International Journal of Modern Physics D

In this paper, we consider an inflation scenario in which the inflation roll rate, defined by $\frac{\ddot{\varphi }}{H\dot{\varphi }}$ is supposed to be constant and study constant-roll inflation by a scalar field with minimal coupling to gravity in the presence of non-commutative (NC) parameters. For this purpose, we use the deformation approach and obtain the corresponding Lagrangian to the model by employing new variables. Then, we find exact solutions for the inflation potential, which include power-law, quadratic hilltop, and natural inflation. Further, we discuss the effect of parameters on the inflation model in NC space.

We explore the swampland conjectures of quintessence and tachyon scalar field models in $f(T)$ and Einstein gravities, respectively. In $f(T)$ gravity, we consider cold and warm (by assuming generalized dissipative coefficient) inflationary scenarios and develop constraints on de-Sitter conjectures through Bekenstein entropy relation. In usual inflation, the de-Sitter conjecture constraint becomes constant (in terms of models constant parameters) which can be easily analyzed for its validity (i.e., $\frac{\left|V^{\prime }\right|}{V}\le O(1)$). However, in warm inflation, we analyze the de-Sitter conjecture constraint through $\frac{{\tau }^{\prime }V}{\tau V^{\prime }}$, i.e., if $\frac{{\tau }^{\prime }V}{\tau V^{\prime }}<1$ then $\frac{\left|V^{\prime }\right|}{V}\le O(1)$ and hence we can obtain the required result. For evaluating this condition, we choose three well-known potentials such as monomial chaotic, hilltop and generalized exponential. It is observed that the condition $\frac{{\tau }^{\prime }V}{\tau V^{\prime }}<1$ satisfied for all three potentials in both regimes of dissipative coefficient for specific choice of constants. We also obtain satisfactory results of de-Sitter conjecture for tachyon and polytropic (with quintessence scalar field) in general relativity. We investigate the consistency of assumed potentials through inflationary parameters $n_s$ and $r$ comparing with Planck’s observational data 2018 and found them compatible with the recent observations.

We study the geodesic deviation equation for a quantum particle in a linearized quantum gravitational field. Particle’s Heisenberg equations of motion are treated as stochastic equations with a quantum noise. We explore the stochastic equation beyond its local approximation as a differential equation. We discuss the squeezed states resulting from an inflationary evolution. We calculate the noise in the thermal and squeezed states.

Recent research works have shown the existence of super-massive neutron stars (NSs) with mass about $2.2M_{\odot }$ or even more. The query about those super-massive NSs inspires the researchers to analyze their features and structures immensely. Here, we have inspected the behavior and properties of some of those super-massive NSs in $f(T)$ modified gravity with $T=T+\alpha T^2$, where $T$ is the torsional scalar and $\alpha$ is a regulatory parameter. In this framework of teleparallel formalism of modified gravity, we obtain the equations of motion by considering quintessence field, modified Chaplygin gas (MCG) and electromagnetic field. For our model, we use matching conditions under spherical symmetry, in order to find out the numerical values of different unknown constants of our model. This helps us to acquire various physical quantities thoroughly and to understand about the nature of those super-massive NSs deeply and quite clearly. Moreover, from our work, we can also explain the role of quintessence field and MCG in case of massive compact stars. The mass–radius relationship curve of this model can effectively describe the mass of the heaviest NS (about $2.6M_{\odot }$) ever detected via gravitational wave detection. Again, we overall investigate the anisotropic behavior, density profile, pressure profile, core repulsive force, stability, equilibrium and energy conditions of those massive compact objects. We further analyze different important parameters like anisotropic stress, surface redshift, adiabatic behavior, compactness factor, sound speed, etc. in case of super-massive NSs for better realization and future study.

Gravitational waves from binary black-hole mergers can be used to provide distance and angular location information of these sources, which, upon comparison with galaxy catalogs, can be used to measure the Hubble Constant. For a given galaxy catalog, and binary merger rates associated with each galaxy, a Fisher information approach can be used to estimate the measurement error for the Hubble Constant from the dark siren approach. In this paper, we validate the predictions from the Fisher information approach by carrying out a series of Monte Carlo simulations. Except in situations with very low event rates, the Fisher information approach is shown to predict the statistical errors of the Bayesian approach with good accuracy.

Motivated by the increasing interest in finding physically viable rotating sources, we present a new class of anisotropic rotating solutions. The energy–momentum tensor compatible with the metric is composed of anisotropic matter with a nonvanishing energy flow around the symmetry axis and vanishing viscosity. The new class of solutions can be used to find new possible sources for the Kerr metric, to obtain new regular black hole solutions and to study galaxies with a central rotating black hole and an halo of dark matter. As an example, we obtain a five-parameter class of solutions representing a two-way traversable wormhole smoothly matched to the Kerr one and satisfying all energy conditions outside the wormhole for a wide range of parameters, in particular for compact objects. Finally, with a simple modification of the aforementioned solution, we obtain a source for Kerr metric with a throat geometry, nonrepresenting a two-way traversable wormhole and satisfying all energy conditions.

Through this study, we intend to present a comprehensive summary of the most recent research on complex systems or complexity factor $({{𝒞}}_f)$ in the background of modified gravity theories (MGT). In this way, we examined ${{𝒞}}_f$ for the novel MGT named $f({𝒢},T^2)$ gravity under the anisotropic static fluid configuration. ${{𝒞}}_f$ is defined as one of the structure scalars $(Y_{TF})$ which is trace-free component obtained from the orthogonal splitting of the Riemann tensor. Two mass approaches are used which have immense influence on ${{𝒞}}_f$. Furthermore, vanishing complexity condition is used with an eye towards finding the solution of the nonlinear system. Two extra models are explored which ensure one more condition for the purpose of comprehensive results.

The paper proposes an amendment to the relativistic continuum mechanics which introduces the relationship between density tensors and the curvature of spacetime. The resulting formulation of a symmetric stress–energy tensor for a system with an electromagnetic field leads to the solution of Einstein Field Equations indicating a relationship between the electromagnetic field tensor and the metric tensor. In this EFE solution, the cosmological constant is related to the invariant of the electromagnetic field tensor, and additional pulls appear, dependent on the vacuum energy contained in the system. In flat Minkowski spacetime, the vanishing four-divergence of the proposed stress–energy tensor expresses relativistic Cauchy’s momentum equation, leading to the emergence of force densities which can be developed and parameterized to obtain known interactions. Transformation equations were also obtained between spacetime with fields and forces, and a curved spacetime reproducing the motion resulting from the fields under consideration, which allows for the extension of the solution with new fields.

Mimetic gravity analysis has been studied as a theory in various types of general relativity extensions, such as mimetic $f(R)$ gravity, mimetic $f(R,T)$ gravity, mimetic $f(R,G)$ gravity, etc. in the literature. This paper presents a set of equations arising from mimetic conditions and studies cosmic inflation with a combination of mimetic $f(G)$ gravity and swampland dS conjectures. We analyze and evaluate these results. Therefore, we first thoroughly introduce the mimetic $f(G)$ gravity and calculate some cosmological parameters such as the scalar spectral index, the tensor-to-scalar ratio, and the slow-roll parameters. Also, we investigate the potential according to the mimetic $f(G)$ gravity. Then we will challenge the swampland dS conjectures with this condition. By expressing the coefficient of swampland dS conjectures viz $C_1$ and $C_2$ in terms of $n_s$ and $r$, we plot some figures and determine the allowable range for each of these cosmological parameters and these coefficients, and finally, compare these results with observable data such as Planck and BICEP2/Keck array data. We show $C_1$ and $C_2$ are not ${𝒪}(1)$, so the refining swampland dS conjecture is not satisfied for this inflationary model. Then we examine it with further refining swampland dS conjecture, which has a series of free parameters such as $a,b>0$, $q>2$ and $a+b=1$. By adjusting these parameters, the compatibility of the mentioned conjecture with the inflationary model can be discussed. We determine the further refining swampland dS conjecture is satisfied. when $a<\frac{1}{1.00489}=0.99513$, we can always find $a$, $b$ and $q$ whose value is larger than 2, viz for $q=2.4$, we find $0.99185\le a<1$, which we can choose $a=0.99235$ according to the condition $a<0.99513$. Also we know $b=1-a$, so we will have $1-0.99235=0.00765>0$.

In this paper, a modified Born–Infeld gravitation theory with an $f(R)$ function being added to the determinant action is analyzed from a cosmological viewpoint. The corresponding accelerating dynamics are studied in a simplified conformal approach without matter. Three different structures for the auxiliary metric function are analyzed, with the aim to establish a deeper understanding of the role of this function in cosmology. After performing the analysis, it is seen that by modifying the auxiliary metric function, a Big Rip singularity or either a Little Rip dark energy model may arise.