International Journal of Modern Physics D

This work treats cosmological perturbation in a mixture of standard matter, Chaplygin gas as well as Gauss–Bonnet fluids using a 1+3 covariant approach in the context of modified $f(G)$ gravity. We define the gradient variables to obtain linear perturbation equations. After scalar and redshift transformations, we consider both an original Chaplygin and generalized Chaplygin gas models under Gauss–Bonnet gravity. For pedagogical purposes, the consideration of polynomial $f(G)$ gravity model was used to solve the perturbation equations for short- and long-wavelength modes and investigate the late-time evolution. The numerical solutions were obtained. The results show that the energy overdensity perturbations decay with an increase in redshift. The treatment recovers GR results under limiting cases.

In recent years, the modified theory of gravity known as $f(Q)$ gravity has drawn interest as a potential alternative to general relativity. According to this theory, the gravitational force is determined by a function of the so-called “non-metricity” tensor $Q$, which expresses how far a particle space-time is from the metric geometry. In contrast to general relativity, which describes the gravitational field using the curvature tensor, $f(Q)$ gravity builds a theory of gravity using the non-metricity tensor. For this class of theories, dynamical system analysis of the background and perturbation equations has been carried out in this work to determine how various models behave cosmologically. Here, the critical points are determined for two $f(Q)$ models from the literature: the power law, $f(Q)=Q+m{Q}^n$, and the logarithmic, $f(Q)=\alpha +\beta logQ$ models. The stability behavior and corresponding cosmology are displayed for each critical point. For the power law model, we achieve a matter-dominated saddle point with the right matter perturbation growth rate. For the logarithmic model, we get a saddle point dominated by the geometric component of the $f(Q)$ model with perturbations in the decomposition of matter. For both models, we later achieved a stable and accelerating Universe with constant matter perturbations.

In this paper, we characterize weakly Ricci-symmetric (shortly, ${\mathrm{\text{(}}\text{WRS})}_4$) spacetimes and their solutions in $f({ℛ})$-gravity. It is demonstrated that a ${\mathrm{\text{(}}\text{WRS})}_4$ spacetime represents a stiff matter fluid. In addition, we obtain that a conformally flat ${\mathrm{\text{(}}\text{WRS})}_4$ spacetime is a space of quasi-constant sectional curvature. Moreover, we establish that a Ricci symmetric ${\mathrm{\text{(}}\text{WRS})}_4$ spacetime represents a static spacetime. Finally, we investigate the effect of ${\mathrm{\text{(}}\text{WRS})}_4$ spacetime solutions in $f({ℛ})$-gravity.

Dynamical system theory is a widely used technique in the analysis of cosmological models. Within this framework, the equations describing the dynamics of a model are recast in terms of dimensionless variables, which evolve according to a set of autonomous first-order differential equations. The fixed points of this autonomous set encode the asymptotic evolution of the model. Usually, these points can be written as analytical expressions for the variables in terms of the parameters of the model, which allows a complete characterization of the corresponding parameter space. However, a thoroughly analytical treatment is impossible in some cases. In this work, we give an example of a dark energy model, a scalar field coupled to a vector field in an anisotropic background, where not all the fixed points can be analytically found. Then, we put forward a general scheme that provides a numerical description of the parameter space. This allows us to find interesting accelerated attractors of the system with no analytical representation. This work may serve as a template for the numerical analysis of highly complicated dynamical systems.

In this work, we investigate two mechanisms for locating fermions on the brane in a modified teleparallel gravity $f(T,{𝒯})$, where $T$ is the torsion scalar and ${𝒯}$ is the trace of the energy–momentum tensor. The first mechanism is a Yukawa-type minimal coupling between the fermion and the background scalar field. The second mechanism is a nonminimal coupling between the fermion and the torsion. The geometric coupling presents a greater sensitivity to the influence of torsion and to the trace of the energy–momentum tensor.

We discuss a cosmological scenario with a stochastic background of gravitational waves sourced by the tensor perturbation due to a hybrid inflationary model with cubic potential. The tensor-to-scalar ratio for the present hybrid inflationary model is obtained as $r\approx 0.0006$. Gravitational wave spectrum of this stochastic background, for large-scale CMB modes, $10^{-4}M{\mathrm{\text{pc}}}^{-1}$ to $1M{\mathrm{\text{pc}}}^{-1}$ is studied. The present-day energy spectrum of gravitational waves ${\mathrm{\Omega }}_0^{\mathrm{\text{g}}w}(f)$ is sensitively related to the tensor power spectrum and r which is, in turn, dependent on the unknown physics of the early cosmos. This uncertainty is characterized by two parameters: ${\widehat{n}}_t(f)$ logarithmic average over the primordial tensor spectral index and $ŵ(f)$ logarithmic average over the effective equation-of-state parameter. Thus, exact constraints in the ${\widehat{n}}_t(f)$-$ŵ(f)$ plane can be obtained by comparing theoretical constraints of our model on r and ${\mathrm{\Omega }}_0^{\mathrm{\text{g}}w}(f)$. We obtain a limit on $ŵ(10^{-15}\mathrm{\text{Hz}})<0.33$ around the modes probed by CMB scales.

The study of cosmic expansion history and the late time cosmic acceleration from observational data depends on the nuisance parameters associated with the data. For example, the absolute peak magnitude of type Ia supernova associated with the type Ia supernova observations and the comoving sound horizon at the baryon drag epoch associated with baryon acoustic oscillation observations are two nuisance parameters. The nuisance parameters associated with the gamma-ray bursts data are also considered. These nuisance parameters are constrained by combining the cosmological observations using the Gaussian process regression method with minimal model dependence. The bounds obtained in this method can be used as the prior for the data analysis while considering the observational data accordingly. Along with these nuisance parameters, the cosmic curvature density parameter is also constrained simultaneously. We find that the constraints on the cosmic curvature density parameter show no significant deviations from a flat Universe.

A new quark star model for a charged anisotropic stellar object is generated using the Einstein–Maxwell field equations. We use a metric function, linear equation of state, and a new measure of anisotropy in form of logarithmic function to formulate the model. For particular choices of parameters in the anisotropic measure, some anisotropic and isotropic models are regained as a special case. Physical analysis indicates that matter variables and gravitational potentials in the model are well behaved. The generated model satisfies the energy, regularity, causality, and stability conditions. The speed of sound is consistent with quark stars.