^{49}$ g cm${}^2$. The O-C diagram of V543 And shows a downward parabolic trend, which suggests a secular period decrease with a rate of $0.080\pm 0.012$ s/year. The parabolic O-C variation of V543 And was interpreted in terms of the non-conservative mass transfer mechanism. According to this scenario, the range of possible values of the mass gain rate (${\dot{M}}_1$) of the primary component of V543 And as well as the mass-loss rate ($\dot{M}$) of the system were found to be $10^{-5}$–$10^{-11}$ M${}_{\odot }$/year and $10^{-6}$–$10^{-8}$ M${}_{\odot }$/year, respectively.     

Analysis of resonant curves and phase portrait in the earth–moon system by using its unperturbed solution and earth’s equatorial ellipticity

In this research article, we have investigated resonant curves due to the rate of change of earth’s equatorial ellipticity parameter $\left(\dot{\gamma }\right)$, steady-state value of the angular velocity of the moon $\left({\dot{\theta }}_{mo}\right)$, and angular velocity of barycenter $\left(\dot{{\alpha }_0}\right)$ in the Earth-Moon system. Equations of motion of the moon are determined in a spherical coordinate system with the help of the gravitational potential of the earth. By using the unperturbed solution, equations of motion of the moon reduced into the second-order differential equation. From the solution it is observed that resonance occurs due to the frequencies $\dot{\gamma }$, ${\dot{\theta }}_{m0}$, and $\dot{{\alpha }_0}$ at the resonant points ${\dot{\theta }}_{m0}=2\dot{\gamma }$, $3{\dot{\theta }}_{m0}=2\dot{\gamma }$, ${\dot{\theta }}_{m0}=\dot{\gamma }$, ${\dot{\theta }}_{m0}={\dot{\alpha }}_0$. Finally, we have analyzed the phase portrait and phase space by method of Poincaré section when the system is free from forces.     

Relativistic isotropic stellar model in f(R,T) gravity with Durgapal- IV metric

In this work, a new static, non-singular, spherically symmetric fluid model has been obtained in the background of $f(R,T)$ gravity. Here we consider the isotropic metric potentials of Durgapal-IV (Durgapal, 1982) solution as input to handle the Einstein field equations in $f(R,T)$ environment. For different coupling parameter values of $\chi$, graphical representations of the physical parameters have been demonstrated to describe the analytical results more clearly. It should be highlighted that the results of General Relativity (GR) are given by $\chi =0$. With the use of both analytical discussion and graphical illustrations, a thorough comparison of our results with the GR outcomes is also covered. The numerical values of the various physical attributes have been given for various coupling parameter $\chi$ values in order to discuss the impact of this parameter. Here we apply our solution by considering the compact star candidate LMC X-4 (Rawls et al., 2011) with mass $=(1.04\pm 0.09)M_{\odot }$ and radius $=8.301_{-0.2}^{+0.2}$ km. respectively, to analyze both analytically and graphically. To confirm the physical acceptance of our model, we discuss certain physical properties of our obtained solution such as energy conditions, causality, hydrostatic equilibrium through a modified Tolman–Oppenheimer–Volkoff (TOV) conservation equation, pressure–density ratio, etc. Also, our solution is well-behaved and free from any singularity at the center. From our present study, it is observed that all of our obtained results fall within the physically admissible regime, indicating the viability of our model.