<list id='lst0001'><list-item id='lstitem0001'><label>&#8226;</label><para id='p0001'>We develop a Barrow-Ricci-Gauss-Bonnet holographic dark energy (BRGB-HDE) model within the symmetric teleparallel f(Q) gravity framework.</para></list-item><list-item id='lstitem0002'><label>&#8226;</label><para id='p0002'>The reconstructed equation of state parameter exhibits quintessence-like behavior and asymptotically approaches the cosmological constant boundary at late times.</para></list-item><list-item id='lstitem0003'><label>&#8226;</label><para id='p0003'>A numerical reconstruction of the f(Q) function reveals strong early-time geometric corrections that gradually weaken during cosmic evolution.</para></list-item><list-item id='lstitem0004'><label>&#8226;</label><para id='p0004'>The generalized second law of thermodynamics is satisfied throughout the evolution, confirming the thermodynamic consistency of the model.</para></list-item><list-item id='lstitem0005'><label>&#8226;</label><para id='p0005'>The squared speed of sound remains positive for suitable values of the Barrow parameter, ensuring dynamical stability of the reconstructed model.</para></list-item></list>

India

Preeti Joshi

Türkiye

Ertan Gudekli

Surajit Chattopadhyay

Cosmological and thermodynamic insights into Barrow-Ricci-Gauss-Bonnet holographic dark energy in the symmetric teleparallel framework of <italic>f</italic>( <italic>Q</italic>) gravity

This paper presents a gravastar model developed within the framework of <math altimg='si1.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>Q</mi><mo>)</mo></mrow></math> gravity using the Durgapal metric potential, allowing for a smooth and regular spacetime throughout the entire configuration. The model is structured with three distinct regions that include a central core filled with dark energy having negative pressure, a surrounding shell made of ultrarelativistic stiff matter, and an outer region that follows the Schwarzschild solution. By solving the modified field equations, we obtain exact expressions for physical quantities such as energy density, pressure, and metric components. The analysis focuses on the shell region, where proper length, total energy, entropy, and surface redshift are examined to understand the physical nature and stability of the configuration. Numerical values are determined using observational data from the compact star Vela X1, showing that the model remains free from singularities and does not form an event horizon. These results suggest that gravastars described in <math altimg='si1.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>Q</mi><mo>)</mo></mrow></math> gravity offer a meaningful and realistic alternative to black holes and provide valuable insight into the study of compact objects through modified theories of gravity.

Chaitra Chooda Chalavadi

V. Venkatesha

Phalaksha Murthy B

Geometric analysis of gravastars in <math altimg='si1.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>Q</mi><mo>)</mo></mrow></math> gravity with Durgapal metric potential

We investigate the (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi></math>-deformed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>SU</mi><mo stretchy="false">(</mo><mi>N</mi><msub><mo stretchy="false">)</mo><mi>k</mi></msub></math> Yang-Mills theory in the lattice Hamiltonian formalism, which is characterized by three parameters: the number of colors <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math>, the coupling constant <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi></math>, and the level <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>k</mi></math>. By treating these as tunable parameters, we explore how key properties of the theory, such as confinement and topological order, emerge in different regimes. Employing a variational mean-field analysis that interpolates between the strong- and weak-coupling regimes, we determine the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> phase structure in terms of the ’t Hooft coupling <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>λ</mi><mi>tH</mi></msub><mo>=</mo><msup><mi>g</mi><mn>2</mn></msup><mi>N</mi></math> and the ratio <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>k</mi><mo>/</mo><mi>N</mi></math>. We find that the topologically ordered phase remains robust at large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> under appropriate scalings of these parameters. This result indicates that the continuum limit of large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> gauge theory may be more intricate than naively expected, and it motivates studies beyond the mean-field theory, both to achieve a further understanding of confinement in gauge theories and to guide quantum simulations of large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> gauge theories.

Japan

Tomoya Hayata

Yoshimasa Hidaka

Hiromasa Watanabe

Phases of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi></math>-deformed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></math> Yang-Mills theory at large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math>

I present a calculation of the ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mfrac><msub><mi>σ</mi><mi>r</mi></msub><msub><mi>F</mi><mn>2</mn></msub></mfrac><mrow><mo>(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></mrow></mrow></math> in a momentum-space approach using the Block-Durand-Ha parametrization of the proton structure function <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>F</mi><mn>2</mn></msub><mrow><mo>(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></mrow></mrow></math>. The results are compared with the H1 data and extended to high inelasticity. I also examine the ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mfrac><msub><mi>σ</mi><mi>r</mi></msub><msub><mi>F</mi><mn>2</mn></msub></mfrac><mrow><mo>(</mo><mfrac><msup><mi>Q</mi><mn>2</mn></msup><mi>s</mi></mfrac><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></mrow></mrow></math> obtained at a fixed <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mi>s</mi></msqrt></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>Q</mi><mn>2</mn></msup></math> to the minimum value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>Q</mi><mn>2</mn></msup><mo>/</mo><mi>s</mi></mrow></math>, comparing them with both the HERA data and the color dipole model bounds. These results and comparisons with HERA data demonstrate that the suggested method for the ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>σ</mi><mi>r</mi></msub><msub><mi>F</mi><mn>2</mn></msub></mfrac></math> can be applied in analyses of the CERN Large Hadron Collider and Future Circular Collider projects. The effect of adding a simple higher twist term of the form <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>F</mi><mn>2</mn></msub><mo>*</mo><msub><mi>H</mi><mn>2</mn></msub><mo>/</mo><msup><mi>Q</mi><mn>2</mn></msup></mrow></math> to the description of the ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mfrac><msub><mi>σ</mi><mi>r</mi></msub><msub><mi>F</mi><mn>2</mn></msub></mfrac><mrow><mo>(</mo><mfrac><msup><mi>Q</mi><mn>2</mn></msup><mi>s</mi></mfrac><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></mrow></mrow></math> at low-<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> and low-<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>Q</mi><mn>2</mn></msup></math> values for comparison with the color dipole bounds and the HERA data is investigated.

Iran

G.R. Boroun

Investigation of the ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mfrac><msub><mi>σ</mi><mi>r</mi></msub><msub><mi>F</mi><mn>2</mn></msub></mfrac><mrow><mo>(</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>/</mo><mi>s</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></mrow></mrow></math> in the momentum-space approach

We compute the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mi>g</mi></math> contribution to the diffractive structure functions in high-energy deep inelastic scattering. The obtained result corresponds to a finite part of the next-to-leading-order contribution to the diffractive cross section. Previous phenomenological applications have included this contribution only in the high-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Q</mi><mn>2</mn></msup></math> or high-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>M</mi><mi>X</mi><mn>2</mn></msubsup></math> limits in the case of a soft gluon, and we numerically demonstrate that these existing estimates do not provide a good approximation for the full <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mi>g</mi></math> contribution. Furthermore, we demonstrate that in addition to the soft gluon contribution, there is an equally important soft quark contribution to the diffractive structure functions at high <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Q</mi><mn>2</mn></msup></math>.

Finland

Abhiram Kaushik

Heikki Mäntysaari

United States

Jani Penttala

Diffractive deep inelastic scattering in the dipole picture: The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mi>g</mi></math> contribution in exact kinematics

In the present article, we introduce $\textit{Q}$-solitons, a generalization of Riemann solitons, on (almost) coKähler manifolds ( , in short). Here we obtain a necessary condition from which we establish that a compact admitting $\textit{Q}$-soliton whose soliton vector field is pointwise collinear with the Reeb vector field is a $\textit{K}$- . We also prove that the soliton vector field of a $\textit{Q}$-soliton on $$(\kappa ,\mu )$$ - with $$\kappa <0$$ is an infinitesimal contact transformation. For the gradient case, we show that under certain restriction a $$(\kappa ,\mu )$$ - $$(\kappa <0)$$ reduces to $\textit{N}$($\textit{K}$)- . We deduce that a three dimensional coKähler manifold admitting $\textit{Q}$-soliton obeys $$\Delta \mathfrak {R}+\Delta \Psi =0$$ . Also we construct an example to verify our deduced results. Moreover, we explore certain results on $\textit{Q}$-solitons in the context of relativistic magneto-fluid spacetimes.

Gaurab Mitra

Avijit Sarkar

Tarak Mandal

Characterizations of $\textit{Q}$-solitons on (almost) coKähler manifolds and its applications in magneto-fluid spacetimes

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.

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.

China

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 static black hole solutions in three-dimensional <math altimg='si1.svg'><mrow><mo>(</mo><mn>2</mn><mo linebreak='goodbreak'>+</mo><mn>1</mn><mo>)</mo></mrow></math> spacetime within the framework of modified <italic>F</italic>( <italic>Q, T</italic>) gravity, where the gravitational action depends on the non-metricity scalar <italic>Q</italic> and the trace of the energy-momentum tensor <italic>T</italic>. Considering a linear model <math altimg='si11.svg'><mrow><mi>F</mi><mrow><mo>(</mo><mi>Q</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><msub><mi>C</mi><mn>1</mn></msub><mi>Q</mi><mo linebreak='goodbreak'>+</mo><msub><mi>C</mi><mn>2</mn></msub><mi>T</mi></mrow></math>, we derive the modified field equations under a Schwarzschild-like gauge and obtain both perturbative and numerical solutions. The weak-field expansion is shown to be valid in the asymptotic regime | <italic>a</italic>( <italic>r</italic>)|&#8239;&#8810;&#8239;1, while the near-horizon structure is analyzed through full numerical integration of the coupled differential system. The horizon is defined consistently in <math altimg='si12.svg'><mrow><mn>2</mn><mo linebreak='goodbreak'>+</mo><mn>1</mn></mrow></math> dimensions via <math altimg='si4.svg'><mrow><mi>A</mi><mo>(</mo><msub><mi>r</mi><mo>+</mo></msub><mo>)</mo><mo>=</mo><mn>0</mn></mrow></math>, and the Hawking temperature is obtained from surface gravity without invoking four-dimensional Schwarzschild relations. Using the Wald formalism adapted to non-metricity gravity, we derive the entropy and show that it reduces to <math altimg='si13.svg'><mrow><mi>S</mi><mo linebreak='goodbreak'>=</mo><mi>&#960;</mi><msub><mi>C</mi><mn>1</mn></msub><msub><mi>r</mi><mo>+</mo></msub><mo linebreak='goodbreak'>/</mo><mn>2</mn></mrow></math>, recovering the BTZ result in the limit <math altimg='si14.svg'><mrow><msub><mi>C</mi><mn>1</mn></msub><mo linebreak='goodbreak'>=</mo><mn>1</mn></mrow></math>. A general expression for the heat capacity is obtained, demonstrating that its sign depends on the second radial derivative of the metric function. While BTZ-like geometries yield positive heat capacity and thermodynamic stability, the numerical <italic>F</italic>( <italic>Q, T</italic>) solutions exhibit regions where <math altimg='si15.svg'><mrow><msup><mi>A</mi><mrow><mo>&#8243;</mo></mrow></msup><mrow><mo>(</mo><msub><mi>r</mi><mo>+</mo></msub><mo>)</mo></mrow><mo linebreak='goodbreak'>&lt;</mo><mn>0</mn></mrow></math>, leading to negative heat capacity and instability. Our results show that although the leading-order horizon structure coincides with BTZ geometry, the matter non-metricity coupling significantly modifies the radial structure and thermodynamic stability. This demonstrates that <italic>F</italic>( <italic>Q, T</italic>) gravity in three dimensions admits black hole solutions that are geometrically BTZ-like but thermodynamically distinct.

S. Davood Sadatian

S. Mohamad Reza Hosseini

Black hole solutions in three-dimensional gravity within the framework of the modified <italic>F</italic>( <italic>Q, T</italic>) gravity model