We study the local horizon residue and minimally coupled massless-scalar quasinormal modes of the logarithmic connection-hair background obtained perturbatively in the quadratic model $$f(Q)=Q+\alpha Q^2$$ . After mass renormalization the displayed order- $$\alpha ^2$$ blackening function is $$F(r)=1-[2M+\eta \ln (r/r_\star )]/r$$ , with $$\eta =\alpha ^2\mu $$ . Euclidean regularity and the simple pole of 1/$\textit{F}$ give the same Hawking temperature, while the same residue multiplies the near-horizon logarithm of the scalar tortoise coordinate. We derive the massless-scalar master equation, its effective potential, the photon-sphere equation, and the controlled first-order shifts of the eikonal scalar frequency and damping rate. We do not identify the integration parameter $\textit{M}$ with a Hamiltonian or Noether mass: the logarithmic tail leaves the perturbative regime at large radius and does not satisfy the standard falloff required for a finite ADM charge. Consequently no physical entropy, heat capacity, Ruppeiner metric, or gravitational quasinormal-mode spectrum is claimed. For comparison only, we retain an explicitly labelled auxiliary Hessian construction and an algebraic evaluation of the resummed truncated metric at $$r_h=2\eta $$ . That point has $$|\eta |/r_h=1/2$$ and is therefore outside perturbative control; its finite scalar null-orbit and WKB frequencies are properties of the truncated function, not predictions of quadratic $\textit{f}$($\textit{Q}$) gravity. The controlled result is the local temperature–scalar-monodromy residue identity and the distinct small-hair shifts sampled at the horizon and photon sphere.

China

Wen-Xiang Chen

Horizon residues and test-scalar quasinormal modes of a perturbative Schwarzschild-type black hole in quadratic $\textit{f}$($\textit{Q}$) gravity

The <italic>f</italic>( <italic>R, T, Y</italic>) gravity is a modified theory that involves the Ricci scalar <italic>R</italic>, the trace of the energy-momentum tensor <italic>T</italic>, and the non-minimal matter geometry coupling term <math altimg='si3.svg'><mrow><mi>Y</mi><mo linebreak='goodbreak'>=</mo><msub><mi>R</mi><mrow><mi>a</mi><mi>b</mi></mrow></msub><msup><mi>T</mi><mrow><mi>a</mi><mi>b</mi></mrow></msup></mrow></math>. In this article, we are eager to explore the imprints of <italic>f</italic>( <italic>R, T, Y</italic>) cosmology on the early universe through the observational constraints of Big Bang nucleosynthesis. To analyze the early universe scenario, we investigate the deviation of freeze-out temperature through the ratio <math altimg='si1.svg'><mrow><mrow><mo>|</mo><mstyle mathvariant='normal'><mi>&#916;</mi></mstyle></mrow><msub><mi mathvariant='script'>T</mi><mi>f</mi></msub><mo linebreak='goodbreak'>/</mo><msub><mi mathvariant='script'>T</mi><mi>f</mi></msub><mrow><mo>|</mo></mrow></mrow></math> that has observation limits <math altimg='si4.svg'><mrow><mrow><mo>|</mo><mstyle mathvariant='normal'><mi>&#916;</mi></mstyle></mrow><msub><mi mathvariant='script'>T</mi><mi>f</mi></msub><mo linebreak='goodbreak'>/</mo><msub><mi mathvariant='script'>T</mi><mi>f</mi></msub><mrow><mo>|</mo><mo>&#8804;</mo><mn>4.7</mn><mo linebreak='badbreak'>&#215;</mo></mrow><msup><mn>10</mn><mrow><mo>&#8722;</mo><mn>4</mn></mrow></msup></mrow></math> and the primordial helium mass fraction <italic>Y<inf>p</inf></italic> of the light nuclear species having observational limits <math altimg='si5.svg'><mrow><msub><mi>Y</mi><mi>p</mi></msub><mo linebreak='goodbreak'>=</mo><mn>0.245</mn><mo>&#177;</mo><mn>0.003</mn></mrow></math>. For instance, we consider two models <math altimg='si6.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>,</mo><mi>Y</mi><mo>)</mo><mo>=</mo><mi>R</mi><mo linebreak='goodbreak'>+</mo><mi>&#945;</mi><mi>Y</mi></mrow></math> and <math altimg='si7.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>,</mo><mi>Y</mi><mo>)</mo><mo>=</mo><mi>R</mi><mo linebreak='goodbreak'>+</mo><mi>&#945;</mi><mi>Y</mi><mo linebreak='goodbreak'>+</mo><mi>&#947;</mi><mi>T</mi></mrow></math> to evaluate the viability of observational limits. We analyzed these models for the radiation-dominated era ( <math altimg='si8.svg'><mrow><mi>&#961;</mi><mo linebreak='goodbreak'>=</mo><mn>3</mn><mi>p</mi></mrow></math>) in the early universe. Our findings indicate that <italic>f</italic>( <italic>R, T, Y</italic>) gravity can agree with recent observational bounds on big bang nucleosynthesis via deviations in freeze-out temperature and primordial helium abundances, leading to a viable cosmology in the early cosmic epoch.

Pakistan

Abdul Malik Sultan

Saudi Arabia

Ibrahim Aldayel

Kainat Naseer

Manahil Ali

Meraj Ali Khan

Azerbaijan

Abdul Jawad

Observational signatures of <italic>f</italic>( <italic>R, T, Y</italic>) gravity on early universe evolution

In this work, the classical Godel solution from general relativity is extended into the framework of modified gravity theories based on non-metricity <italic>Q</italic> and the trace of the energy-momentum tensor <italic>T</italic> in the context of <italic>f</italic>( <italic>Q, T</italic>) gravity. The main feature of the Godel solution is the existence of closed time-like curves, which allow for causality violation and time travel. Since general relativity and its extensions do not demand spacetime to be globally causal, there is good motivation to explore such solutions. We have found classes of solutions with different matter content, like perfect fluid, cosmological constant, massless scalar field, etc. It is observed that, for suitable initial conditions, there are possibilities of obtaining feasible solutions that violate causality in our setup. The presence of non-metricity and its coupling with matter in such solutions produce significant deviations that are noteworthy.

India

Tuhina Ghorui

Prabir Rudra

Farook Rahaman

Godel universe in <italic>f</italic>( <italic>Q, T</italic>) gravity: Exploring causality violation and closed time-like curves

We present a nonsingular bouncing cosmological model in the framework of modified <italic>f</italic>( <italic>R, T</italic>) gravity within a spatially flat Friedmann - Lemaitre - Robertson - Walker universe. A logarithmic time-dependent scale factor is assumed to realize a smooth transition from a contracting phase to an expanding phase without encountering an initial singularity. Based on this assumption, the dynamical evolution of the Hubble parameter, deceleration parameter, energy density, and pressure is obtained for various choices of the model and the matter&#8211;geometry coupling parameter to confirm the occurrence of a successful bounce. The effective equation of state parameter is examined to characterize the cosmic fluid during different evolutionary phases. The violation of energy conditions, necessary for the realization of the bouncing behavior, is also discussed. The stability of the model is investigated using the squared speed of sound and is found to remain positive within the allowed parameter space, indicating classical stability. Furthermore, constraints on the matter&#8211;geometry coupling parameter are obtained by demanding positive energy density, negative pressure, and a viable cosmological evolution. The obtained cosmological constraint on the coupling parameter is also shown to be compatible with the currently available compact-object constraints. The thermodynamic behavior of the model is examined by testing the generalized second law of thermodynamics. The total entropy production rate remains negative during the contracting phase and changes its sign to positive during the expanding phase. However, it becomes singular at the bouncing point, reflecting the breakdown of the standard thermodynamic description during the transition phase.

 Anjani

Pankaj Kumar

Kazakhstan

S.H. Shekh

Milan Srivastava

A nonsingular logarithmic bouncing cosmology in <italic>f</italic>( <italic>R, T</italic>) gravity with thermodynamic viability

We extend the results of Lappi et al. [<a href="http://dx.doi.org/10.1140/epjc/s10052-023-12365-2">Eur. Phys. J. C 84, 84 (2024)</a>] to show that it is possible to obtain expressions for the longitudinal, singlet, and gluon structure functions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mi>L</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mi>S</mi></msub></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi></math> in deep inelastic scattering directly in terms of the measured functions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mn>2</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><msub><mi>F</mi><mn>2</mn></msub><mo>/</mo><mi>ln</mi><mo stretchy="false">(</mo><msup><mi>Q</mi><mn>2</mn></msup><mo stretchy="false">)</mo></math> modulo nonsinglet corrections expected to be small at very small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>. The latter can be treated at low <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> using existing quark distributions. Our results are presented consistently to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>O</mi><mo stretchy="false">(</mo><msubsup><mi>α</mi><mi>s</mi><mn>2</mn></msubsup><mo stretchy="false">)</mo></math>, correcting and extending the mixed-order results of Lappi et al..

Iran

G.R. Boroun

United States

Loyal Durand

Phuoc Ha

Direct determination of the structure functions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mi>L</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mi>S</mi></msub></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi></math> from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mn>2</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi><msub><mi>F</mi><mn>2</mn></msub><mo>/</mo><mi>d</mi><msup><mi>Q</mi><mn>2</mn></msup></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>O</mi><mo stretchy="false">(</mo><msubsup><mi>α</mi><mi>s</mi><mn>2</mn></msubsup><mo stretchy="false">)</mo></math>

We revisit the effective coupling of the scalaron to gauge fields in $\textit{f}$ ($\textit{R}$) gravity minimally coupled to the Standard Model, focusing on the scalaron decay into two photons. Treating the scalaron as an intrinsic component of the Jordan-frame metric, we analyse quantum effects arising from its coupling to the energy-momentum tensor. In this framework, the trace anomaly contributes to the scalaron-gauge boson interaction.

Ukraine

Yuri Shtanov

Effective scalaron-photon interaction in $\textit{f}$ ($\textit{R}$) gravity

We consider a general class of large $\textit{N}$ vector-like theories in $\textit{d}$ = 2 + 1 in a Hamiltonian approach. We show that by using lightcone quantization and the $\textit{N}$ → ∞ limit, we can diagonalize the Hamiltonian exactly and construct the eigenstates, spectral density, S-matrix, and form factors for the theory. For concreteness, we mainly focus on QED at large $\textit{N}$ as an explicit example. We comment on extending the approach to finite $\textit{N}$ calculations.

A. Fitzpatrick

Anastasiia Novikova

Noah Ring

Hamiltonian truncation of large $\textit{N}$ $\textit{f}$ QED and large $\textit{N}$ vector-like theories in $\textit{d}$ = 2 + 1

We investigate <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mi>P</mi><mtext>−</mtext><mn>1</mn><mi>F</mi></mrow></math> mixing in charmonium, focusing on the close-in-mass <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><mn>2</mn><mi>P</mi><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>χ</mi><mrow><mi>c</mi><mn>2</mn></mrow></msub><mo stretchy="false">(</mo><mn>1</mn><mi>F</mi><mo stretchy="false">)</mo></math> states. The conventional tensor force yields negligible mixing, motivating the inclusion of coupled-channel effects. Our unquenched calculation reveals sizable mixing angles of 7.5° and 15.4°. We predict the corresponding two-photon and two-gluon decay widths as key observables for experimental verification. Additionally, we discuss the production of these two <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mi>P</mi><mtext>−</mtext><mn>1</mn><mi>F</mi></mrow></math> mixed states of charmonium via <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi><mi>γ</mi></math> fusion. Current data are insufficient to determine the mixing, highlighting the need for precise future measurements to resolve this aspect of charmonium spectroscopy.

Peng-Yu Sun

Tian-Le Gao

Zi-Long Man

Xiang Liu

Proposed mixing between <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>P</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mi>F</mi></math> wave charmonia

We discuss the reconstruction of scalar field potential necessary to witness inflation at the very early phase of the Universe. A minimally coupled inflaton field is considered along with a modified teleparallel gravity where the action contains a function of torsion. Reconstruction mechanism in a most general way is discussed. Constant roll inflation is imposed upon the field equations to simplify the reconstruction procedure. Considering a functional form of $\textit{f}$($\textit{T}$), we obtained the effective scalar field potential and Hubble parameter in an analytic manner.

B. Mishra

S. Tripathy

Constant roll inflation and reconstruction of scalar field potential in $\textit{f}$($\textit{T}$) gravity

In this study, we explore the cosmological evolution of the Universe in the framework of covariant $\textit{f}$($\textit{Q}$) gravity, with a coupling function that evolves dynamically in proportion to the Hubble parameter. Two specific forms of the function are examined: a power-law model and a logarithmic model. By rewriting the cosmological field equations as an autonomous dynamical system, we determine and classify the corresponding critical points and analyze their stability. Our results show that both models are able to reproduce the sequence of cosmic evolution, including radiation, matter, and dark energy-dominated eras, along with the transitions between them. The physical properties at each critical point are described using key cosmological quantities such as the total EoS parameter, density parameters, and the deceleration parameter. The stability of the non-hyperbolic critical point is analyzed through center manifold theory. In addition, we present phase space trajectories along with the stability behavior of each critical point. The evolution plots for the density parameters of radiation, matter, and dark energy, along with the Equation of State (EoS) parameter for the total, are illustrated for further analysis. Overall, the analysis suggests that the $\textit{f}$($\textit{Q}$) models considered here, within the context of covariant formulation, provide a consistent description of cosmic evolution and offer a promising approach to explaining the late-time acceleration of the Universe.

S. Narawade

S. Kadam

Dynamical analysis of the covariant $\textit{f}$($\textit{Q}$) gravity models