General Relativity and Quantum Cosmology (gr-qc)

Abstract: We consider marginally trapped surfaces in a spherically symmetric spacetime evolving due to the presence of a perfect fluid in D-dimensions and look at the various definitions of the surface gravity for these marginally trapped surfaces. We show that using Einstein equations it is possible to simplify and obtain general formulae for the surface gravity in terms of invariant quantities defined at these marginally trapped surfaces like area radius, cosmological constant and principal values of the energy-momentum tensor \r{ho}, p. We then correlate these expressions of surface gravity to the cases of dynamical horizons and timelike tubes and find which proposals of surface gravity are causally sensitive as these surfaces undergo causal transitions from spacelike to timelike and vice versa.

Abstract: This work aims to investigate the behaviour of compact stars in the background of $f(R, T)$ theory of gravity. For current work, we consider the Krori-Barua metric potential i.e., $\nu(r)= Br^2+C$ and $\lambda(r)= Ar^2,$ where, $A, B$ and $C$ are constants. We use matching conditions of spherically symmetric space-time with Schwarzschild solution as an exterior geometry and examine the physical behaviour of stellar structure by assuming the exponential type $f(R, T)$ gravity model. In the present analysis, we discuss the graphical behaviour of energy density, radial pressure, tangential pressure, equation of state parameters, anisotropy and stability analysis respectively. Furthermore, an equilibrium condition can be visualized through the modified Tolman-Oppenheimer-Volkov equation. Some extra features of compact stars i.e. mass-radius function, compactness factor and surface redshift have also been investigated. Conclusively, all the results in current study validate the existence of compact stars under exponential $f(R, T)$ gravity model.

Abstract: We use the Hamilton-Jacobi formalism to derive asymptotic solutions to the dynamical equations for inflationary T-models in a flat Friedmann-Lema\^itre-Robertson-Walker spacetime in the kinetic dominance stage and in the slow-roll stage. With an appropriate Pad\'e summation, the expansions for the Hubble parameter can be matched, which in turn determines the relation between the expansions for the scale factor and allows us to compute the total amount of inflation as a function of the initial data or, conversely, to select initial data that correspond to a fixed total amount of inflation. Other magnitudes of interest, like the first slow roll parameter (and consequently the equation of state parameter) can be described in parametric form using the inflation field itself as a parameter.

Abstract: We propose a logarithmic parametrization form of energy density for the scalar field dark energy in the framework of the standard theory of gravity, which supports the necessary transition from the decelerated to the accelerated periods of the Universe. The analyzed model has a parameter space that is constrained by available observational data, including cosmic chronometers data-sets (CC), Baryonic Acoustic Oscillation (BAO) data-sets, and Supernovae (SN) data-sets, consisting of only two parameters $\alpha$ and $\beta$. The combined $CC$+$BAO$+$SN$ data-sets yields a transition redshift of $z_{tr}=0.79^{+0.02}_{-0.02}$, where the model exhibits signature-flipping and is consistent with recent observations. For the combined data-sets, the present value of the deceleration parameter is calculated to be $q_{0}=-0.43^{+0.06}_{-0.06}$. Furthermore, the analysis yields constraints on both the parameter density value for matter and the present value of the Hubble parameter, with values of $\Omega_{m0}=0.25849^{+0.00026}_{-0.00025}$ and $H_{0}=67.79_{-0.59}^{+0.59}km/s/Mpc$, respectively, consistent with the results obtained from Planck 2018. Finally, the study investigates how the mass of a black hole evolves over time in a Universe with both matter and dark energy. It reveals that the black hole mass increases initially but stops increasing as dark energy dominates.

Abstract: We study the completeness of light trajectories in certain spherically symmetric regular geometries found in Palatini theories of gravity threaded by non-linear (electromagnetic) fields, which makes their propagation to happen along geodesics of an effective metric. Two types of geodesic restoration mechanisms are employed: by pushing the focal point to infinite affine distance, thus unreachable in finite time by any sets of geodesics, or by the presence of a defocusing surface associated to the development of a wormhole throat. We discuss several examples of such geometries to conclude the completeness of all such effective paths. Our results are of interest both for the finding of singularity-free solutions and for the analysis of their optical appearances e.g. in shadow observations.

Abstract: We review a recently proposed definition of complexity of the structure of self--gravitating fluids \cite{ch1}, and the criterium to define the simplest mode of their evolution. We analyze the origin of these concepts and their possible applications in the study of gravitation collapse. We start by considering the static spherically symmetric case, extending next the study to static axially symmetric case. Afterward we consider the non--static spherically symmetric case. Two possible modes of evolution are proposed to be the simplest one. One is the homologous conditio,, however, as was shown later on, it may be useful to relax this last condition to enlarge the set of possible solutions, by adopting the so-called quasi-homologous condition. As another example of symmetry, we consider fluids endowed with hyperbolical symmetry. Exact solutions for static fluid distributions satisfying the condition of minimal complexity are presented.. An extension of the complexity factor to the vacuum solutions of the Einstein equations represented by the Bondi metric is discussed. A complexity hierarchy is established in this case, ranging from the Minkowski spacetime (the simplest one) to gravitationally radiating systems (the most complex). Finally we propose a list of questions which, we believe, deserve to be treated in the future

Abstract: We use Instant Preheating as a mechanism to reheat the universe when its evolution is modeled by a non-oscillating background. Once we obtain the reheating temperature, we calculate the number of e-folds using two different methods, which allows us to establish a relationship between the reheating temperature and the spectral index of scalar perturbations. We explore this connection to constrain the spectral index for different Quintessential Inflation models.