We systematically investigate the quasinormal modes of thick branes in $\textit{f}$($\textit{R}$) gravity by numerically solving the Schrödinger-like perturbation equation of gravitational perturbations. To ensure reliability of the results, we employ three complementary methods: the asymptotic iteration method, direct integration of the wave equation, and time-domain numerical evolution. We analyze how model parameters influence the shape of the effective potential of gravitational perturbations and find that the structure of the potential barrier plays a significant role in shaping the quasinormal frequency spectrum. The results obtained from the three methods exhibit strong consistency, thereby ensuring the reliability of the calculations. In particular, real parts of the quasinormal frequencies exhibit an approximately arithmetic progression, suggesting that quasi-localized states can be understood as resonances between the barriers.

China

Yu-Peng E.

Chun-Chun Zhu

Yu-Xiao Liu

Quasinormal modes of thick branes in $\textit{f}$($\textit{R}$) gravity

We review the recent work by T.F. Dabash, M. Emam, and L. Schöppner (Eur. Phys. J. C 85, 1341, 2025) and identify an essential error in their analysis.

South Africa

Chile

Andronikos Paliathanasis

Comment on: “Symmetry and conserved quantities in $$f\left( R\right) $$ -gravity: Mei vs. Noether approaches”

<p>Our understanding of high-lying states within the charmonium family remains incomplete, particularly in light of recent observations of charmonium states at energies around 4 GeV. In this study, we investigate the spectroscopic properties of several high-lying charmonia, focusing on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>D</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>F</mi></math> states. A mass spectrum analysis is conducted, incorporating the unquenched effects. We then present a detailed study of the strong decay properties, including partial decay widths for two-body strong decays permitted by the Okubo-Zweig-Iizuka rule. Additionally, we explore the primary radiative decay channels associated with these states. Finally, we discuss the radiative transitions of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>D</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>F</mi></math> states via <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> annihilation. Theoretical predictions provided here aim to guide future experimental searches for high-lying charmonium states at facilities such as BESIII, Belle II, LHCb, and the future Super <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>τ</mi></math>–Charm Facility.</p>

Cheng-Xi Liu

Zi-Long Man

Tian-Le Gao

Xiang Liu

Prospects for observing the missing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>D</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>F</mi></math> charmonium states around 4 GeV

F-theory compactifications with a nontrivial Mordell-Weil group realize abelian gauge symmetry through rational sections, but their consistency is ultimately a statement about the quantum effective action. We show that compactification on a circle makes this statement concrete: the quantized, parity-odd Chern-Simons couplings of the resulting three-dimensional theory provide a one-loop exact and scheme-independent encoding of all local four-dimensional abelian anomalies, including the mixed gauge-gravitational terms, together with their Green-Schwarz cancellation. We determine these Chern-Simons couplings in two logically independent ways, first from flux-induced terms in the M-theory dual description, and second from an explicit one-loop integration over the complete massive spectrum, including Kaluza-Klein towers and Coulomb-branch states. The agreement fixes all normalizations and clarifies how large gauge transformations reorganize the spectrum. We then show compatibility with type IIB modular duality once the known ten-dimensional duality counterterm is included, and we present a fully explicit rank-two example over projective three-space.

Canada

United Kingdom

Belgium

Mir Faizal

Arshid Shabir

Chern-Simons couplings, modular duality, and anomaly cancellation in abelian F-theory

Understanding the late-time cosmic phenomenon of the universe commonly referred to as the dark energy problem, which is one of the prominent tension in the field of theoretical as well as observational cosmology. In this work, we attempt to analyze the nature of the missing fluid of the universe. In order to do so, we employ a polytropic equation of state consisting of free parameters rather assuming directly a particular form of the fluid. In addition, for the background geometry we consider a <italic>f</italic>( <italic>Q</italic>) cosmology exhibiting power-law assumption, which is recently proposed and found to be attractive in the study of late-time cosmology. We find exact cosmological solution along with a rigorous data analysis, utilizing the Bayesian statistics approach and the emcee ensemble sampler, to find the parameter constraints and then we interpret the parameters of physical interests such as deceleration and statefinder parameter. Also, we present status of the <italic>H</italic> <inf>0</inf> tension predicted by our polytropic <italic>f</italic>( <italic>Q</italic>) cosmological model.

India

Raja Solanki

Polytropic <italic>f</italic>( <italic>Q</italic>) cosmology and its implications for the <italic>H</italic> <inf>0</inf> tension

We systematically investigate static plane symmetric configurations in $\textit{f}$($\textit{Q}$) gravity. For vacuum regions, we discuss the constancy of the nonmetricity scalar $\textit{Q}$ and derive general vacuum solutions, which correspond effectively to Taub-(anti) de Sitter spacetimes with a cosmological constant determined by the specific $\textit{f}$($\textit{Q}$) model. By matching a singular thin shell source to the vacuum solutions, we relate the shell’s energy density and pressure to the integration constants of the exterior geometry. We also examine a finite-thickness slab as another matter source supporting the vacuum solution. Through numerical analysis of a quadratic model $$f(Q)=Q+\alpha Q^2$$ with isotropic matter, we show that the maximum pressure inside the slab generally does not coincide with the geometric center. Moreover, a negative $$\alpha $$ with larger magnitude leads to higher internal pressure and a thicker slab, while models with positive $$\alpha $$ are incompatible with a self-gravitating slab of positive pressure.

Jun-Qin Long

Rui-Hui Lin

Xiang-Hua Zhai

Static plane symmetric solutions in $\textit{f}$($\textit{Q}$) gravity

We investigate the consistency of linear dark sector interactions within coincident <italic>f</italic>( <italic>Q</italic>) gravity restricting to a &#923;CDM-mimicking background. We focus on a linear model supplemented by a geometrically motivated background-inert <math altimg='si23.svg'><msqrt><mi>Q</mi></msqrt></math> correction ensuring expansion history identical to &#923;CDM, with all the gravitationally motivated effects arising exclusively at the perturbation level. We show that background consistency enforces a nontrivial structural restriction - any interaction proportional to the matter density is mathematically incompatible leading to a unique dark energy proportional coupling. This unique no-go result reflects the geometric origin of the effective dark energy sector in <italic>f</italic>( <italic>Q</italic>) gravity. The parameter space of this residual interacting sector is quantified using Markov Chain Monte Carlo analysis using late-time cosmological data including Redshift-Space Distortions, updated Cosmic Chronometers, DESI DR2 BAO and Type Ia Supernovae. The <math altimg='si23.svg'><msqrt><mi>Q</mi></msqrt></math> term modifies growth structure through a gravitational coupling, introducing perturbation level sensitivity in <italic>f&#963;</italic> <inf>8</inf>. We find that all the parameters are tightly constrained and are compatible with zero, indicating the strong observational limits on perturbation level departures from &#923;CDM. The model remains statistically compatible with &#923;CDM according to information criteria, while preserving a viable growth history. Our results therefore establish sharp structural and observational bounds on interacting dark energy scenarios in Symmetric Teleparallel Gravity, providing a benchmark consistency test for future high precision surveys.

Ameya Kolhatkar

Preet Dalal

P.K. Sahoo

Structural constraints on interacting dark sector in ΛCDM-mimicking <italic>f</italic>( <italic>Q</italic>) gravity

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

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