arXiv subjects

A. Eid

Publications and source records attributed to A. Eid.

6 recordsLinked to original sources

arXiv2026

Late-Time Cosmology and Structure Formation in Quadratic $f(Q)$ Gravity

We investigate the cosmological evolution associated with the quadratic symmetric teleparallel gravity framework, $ f(Q)=Q+\alpha Q^{2}+\beta $ where the relation $Q\propto H^{2}$ generates an additional $H^{4}$ contribution to the Friedmann equation. Using the exact algebraic solution for $H(z)$, we reconstruct the effective dark-energy sector and compare the background evolution with $\Lambda$CDM using Type Ia supernovae, BAO, and cosmic-chronometer data. At the perturbative level, the model modifies the Poisson equation through a time-dependent effective gravitational coupling $G_{\textrm eff}(z)=G\big[1+\tfrac{2}{3}A E^{2}(z)\big]^{-1}$, where $A=18\alpha H_{0}^{2}$. For $\alpha>0$ this produces a weakened gravitational interaction, suppressing the linear growth factor $D(z)$, the growth rate $f(z)$, and the RSD observable $f\sigma_{8}(z)$. In the nonlinear regime, the reduced gravitational strength increases the spherical-collapse threshold and suppresses the halo mass function, leading to a lower predicted value of $S_{8}=\sigma_{8}\sqrt{\Omega_{m}/0.3}$. Thus, the quadratic $f(Q)$ extension can reproduce mild deviations from $\Lambda$CDM at the background level while naturally alleviating the $S_{8}$ tension, offering a viable modified-gravity explanation for recent observational hints of dynamical dark energy.

physics.gen-ph↗

arXiv2026

A Minimal and Stable Vacuum Bounce in Exponential $f(R)$ Gravity

We investigate the realization of a nonsingular cosmological bounce in metric $f(R)$ gravity using a controlled exponential deformation of the Starobinsky $R^{2}$ model. Adopting a smooth Gaussian-type bouncing scale factor, we first demonstrate a no-go result showing that a positive-curvature vacuum bounce cannot be supported by the model $f(R)=R+\alpha R^{2}(1-e^{-R/R_b})$ alone. We then show that a minimal extension obtained by introducing a constant term restores the bounce exactly, with the constant fixed algebraically by the bounce condition. A systematic parameter-space scan is performed to identify regions free of ghost and tachyonic instabilities. Working in the Einstein frame, we study the evolution of scalar and tensor perturbations across the bounce and show that both remain finite and well behaved. Our results establish a minimal, perturbatively stable realization of a vacuum bounce in $f(R)$ gravity that goes beyond background-level constructions.

gr-qc↗

arXiv2026

Black Hole Topologies and Geodesic Structures in Symmetric Teleparallel f(Q) Gravity

Black hole solutions are studied here within the symmetric teleparallel formulation of gravity, employing the $f(Q)$ model in which the gravitational dynamics are governed by the non-metricity scalar $Q$. We focus on static, circularly symmetric spacetimes in $(2+1)$-dimensions, analyzing both charged and uncharged cases. By adopting a power-law form for $f(Q)$, we derive exact black hole solutions and explore their thermodynamic and geometric properties. Curvature and non-metricity scalars reveal central singularities stronger than those in general relativity. we find that the horizon radii increase with the charge parameter while higher values of the non-metricity coefficient, $c_{4}$, or the cosmological constant $\Lambda$ tend to merge or eliminate horizons, reducing their total number and altering the near-origin structure of the spacetime. We perform a detailed topological analysis based on the Euler characteristic and examine the geodesic completeness of the spacetime. Our findings show that, depending on the presence of electric charge, the singularity may or may not be reachable by geodesics. The thermodynamic stability is confirmed via temperature, entropy, and heat capacity calculations. This study highlights the rich structure of $f(Q)$ gravity in lower-dimensional settings and offers new insights into the nature of singularities and black hole topologies in modified gravity theories.

gr-qc↗

arXiv2026

Holographic Dark Energy as a Source for Wormholes in Modified Gravity

Traversable wormhole solutions are explored in $f(\mathcal{R},\mathbb{T})$ gravity, a curvature--matter extension in which $\mathcal{R}$ is the Ricci scalar and $\mathbb{T}$ denotes the trace of the energy--momentum tensor. To generate explicit wormhole models, we prescribe holographic dark-energy densities based on entropy formalism proposed by R\'enyi, Moradpour, and Bekenstein--Hawking, namely \[ \rho_{\textit{R}} = \frac{\alpha}{4\alpha_1 r^4 c^2 \kappa}\ln\!\left(1+\pi \alpha_1 r^2\right), \qquad \rho_{\textit{M}} = \frac{\alpha}{4\pi r^2 c^2 \kappa \left(\pi \alpha_1 r^2 + 1\right)}, \qquad \rho_{\textit{BH}} = \frac{\alpha}{4 c^2 \kappa r^2}, \] with $\alpha$ and $\beta$ carrying dimensions of $L^{-2}$. The corresponding shape functions obtained from the field equations satisfy the standard throat and flare-out requirements for traversability. We then study how varying $\alpha$ and $\beta$ affects (i) the balance of forces associated with equilibrium and (ii) the status of the energy conditions. In particular, the null energy condition is found to be violated, indicating that exotic matter (or an effective exotic sector) is required to support the wormhole geometry. The spatial structure of the solutions is further visualized through embedding surfaces.

gr-qc↗

arXiv2026

Primordial Black Hole Formation in $f(R)=R+\alpha R^2$ Gravity: Perturbative and Non-Perturbative Analysis

We present a complete analytic and semi-analytic study of gravitational collapse and primordial black hole (PBH) formation in the quadratic $f(R)$ model $f(R)=R+\alpha R^2$. We first derive the perturbative expansion around General Relativity (GR), working to first order in the small parameter $\alpha$. For a collapsing flat FLRW dust interior we compute the explicit first-order corrections to the scale factor, the stellar radius, and the horizon formation time. { We then use these results to infer the expected trend in the PBH formation threshold $\delta_c$, rather than a direct quantitative determination. Within this perturbative framework, the quadratic correction modifies the dust collapse dynamics at first order, while the flat radiation-dominated background does not receive a nontrivial correction at the same order. As result, any modification of PBH formation in the radiation era must arise from nonlinear or non-perturbative effects. The perturbative analysis therefore provides qualitative insight into how curvature corrections influence collapse, particularly in high-curvature regimes.} To access this regime we reformulate the theory in the Einstein frame, where the model becomes GR plus the scalaron field $\phi$ with the Starobinsky potential. We provide the complete ODE system governing both the cosmological background and the evolution of an overdense closed FLRW patch. This system can be numerically integrated to obtain the critical overdensity $\delta_c(k)$ for PBH formation near the end of inflation.

gr-qc↗

arXiv2025

Four-scalar model and spherically symmetric solution in $f({\cal T})$ theory

In this work, we investigate the construction of spherically symmetric solutions within the framework of modified teleparallel gravity, focusing in particular on $f({\cal T})$ theory, where ${\cal T}$ represents the torsion scalar. Conventional mimetic gravity and its extension with two scalar fields are unable to reproduce general spherically symmetric geometries in $f({\cal T})$ gravity, since consistency requires either a constant torsion scalar or a linear form of $f({\cal T})$, which corresponds to the teleparallel equivalent of General Relativity (TEGR). To overcome this restriction, we introduce a four-scalar field formulation that generalizes the two-scalar model and enables the realization of arbitrary spherically symmetric spacetimes. We further demonstrate that the model avoids ghost degrees of freedom by imposing appropriate constraints through Lagrange multipliers. As an application of the formalism, we examine a specific spherically symmetric metric and determine the corresponding four scalar fields, analyzing their properties. In the presence of a quadratic extension of the action, ${\cal T} + \tfrac{\alpha}{2}{\cal T}^2$, our approach successfully reconstructs physically viable solutions free from ghost instabilities. These findings highlight the potential of scalar-field-based constructions for generating consistent spacetime geometries in modified gravity theories, thereby extending beyond the standard formulations.

gr-qc↗