International Journal of Modern Physics D

In this paper, we discuss a cosmological model for a universe with self-regulating features. We set up the theoretical framework for the model and determine the time evolution of the scale-factor $a(t)$. It is shown that such a universe repeatedly goes through alternate periods of matter and dark energy domination. The resulting dynamics oscillates about the would-be ideal time-linear or coasting path, with monotonic expansion. When compared to dynamics of the observed physical universe, the model recovers the observationally established evolutionary features of the latter, from the big bang to the current acceleration, and farther. It suggests a universe that initially emerges from a nonsingular state, associated with a non-exponential acceleration, and which acceleration it exits naturally with matter–energy generation. The model does not have a horizon problem or a flatness problem. It reproduces the observed current values of standard cosmic parameters, including the age $t_0$, the current Hubble parameter $H_0$ and dark energy ${\mathrm{\Omega }}_{\mathrm{\text{de}}}$ and matter ${\mathrm{\Omega }}_m$ density parameters. The model is falsifiable. It makes predictions that can be tested, as suggested. Finally, we discuss the dimensionless age $(H_0{t}_0\simeq 1)$ paradox as an example of the model’s ability to address standing puzzles. The findings suggest that dynamics of the physical universe may be self-regulating and predictable.

In this paper, we examine the homogeneous and isotropic flat Universe in the frame of symmetric teleparallel gravity say $f(Q)$ gravity (where $Q$ is the nonmetricity scalar). In this work, we parametrized the field equations with the help of Hubble’s parameter defined as $H(z)=\eta [1+{(z+1)}^{-\gamma }]$, where $\eta$ and $\gamma$ are model/free parameters which are constrained with updated 57 data points of the Hubble data set within the redshift range $0.07<z<2.36$. For this, we have used a Markov Chain Monte Carlo Technique (MCMCT). Some physical parameters of the model are discussed. In addition, we analyze the jerk parameter and the statefinder parameters and we also study the energy conditions to assess the compatibility of our model with dark energy models; we determine that the Strong Energy Condition (SEC) is violated due to the fact that the Universe is currently accelerating.

In this work, we utilize the Wentzel–Kramers–Brillouin (WKB) approximation to determine the Hawking temperature corresponding to the Kerr–Newman–de Sitter (KNdS) spacetime. Specifically, we calculate the low frequency absorption cross-section for the KNdS black hole in a charged scalar field and analyzed its dependence on the characteristics of the black hole. Through our research, we have established a correlation between the absorption cross-section (${\sigma }_{\mathrm{\text{abs}}}$) and the Hawking temperature ($T_H$) of the black hole, demonstrating an inverse proportionality between the two quantities. Furthermore, we also deduce the absorption cross-sections for Kerr–de Sitter, Reissner–Nordstrom–de Sitter, Schwarzschild–de Sitter and Schwarzschild black holes, and compare them with previously obtained results. The validity of our findings is demonstrated by these comparisons.

In this paper, we derive and solve the causal heat transport equation, for a collapsing self-similar radiation shell described by the Vaidya geometry, using a semi-tetrad covariant formalism. This enables us to gain a meaningful insight on how the geometrical quantities associated with this spacetime relate to the causal Maxwell–Cattaneo type hyperbolic transport equations obtained in the phenomenological theories of Muller, Stewart and Israel. It is shown that the causal temperature profile in the collapsing shell is distinct from the Eckart temperature, and this temperature profile can be given explicitly.

We investigate the behavior of expansion free collapsing fluids, as studied by L. Herrera, A. Di Prisco and J. Ospino [Symmetry 15 (2023) 754], in the framework of $f(R)$ gravity, which represents a modification of Einstein’s general relativity by establishing a function of the Ricci scalar $R$ in the gravitational action. We explore dynamical equations from Bianchi identities that demonstrate the motion and evolution of physical systems under the influence of gravitational fields. We match the inner and outer geometries of spacetime on the hypersurface to develop junction conditions by using the Misner–Sharp formalism. This allows us to identify the connection between mass functions for the inner and outer space as well as the relationship for heat flux $q$ and radial pressure ${\mathbb{P}}_r$. We also investigate analytical solutions of dissipative fluid distribution that fulfill the vanishing expansion condition together with the vanishing complexity factor constraint. For this, we introduce new constraints that permit the integration of the complex system in $f(R)$ gravity. Next, we extract a set of differential equations that explain the dynamical structure of the dissipative spheres both in geodesic and non-geodesic fluids. Furthermore, we explore the physical characteristics of the obtained solutions, such as heat flux, energy density, shear stress, fluid’s temperature along with tangential and radial pressure, to assess their viability in describing real astrophysical systems.

A nonrelativistic quantum theory of dark matter particles in a spherical halo is developed by using a new asymmetric equation, which is complementary to the Schrödinger equation. The theory predicts that each dark matter halo has its core and envelope with very distinct physical properties. The core is free of any quantum structure and its dark matter particles are in random motion and frequently collide with each other. However, the envelope has a global quantum structure that contains quantized orbits populated by the particles. Applications of the theory to dark matter halos with given density profiles are described, and physical implications and predictions of the theory are discussed.

In this paper, we present a study of basic classes of stationary observers orbiting in stationary and axially symmetric Kerr-de Sitter spacetimes. Along with proper definitions of these classes, we focus on their possible matching on particular circular orbits. Especially, we determine a number of such orbits in a given spacetime characterized by its rotational and cosmological parameters that leads to a comprehensive classification of the Kerr-de Sitter spacetimes. Studied profiles of orbital velocities of the observers and of forces keeping them on their orbits directly reflect complex structure of the Kerr-de Sitter spacetimes that is caused by a unique interplay of attraction and rotation of a central object and an ambient cosmic repulsion.

In this study, we propose a reparametrization of a specific viable $f(R)$ gravity model to represent it as a perturbation of the $\mathrm{\Lambda }$CDM model. The $f(R)$ gravity model under consideration includes two parameters, $b$ and $n$, which control how close the proposed model can be to $\mathrm{\Lambda }$CDM, allowing for arbitrary proximity. Furthermore, it is shown that the Hu–Sawicki (HS) model is a limiting case of this reparametrized model. Following the existing literature, we also derive an analytical approximation for the expansion rate $H(z)$, which shows an excellent agreement between this analytical approximation and the numerical solution over a wide range of redshifts for realistic values of the deviation parameter $b$. By appropriately selecting values for the model parameters, we plot the cosmological parameters $w_{\mathrm{\text{DE}}}$, $w_{\mathrm{\text{eff}}}$, ${\mathrm{\Omega }}_{\mathrm{\text{DE}}}$ and $H(z)$, as well as the statefinder quantities $q$, $j$, $s$ and $\mathrm{\text{Om}}(z)$. We find that their present values (at $z=0$) are consistent with the observations from Planck 2018 and the values predicted by the $\mathrm{\Lambda }$CDM model. It is important to note that the examined cosmological and statefinder parameters do not exhibit significant oscillations of effective dark energy, which could lead to singular and unphysical solutions at high redshifts. This anomalous behavior has been avoided here by utilizing the approximate analytical solution for $H(z)$. Additionally, we conduct a detailed analysis of the evolution of matter density perturbations within the introduced $f(R)$ gravity model. The results demonstrate that this viable $f(R)$ gravity model is practically indistinguishable from the $\mathrm{\Lambda }$CDM model at the background level.