The <italic>R</italic> 2 and the single-field-like regime of <italic>R</italic> 2-Higgs inflation are disfavored by the observed high spectral index <italic>n<inf>s</inf></italic> from the combined cosmic microwave background (CMB) and baryon acoustic oscillation (BAO) measurements at the &#8239;&#8764;&#8239;2 <italic>&#963;</italic> level. The addition of a dimension-six <italic>R</italic> 3 term in the action helps alleviate this tension. We show that the parameter space accounting for the observed high <italic>n<inf>s</inf></italic> also induces rapid Goldstone and Higgs preheating. The preheating, especially from Goldstone modes, helps match the CMB and inflationary scales, which in turn supports the observed <italic>n<inf>s</inf></italic>.

India

Tanmoy Modak

Echoes of <italic>R</italic> 3 modification and Goldstone preheating in the CMB-BAO landscape

We investigate the realization of a nonsingular cosmological bounce in metric $\textit{f}$($\textit{R}$) 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 $\textit{f}$($\textit{R}$) gravity that goes beyond background-level constructions.

Egypt

South Africa

G. Nashed

Saudi Arabia

A. Eid

A minimal and stable vacuum bounce in exponential $\textit{f}$($\textit{R}$) gravity

<italic>f</italic>( <italic>R</italic>) gravity is a well-known modification of General Relativity, which is used in various models of dark matter and dynamical dark energy. We study static spherically symmetric (SSS) asymptotically flat configurations of the <italic>f</italic>( <italic>R</italic>) gravity in the Einstein frame for three known scalaron potentials with different asymptotic properties. The main attention is paid to the case of astrophysically relevant configuration mass <italic>M</italic> and scalaron mass <italic>&#956;</italic> greater than several <italic>meV</italic>, according to existing experimental constraints. This means very large values of the dimensionless (in geometrized units) parameter <italic>M&#956;</italic>, leading to specific properties of the SSS solutions. We consider a sufficiently large size of a scalarization region <italic>r</italic> <inf>0</inf>&#8239;&#8811;&#8239; <italic>r<inf>g</inf></italic>, where the space-time metric is essentially different from the Schwarzschild one. It turns out that the scalaron field has universal behavior regardless of <italic>M&#956;</italic> and <italic>r</italic> <inf>0</inf> and is practically the same for different scalaron potentials. Asymptotic parameters of the metric near the naked singularity at the center of the SSS configuration are obtained analytically for all the models. The test body circular orbits are discussed in view of observational signatures, which can distinguish these configurations from a regular black hole.

Ukraine

V.I. Zhdanov

Universality in static spherically symmetric solutions of <italic>f</italic>( <italic>R</italic>) gravity

This study presents a novel interpretation of complexity in the formalism of <math altimg='si1.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>,</mo><mi mathvariant='script'>T</mi><mo>)</mo></mrow></math> gravity, where <italic>R</italic> specifies the Ricci scalar, <math altimg='si2.svg'><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub></math> is written as matter Lagrangian that describes characteristics of the matter fields, and <math altimg='si3.svg'><mi mathvariant='script'>T</mi></math> represents the trace of energy-momentum tensor. We commence with the contemplation of the inner sector as a cylindrical configuration having anisotropic matter and linked with the exterior region through a hypersurface. We determine the modified field equations associated with <math altimg='si1.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>,</mo><mi mathvariant='script'>T</mi><mo>)</mo></mrow></math> gravity and assume the preliminarily established relations between the conformal tensor and the intrinsic curvature. We consider the generally employed mathematical expressions for Tolman mass and C-Energy and evaluate their relationship with the conformal tensor. The structural scalars are calculated from orthogonal splitting of Riemann tensor, out of which <italic>Y<inf>TF</inf></italic> is categorized as complexity factor for the inferred fluid composition. It is important to specify that the complexity factor is eradicated in the framework of uniform matter configuration and also in the scenario when anisotropic terms are canceled with each other. Significant results related to the Weyl scalar, Tolman mass, and the complexity factor are derived in <math altimg='si1.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>,</mo><mi mathvariant='script'>T</mi><mo>)</mo></mrow></math> gravity. The vanishing complexity constraint is considered in order to deal with the modified field equations that have extra degrees of freedom and to find particular solutions corresponding to the specific models.

Pakistan

A. Rehman

Azerbaijan

M. Yousaf

Uzbekistan

Bekzod Rahmatov

Javlon Rayimbaev

Munisbek Akhmedov

Complexity evaluation related to the cylindrically symmetric anisotropic matter in <math altimg='si1.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>,</mo><mi mathvariant='script'>T</mi><mo>)</mo></mrow></math> theory

This paper examines realistic configurations of anisotropic matter for spherical symmetry in modified gravity. With the Starobinsky <math altimg='si6.svg'><mrow><mi>f</mi><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mi>R</mi><mo linebreak='goodbreak'>+</mo><mi>&#945;</mi><msup><mi>R</mi><mn>2</mn></msup></mrow></math> model, the behavior of compact stars <math altimg='si7.svg'><mrow><mi>S</mi><mi>A</mi><mi>X</mi><mspace width='0.33em' /><mi>J</mi><mn>1808.4</mn><mo linebreak='goodbreak'>&#8722;</mo><mn>3658</mn></mrow></math> and <math altimg='si3.svg'><mrow><mn>4</mn><mi>U</mi><mn>1608</mn><mo linebreak='goodbreak'>&#8722;</mo><mn>52</mn></mrow></math> in the presence of an electromagnetic field. A core-envelope model is developed with polytropic and linear equation of state (EoS). The core, envelope, and Reissner Nordstr <math altimg='si8.svg'><mover accent='true'><mi>o</mi><mo>&#168;</mo></mover></math>m regions of compact stars match smoothly at the boundary. The graphs are plotted to discuss the physical behavior of density, pressure, mass, redshift, energy conditions, and compactification. To test stability of our model Tolman-Volkoff-Oppenheimer (TOV) equation and adiabatic index are presented graphically.

S.A. Mardan

Czechia

A. Khalid

Türkiye

Muhammad Bilal Riaz

Rubab Manzoor

Core-Envelope model of Einstein-Maxwell field equations under the influence of <italic>f</italic>( <italic>R</italic>) gravity

We derive the Seiberg-Witten map to first order in the non-commutativity parameter for D-branes in the presence of a large R-R background field. This result enables a systematic investigation of the commutative formulation of the corresponding Lagrangian. In the SU( <italic>N</italic>) sector, the map introduces a non-local operator. In contrast, in the U(1) sector, this non-locality can be removed. This contrast suggests that the essential source of non-local behavior lies in the non-Abelian degrees of freedom. The commutative description obtained here offers further insight into both the Dirac-Born-Infeld structure and its possible extensions to the dynamics of M5-branes.

China

Chen-Te Ma

Relation between commutative and non-commutative descriptions of D-branes in large R-R field background

In this work, we investigate exact black string solutions in the context of $\textit{f}$($\textit{R}$, $\textit{T}$) gravity. Adopting the specific form $$f(R,T) = R + 2\chi T$$ , we consider an anisotropic Kiselev fluid as the matter content and obtain static cylindrical solutions, which are then extended to the rotating case through a suitable coordinate transformation. The influence of the quintessence state parameter $$w_q$$ and the matter–geometry coupling constant $$\chi $$ on the geometry is analyzed. We examine the weak, null, and strong energy conditions, identifying the regions in the parameter space where they are satisfied. Furthermore, we apply the Hamilton–Jacobi method to study the tunneling of scalar particles across the event horizon and derive the corresponding Hawking temperature. The thermodynamic stability of the solutions is investigated by computing the heat capacity, and the conditions for phase transitions are discussed. The results provide a characterization of black strings in $\textit{f}$($\textit{R}$, $\textit{T}$) gravity surrounded by quintessence, highlighting the combined effects of anisotropic matter and modified gravity on their physical properties.

Brazil

L. Santos

L. Barbosa

C. Barros

Kiselev black strings in $\textit{f}$($\textit{R}$, $\textit{T}$) gravity

This research paper explores the structure of hypothetical compact stars, known as strange stars, within the framework of a novel modified theory of gravity called $$f(R,\Sigma ,T)$$ gravity. This theory extends General Relativity by making gravity dependent not only on the Ricci curvature scalar $\textit{R}$ but also on a torsion scalar $$\Sigma $$ and the trace of the matter energy–momentum tensor $\textit{T}$. This introduces a richer coupling between geometry and matter. The study presents a highly exotic, multi-layered stellar model composed of five distinct regions, each with a unique equation of state and geometric properties. The model features a dark-energy-like core with powerful repulsive gravity (anti-gravity), surrounded by successive layers of dust, exotic radiation, and a stiff matter crust, all enveloped by a standard Schwarzschild vacuum exterior. A key finding is the prevalence of negative energy densities and pressures in several layers, a hallmark of exotic matter. These configurations, enabled by the $$f(R,\Sigma ,T)$$ framework, lead to repulsive gravitational effects that radically alter the star’s internal equilibrium. The analysis demonstrates how additional geometry-driven forces within this theory can support such exotic structures, potentially preventing gravitational collapse and resulting in a stable, non-singular object. This work demonstrates that $$f(R,\Sigma ,T)$$ gravity allows for new and complex classes of compact objects with stratified, exotic matter distributions, whose properties and observational signatures would differ significantly from those predicted by standard General Relativity.

M. Bakry

Tahia Dabash

The impact of $$f(R,\Sigma ,T)$$ gravity on strange star structure

In this study, we analyze $\textit{f}$($\textit{R}$) gravity employing the $$ f(R) = R+ \alpha _1 R^p - \alpha _2 R^{-q} $$ model within the Friedmann–Lemaître–Robertson–Walker (FLRW) background. We derive the Friedmann equations via modified gravity action and subsequently reexpress them in terms of the standard Friedmann equations. Our investigation explores the behavior of a bouncing cosmological model within this modified gravity context, offering a potential solution to the singularity problem encountered in the standard Big Bang cosmology. We represent cosmological parameters as functions of cosmic time and scrutinize the conditions for a cosmic bounce. Additionally, we reconstruct the $\textit{f}$($\textit{R}$) gravity model using the redshift parameter and graphically present cosmological parameters as functions of redshift. These plots reveal an accelerated nature of Universe expansion. Furthermore, we reconstruct $\textit{f}$($\textit{R}$) gravity models for scale factors, $$a(t) = e^{e^{\lambda t}}$$ which exhibits the bouncing behavior. Finally, we investigated the stability scenario by examining the sound speed. The resulting graph of sound speed plotted against redshift confirms late-time stability.

M. Ilyas

Khalid Masood

South Korea

Nehad Shah

Dynamical analysis of bouncing cosmology in the Capozziello–De Laurentis model of $\textit{f}$($\textit{R}$) gravity

In the present paper we consider the usage of classical dynamical non-skew-symmetric <italic>r</italic>-matrices with spectral parameters in the theory of integrable systems. We construct &#8212; in complete analogy with non-dynamical case [26, 27] &#8212; general position Lax matrices satisfying classical <italic>r</italic>-matrix Poisson brackets. We consider an example of the Lie algebra <italic>gl</italic>( <italic>n</italic>), dynamical <italic>r</italic>-matrix of Calogero model (equivalent to that of [8]) and many-poled Lax matrix with <italic>N</italic> first order poles. With its help we obtain a new variant of <italic>gl</italic>( <italic>n</italic>) multi-spin-Calogero (Gaudin-Calogero) model, integrable without an additional reduction. The <math altimg='si1.svg'><mrow><mi>N</mi><mo linebreak='goodbreak'>=</mo><mn>1</mn></mrow></math> spin-Calogero case is considered in details.

T. Skrypnyk

On classical dynamical <italic>r</italic>-matrices, Lax algebras and integrable <italic>gl</italic>( <italic>n</italic>) spin-Calogero models