We develop a unified dynamical systems framework for spatially flat FLRW cosmology in $\textit{f}$($\textit{Q}$) gravity, covering all three connection branches using a single set of Hubble-normalised variables without fixing the function $\textit{f}$($\textit{Q}$) a priori. This model-independent and connection-agnostic approach enables direct comparison across connection choices and uncovers structural features of the cosmological dynamics not visible in connection-specific formulations. While the existing works narrowly focus only on fixed point analysis, in our work we put special efforts to identify the invariant submanifolds, model-independent trajectories and physically viable regions of phase space across connections. For a broad class of viable $\textit{f}$($\textit{Q}$) models, we establish the generic existence of de Sitter attractors and matter-dominated fixed points in the two branches of connection, offering a robust route to late-time acceleration without fine-tuning. We further identify an invariant submanifold that yields $$\Lambda $$ CDM-like background evolution despite underlying dynamics distinct from General Relativity, providing a geometric origin for cosmic acceleration distinguishable only at the perturbation level. We also derive a first integral on this submanifold, allowing analytic reconstruction of the dynamical connection and uncovering hidden conservation laws. Another key feature we found is that while trivial connections exhibit strong parameter dependence, the nontrivial branches often feature parameter-independent behaviours. We also study the variation of the effective gravitational coupling, $$k_{\text {eff}}$$ , across branches and show how this can be constrained using astrophysical observations, which bridges theoretical viability with observational consistency in a novel way. Applying our framework to the illustrative model $$f(Q)=\alpha Q + \beta (-Q)^n$$ , we find late-time acceleration and $$\Lambda $$ CDM-like behaviour without vacuum energy. Finally, we propose a general route for extending dynamical systems analysis to broader classes of $\textit{f}$($\textit{Q}$) models using the $$m_i$$ -hierarchy method. This framework enables closure for models previously inaccessible to standard approaches and offers a diagnostic tool for identifying structurally viable cosmologies within modified gravity theories.

India

Jibitesh Dutta

Wompherdeiki Khyllep

Thailand

South Africa

Saikat Chakraborty

China

Daniele Gregoris

Khamphee Karwan

A unified dynamical systems framework for cosmology in $\textit{f}$($\textit{Q}$) gravity: generic features across the connection branches

Realising $\textit{F}$ -term slow-roll inflation in supergravity is non-trivial due to the well-known $\textit{η}$-problem. The common strategy to solve the problem is to impose a shift symmetry on the Kähler potential, but this often leads to a negative potential in the large-field regime. To avoid negative potentials, an additional superfield called the stabiliser is usually added with a desired interaction. An alternative mechanism in supergravity, avoiding the use of a stabiliser superfield, was earlier proposed by two of us in the setup with a single chiral superfield having inflaton and goldstino amongst its field components. In this work, we extend that alternative mechanism to multi-superfield models of inflation, thereby providing a generic framework for embedding a wide class of single- and multi-field inflation models into supergravity. We illustrate our approach by several concrete examples of multi-field inflation and clarify the conditions required to avoid tachyonic instabilities during multi-field evolution. Our proposal significantly broadens the theoretical landscape of $\textit{F}$ -term inflation models in supergravity.

South Korea

Jinn-Ouk Gong

Japan

Russia

Sergei Ketov

Takahiro Terada

$\textit{F}$-term multi-field inflation in supergravity without stabiliser superfields

Exploring exotic matter around black holes (BHs) under different conditions, using equations of state and astrophysical observational data from BHs, may deepen our understanding of the nature of dark matter and theories of gravity. In the present work, we first briefly introduce a BH solution surrounded by a dust field in <italic>f</italic>( <italic>R, T</italic>) gravity and study the properties of the horizon around the BH. We investigate scalar invariants of the spacetime geometry, such as the Ricci scalar, the square of the Ricci tensor, and the Kretchman scalar. We also study the circular motion of test particles. Additionally, we investigate the effects of the dust field on the innermost stable circular orbits (ISCOs) and the particle&#8217;s energy and angular momentum at the ISCO. Moreover, we investigate particle oscillations near ISCO around the BH and calculate the frequencies of Keplerian orbits and vertical oscillations. As an astrophysical application of the studies, we study quasiperiodic oscillations (QPOs) in various QPO models. Finally, we obtain constraints on the dust field and BH parameters using a Monte Carlo Markov Chain (MCMC) simulation across the multidimensional parameter space for the microquasars GRO J1655-40 &amp; GRS 1915-105, the Milky Way, and the M82 X-1 galaxy.

Uzbekistan

Abubakir Shermatov

Javlon Rayimbaev

Sardor Murodov

Pakistan

Bushra Majeed

Inomjon Ibragimov

Bahran Shermatov

Erkaboy Davletov

Ikram Davletov

Circular motion and QPOs near BHs surrounded by dust fields in <italic>f</italic>( <italic>R, T</italic>) gravity

This article examines the impact of <math altimg='si24.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>Q</mi><mo>)</mo></mrow></math> gravity parameters on analytical spherically symmetric solutions for compact objects. We employ two distinct metric ansatz to solve the equations of motion in <math altimg='si24.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>Q</mi><mo>)</mo></mrow></math> gravity. To assess the feasibility and reliability of our models, we analyze various physical properties, including pressure, mass function, energy density, stability, adiabatic index, energy conditions, and hydrostatic equilibrium through a graphical framework. Additionally, we demonstrate how the mass-radius relation and stability are influenced by the <math altimg='si24.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>Q</mi><mo>)</mo></mrow></math> theory parameter <italic>&#958;</italic> <inf>1</inf>. To validate our results, we estimate the radii of well-known compact objects, including PSR J0437-4715, 4U 1608-52, 2S 0921-630, SMC X-4, and Her X-1. Our analysis confirms that the obtained isotropic solutions are physically viable and exhibit significant clarity.

S. Ijaz

M.Z. Bhatti

Investigating compact stars in <math altimg='si24.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>Q</mi><mo>)</mo></mrow></math> gravity: Analytical models and physical viability

In this study, we investigate the inflationary dynamics of Rainbow <italic>f</italic>( <italic>R</italic>) gravity characterized by <italic>f</italic>( <italic>R</italic>)&#8239;&#8771;&#8239; <italic>&#945;Rn</italic>, with the rainbow deformation <math altimg='si8.svg'><mrow><mover accent='true'><mi>f</mi><mo>&#732;</mo></mover><mrow><mo>(</mo><mi>H</mi><mo>)</mo></mrow><mo>&#8764;</mo><msup><mi>H</mi><mi>&#955;</mi></msup></mrow></math> and <math altimg='si9.svg'><mrow><mover accent='true'><mi>g</mi><mo>&#732;</mo></mover><mo linebreak='goodbreak'>=</mo><mn>1</mn></mrow></math>. The effects of the rainbow parameter <italic>&#955;</italic> and the curvature exponent <italic>n</italic> on inflationary observables are analyzed under the Atacama Cosmology Telescope (ACT) constraint 0.9709&#8239;&lt;&#8239; <italic>n<inf>s</inf></italic>&#8239;&lt;&#8239;0.9777. Numerical results reveal a clear correlation among <italic>n, &#955;</italic>, and the tensor-to-scalar ratio <italic>r</italic>, such that decreasing <italic>n</italic> corresponds to increasing <italic>&#955;</italic>, accompanied by a growth in <italic>r</italic> within observational limits. Negative values of <italic>&#955;</italic> (typically for <italic>n</italic>&#8239;&#8776;&#8239;3) yield a quasi&#8211;de Sitter inflationary phase with a nearly constant Hubble parameter and suppressed tensor modes, while positive <italic>&#955;</italic> (for <italic>n</italic>&#8239;&#8818;&#8239;2.2) drive a quintessence&#8211;like inflationary regime with enhanced expansion and a time-dependent curvature. Using power&#8211;law solutions <italic>a</italic>( <italic>t</italic>)&#8733; <italic>tp</italic>, we relate the expansion exponent to the number of <italic>e</italic>-folds <italic>N</italic>&#8239;&#8771;&#8239;50&#8211;60. Small deviations between the matter and effective equations of state indicate a mild breaking of <math altimg='si10.svg'><mrow><msub><mi>w</mi><mi>e</mi></msub><mo linebreak='goodbreak'>=</mo><mi>w</mi></mrow></math>, suggesting the emergence of matter&#8211;like behavior within the quintessence&#8211;like inflationary field. At low curvature, we further show that a logarithmic Nojiri&#8211;Odintsov correction <italic>f</italic>( <italic>R</italic>)&#8239;&#8771;&#8239; <italic>&#945;</italic>&#8242;ln&#8201;( <italic>R</italic>/ <italic>&#956;</italic> 2) naturally dominates the dynamics, giving rise to a late&#8211;time quintessence phase ( <math altimg='si11.svg'><mrow><mo>&#8722;</mo><mn>1</mn><mo linebreak='goodbreak'>&lt;</mo><msub><mi>w</mi><mi>e</mi></msub><mo linebreak='goodbreak'>&lt;</mo><mo>&#8722;</mo><mn>1</mn><mo linebreak='goodbreak'>/</mo><mn>3</mn></mrow></math> for <math altimg='si12.svg'><mrow><mi>&#955;</mi><mo linebreak='goodbreak'>&gt;</mo><mo>&#8722;</mo><mn>1</mn></mrow></math>) that asymptotically approaches a de Sitter attractor ( <math altimg='si13.svg'><mrow><msub><mi>w</mi><mi>e</mi></msub><mo>&#8594;</mo><mo>&#8722;</mo><mn>1</mn></mrow></math> as &#1013; <inf>1</inf>&#8239;&#8594;&#8239;0 or <math altimg='si14.svg'><mrow><mi>&#955;</mi><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mn>1</mn></mrow></math>). Thus, the combined <italic>Rn</italic> and logarithmic contributions provide a unified geometric framework in which early&#8211;time inflation and late&#8211;time cosmic acceleration naturally arise from different curvature regimes of Rainbow <italic>f</italic>( <italic>R</italic>) gravity, consistent with ACT observational data.

Türkiye

A.I. Keskin

Rainbow <italic>f</italic>( <italic>R</italic>) Inflation: de Sitter-Quintessence Phases

In this work, we explore the cosmological dynamics of a modified gravity framework based on the function $$f(Q,B)=\delta Q^{2}+\beta B$$ , where $\textit{Q}$ denotes the nonmetricity scalar and $\textit{B}$ is the boundary term that relates $\textit{Q}$ to the Ricci scalar. The matter sector is modeled using the Modified Chaplygin Gas (MCG) with the equation of state $$p=A\rho -\frac{D_{1}}{\rho ^{\alpha }}$$ , allowing the model to interpolate between early-time matter behavior and late-time cosmic acceleration. By deriving an analytical expression for the Hubble parameter $\textit{H}$($\textit{z}$), we perform a parameter estimation using Markov Chain Monte Carlo (MCMC) techniques in conjunction with the latest cosmological observations: 46 Hubble parameter measurements, 15 BAO data points, DESI DR2 BAO data and the Pantheon+ Type Ia supernovae compilation. The best-fit values are obtained as $$H_0=72.2814^{+3.4702}_{-4.5209}$$ km/s/Mpc, $$A_s = 0.6964^{+0.0779}_{-0.1258}$$ , $$\alpha = 0.0027^{+0.0225}_{-0.0209}$$ and $$A = 0.0024^{+0.0702}_{-0.0464}$$ . The deceleration parameter transitions at redshift $$z_{tr} \approx 0.946$$ , while the present-day value is $$q_0 = -0.789$$ . The model yields an age of the Universe $$t_0 \approx 13.53$$ Gyr and a present EoS parameter $$\omega _0 \approx -0.691$$ , which reflects the late-time acceleration consistent with observational bounds. These results demonstrate that the MCG scenario within $\textit{f}$($\textit{Q}$, $\textit{B}$) gravity provides a viable and observationally consistent framework for explaining the late-time accelerated expansion of the Universe.

Amit Samaddar

S. Singh

A new parametric study of $\textit{f}$($\textit{Q}$, $\textit{B}$) gravity with modified Chaplygin gas and recent observations

General Relativity (GR) is not the only way gravity can be geometrized. Instead of curvature, the Teleparallel Theory attributes gravity to the torsion <italic>T</italic>, which is related to the antisymmetric part of the connection. On the other hand, the Symmetric Teleparallel Theory no longer preserves metricity, describing gravity through the non-metricity tensor <italic>Q<inf>&#945;&#956;&#957;</inf></italic>&#8239;&#8801;&#8239;&#8711; <inf><italic>&#945;</italic></inf> <italic>g<inf>&#956;&#957;</inf></italic>. These descriptions give form to what is known as geometrical trinity of gravity. Recently, the extensions of GR have been intensively investigated in order to solve the theoretical impasses which have arisen. In this sense, it is also useful to investigate the extensions of alternative descriptions of gravity, which leads us to the so-called <italic>f</italic>( <italic>T</italic>) and <italic>f</italic>( <italic>Q</italic>) gravities. In this paper, we consider a family of <italic>f</italic>( <italic>Q</italic>) models and obtain their corresponding Tolman-Oppenheimer-Volkoff equations applied to polytropic stars. It is worth mentioning that the <italic>f</italic>( <italic>Q</italic>) covariant formulation is adopted and we present a new equation that substantially simplifies the numerical calculations. Using numerical integration, it is possible to solve a system of differential equations to calculate, among other things, the maximum mass and mass-radius relation allowed. In addition, we explicitly show the non-metricity behavior inside and outside the star.

Brazil

J.C.N. de Araujo

H.G.M. Fortes

Polytropic stars in <math altimg='si11.svg'><mrow><mi>f</mi><mrow><mo>(</mo><mi>Q</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mi>Q</mi><mo linebreak='goodbreak'>+</mo><mi>&#958;</mi><msup><mi>Q</mi><mn>2</mn></msup></mrow></math> covariant formulation

The anisotropic distribution of ultra high energy cosmic rays (UHECRs) remains a compelling and deeply informative observable in astro-particle physics, illuminating their enigmatic origins, extreme acceleration processes, and trajectories shaped by the cosmic large-scale structure. Among the hierarchy of anisotropy modes, the dipole stands out as a particularly sensitive tracer reflecting both the spatial configuration of sources and the foundational cosmological model. In this work, we conduct a rigorous comparative analysis of dipolar anisotropy within the diffusive propagation regime, evaluating its evolution across three gravitational framework: the standard ΛCDM model, a power-law extension of <italic>f</italic>( <italic>R</italic>) modified gravity, and the Starobinsky inflationary scenario. Our objective is to disentangle the gravitational signatures embedded in UHECR anisotropy, with particular emphasis on deviations arising from extended theories of gravity within the <italic>f</italic>( <italic>R</italic>) formalism. The results reveal a striking dependence on the underlying gravitational paradigm: the power-law model predicts significantly enhanced anisotropies, &#923;CDM consistently produces the most suppressed amplitudes, and the Starobinsky model exhibits an intermediate profile with partial convergence toward &#923;CDM. These findings reinforce the notion that UHECR anisotropy is not merely a reflection of astrophysical processes, but also a subtle messenger of the fundamental gravitational laws governing the universe offering a novel and promising avenue for testing physics beyond the standard cosmological framework.

Iftikhar Ahmad

Muhammad Mahtisham

Azerbaijan

Adnan Malik

Saudi Arabia

Fatemah Mofarreh

Model-dependent predictions for UHECR dipolar anisotropies in a <italic>f</italic>( <italic>R</italic>) modified gravity

We perform a comprehensive investigation of the radiative decays of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-wave charmed baryons in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo></math> flavor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mn mathvariant="bold">6</mn></mrow><mrow><mi>F</mi></mrow></msub></mrow></math> representation, employing the light-cone quantum chromodynamics (QCD) sum rule approach within the framework of heavy quark effective theory. We analyze their electromagnetic transitions into ground-state charmed baryons via photon emission. When combined with the mass spectra and strong decay properties previously studied in Yang and Chen [<a href="http://dx.doi.org/10.1103/PhysRevD.104.034037">Phys. Rev. D 104, 034037 (2021)</a>], our results constitute a systematic and complete QCD sum rule analysis of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-wave singly charmed baryons within the framework of heavy quark effective theory. As summarized in Table V, several excited charmed baryons are found to possess suppressed strong decay widths, thereby rendering their radiative decay channels particularly significant for experimental identification and theoretical understanding.

Xuan Luo

Hua-Xing Chen

Er-Liang Cui

Hui-Min Yang

Dan Zhou

Zhi-Yong Zhou

Radiative decays of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>P</mi></mrow></math>-wave charmed baryons in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo></math> flavor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mn>6</mn><mi mathvariant="normal">F</mi></msub></math> representation

Baryogenesis refers to the physical process responsible for generating the observed baryon asymmetry in the early universe. The presence of a nonzero baryon number density suggests a surplus of matter over antimatter. In this study, a novel approach is proposed to verify the direct consequences of late-time observations on gravitational baryogenesis. The incorporation of two key data sets, DESI and gravitational wave observations, makes the analysis more intriguing. In the teleparallel framework, the methodology connects the primordial time to the late time. The intermediating epochs are also investigated with the help of the deceleration parameter. Our results show that the net remaining asymmetry yields a baryon-to-entropy ratio in excellent agreement with observations.

Sai Swagat Mishra

N.S. Kavya

P.K Sahoo

Effects of DESI and GW observations on <italic>f</italic>( <italic>T</italic>) gravitational baryogenesis