The so-called geometric trinity of gravity is based on three distinct geometric features of spacetime, i.e. curvature, torsion and non-metricity, which give rise to equivalent dynamics for general relativity (GR), teleparallel equivalent of general relativity (TEGR) and symmetric teleparallel equivalent of general relativity (STEGR). Pre-geometric gravity, on the other hand, offers a unifying framework from which all metric-affine theories can emerge. Starting from a gauge formulation $\textit{à la}$ Yang–Mills with a Higgs-like field, a mechanism of spontaneous symmetry breaking can give rise to an effective metric as well as to the classical dynamics of the gravitational field. In particular, the emergence of gravity in the spontaneously broken phase is shown to be consistent with all the different formulations of the geometric trinity of gravity, in terms both of actions and of gauge choices for the affine connection. This general result is achieved by deriving and analysing suitable expressions in the unbroken phase for pre-geometric actions and for pre-geometric gauge-fixing conditions respectively.

Italy

Salvatore Capozziello

United States

Giuseppe Meluccio

The pre-geometric origin of geometric trinity of gravity

We present an analytical treatment of Axion-Like-Particle (ALP)—photon mixing with extragalactic background light (EBL) attenuation for constant, Gaussian-stochastic, and non-Gaussian magnetic field configurations−with direct implications for Very High Energy (VHE) gamma-ray observations such as LHAASO, HAWC, and CTA experiments. For constant fields, we derive exact probabilities and identify a perturbative plateau regime where photon survival scales as quartic order of magnetic field, isolating the four-point magnetic correlation as a sensitive probe of non-Gaussianity. For Gaussian stochastic fields, we obtain−for the first time−analytical formulas for non-exponential-decay components in the strong-attenuation regime. Contrary to the widely used domain-like model, photon survival is suppressed by 4–6 orders of magnitude, while both conversion and survival probabilities exhibit distinct multi-peak structures from mass-equal resonance, stochastic resonance, and EBL attenuation. Extending to non-Gaussian fields, we show that non-Gaussianity can enhance photon survival by several orders of magnitude relative to the Gaussian case, potentially explaining the unexpectedly VHE photon event observed by LHAASO. Our results demonstrate that stochastic magnetic fields cannot be reduced to domain-like coherence without losing essential physics, and that VHE gamma-ray spectra encode observable information about both the power spectrum and non-Gaussian structure of intergalactic magnetic fields−critical as next-generation observatories push toward PeV sensitivities.

China

Andrea Addazi

Yi-Fu Cai

Qingyu Gan

Gaetano Lambiase

The axion-photon mixing and the extragalactic magnetic background: plateau regimes, resonances, and non-Gaussian boosts

We propose a scenario according to which the ultraviolet completion of General Relativity is realized through a stochastic gradient flow towards a topological BF theory. Specifically, we consider the stochastic gradient flow of a pre-geometric theory proposed by Wilczek. Its infrared limit exists, and corresponds to a fixed point where stochastic fluctuations vanish. Diffeomorphism symmetries are restored in this limit, where the theory is classical and expressed by the Einstein-Hilbert action. The infrared phase then corresponds to the classical theory of General Relativity, the quantization of which becomes meaningless. Away from the infrared limit, in the pre-geometric phase of the stochastic gradient flow, the relevant fields of the Wilczek theory undergo stochastic fluctuations. The theory can be quantized perturbatively, generating corrections to the classical Einstein-Hilbert action. The stochastic gradient flow also possesses an ultraviolet fixed point. The theory flows to a topological BF action, to which non-perturbative quantization methods can be applied. Two phase transitions occur along the thermal time dynamics, being marked by: i) the breakdown of the topological BF symmetries in the ultraviolet regime, which originates the pre-geometric phase described by the Wilczek theory; ii) the breakdown of the parental symmetries characterizing the Wilczek theory, from which General Relativity emerges. The problem of quantizing the Einstein-Hilbert action of gravity finally becomes redundant.

Azerbaijan

Jinglong Liu

Antonino Marcianò

Xuan-Lin Su

Emergent gravity from topological quantum field theory: Stochastic gradient flow perspective away from the quantum gravity problem

We study slow-roll inflation driven by a scalar field non-minimally coupled to gravity within the effective framework of Loop Quantum Cosmology (LQC), including inverse-volume corrections. We consider two physically motivated classes of potentials, a Higgs-like quartic potential <italic>V</italic>&#8733; <italic>&#981;</italic> <sup>4</sup> and string-inspired fractional monomial potentials <italic>V</italic>&#8733; <italic>&#981;<sup>p</sup></italic> with <italic>p</italic>&#8239;&lt;&#8239;1. Working at first order in the slow-roll expansion, we derive analytic expressions for the inflationary observables, namely the scalar spectral index <italic>n<inf>s</inf></italic>, the tensor-to-scalar ratio <italic>r</italic>, and the running <italic>&#945;<inf>s</inf></italic>&#8239;&#8801;&#8239; <italic>dn<inf>s</inf></italic>/ <italic>d</italic>ln&#8201; <italic>k</italic>, and then solve the corrected background dynamics numerically to obtain quantitative predictions. Confronting these results with current observational constraints from Planck 2018 and ACT DR6, we find that the model can lie within the allowed region of the ( <italic>n<inf>s</inf>, r, &#945;<inf>s</inf></italic>) parameter space, including a mild preference for slightly larger <italic>n<inf>s</inf></italic>, as suggested by recent ground-based measurements. We also compute the probability of achieving sufficient slow-roll inflation in this setting. Although effective LQC replaces the initial singularity with a nonsingular quantum bounce, the likelihood of a sufficiently long inflationary phase depends on the pre-inflationary dynamics and the inflaton potential. Using the canonical Liouville measure on the effective phase space, we determine the fraction of post-bounce trajectories that yield sufficient inflation and find that the non-minimal coupling parameter <italic>&#958;</italic> substantially enlarges the phase-space volume of favorable initial conditions relative to the minimally coupled case, exhibiting an attractor-like enhancement that saturates at large <italic>&#958;</italic>.

Chile

Rudranil Roy

Giovanni Otalora

Joel Saavedra

Non-minimally coupled loop quantum inflation with inverse-volume corrections

Evidences for evolving dark energy are shown using baryon acoustic oscillation measurements from the recent Dark Energy Spectroscopic Instrument Data Release 2, combined with different Type Ia supernova datasets (Pantheon $$^+$$ , DES-Dovekie, and Union3) and the CMB compressed likelihood. We examine several dark energy parameterizations, including the Logarithmic, Exponential, CPL, BA, JBP, Thawing, Mirage, and GEDE models. Analyzing the DESI DR2 measurements alone, we find that evidence for evolving dark energy is primarily driven by the LRG1-2 tracers, as their inclusion yields a preferred value of $$w_0 > -1$$ . However, as each tracer provides only limited observables, this preference can result in an underconstrained and potentially unstable inference. Further, we find that each dark energy model predicts values in the $$w_0 > -1$$ , $$w_a < 0$$ quadrant, a region characterized by the Quintom-B type dark energy scenario. The logarithmic bayes factor shows that, among all models, the Mirage model shows the inconclusive-to-moderate evidence across all dataset combinations. Consistently, the statistical significance remains modest, with $$N\sigma \sim 1.1$$ -2.3, and no model showing a robust preference for dynamical dark energy using late-time datasets alone. The evolution of $\textit{w}$($\textit{z}$) shows a phantom crossing around $$z \sim 0.5$$ in most dynamical dark energy models, and the evolution of $$f_{\textrm{DE}}(z)$$ converges to $$f_{\textrm{DE}}(0) = 1$$ in all dark energy models.

Romania

Himanshu Chaudhary

India

Vipin Sharma

Switzerland

Isidro Gómez-Vargas

Thailand

G. Mustafa

Evidence for evolving dark energy from DESI DR2 BAO and Pantheon $$^+$$ , DES-Dovekie, and Union3

We investigate Extended Geometric Trinity of Gravity at both classical and quantum cosmological levels using the minisuperspace approach. Adopting Noether symmetries to select viable models, we examine metric-affine theories of gravity, in particular the extensions of General Relativity, Teleparallel Equivalent General Relativity and Symmetric Teleparallel Equivalent General Relativity, and show that the equivalence among these different formulations can be restored by including in the Lagrangian the divergence terms that relate their respective geometric invariants to the Ricci scalar. Exact cosmological solutions are derived and compared in the different models.

Emmanuele Battista

Stefano Pastore

Minisuperspace cosmology in extended geometric trinity of gravity

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.

Pakistan

M. Ilyas

Saudi Arabia

Khalid Masood

South Korea

Nehad Shah

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

Recent observations from the Atacama Cosmology Telescope (ACT), especially when combined with DESI baryon acoustic oscillation data, indicate a scalar spectral index $$ n_s $$ higher than the value reported by $\textit{Planck}$ 2018, placing tension on universal inflationary attractor models. Motivated by this discrepancy, we investigate the inflationary predictions of the $$\beta $$ -exponential potential, $$ V(\phi )=V_0\left( 1-\lambda \beta \phi /M_p\right) ^{1/\beta }$$ considering both minimally and non-minimally coupled realizations. This potential generalizes standard exponential inflation and naturally arises in braneworld scenarios. We derive analytical expressions for the slow-roll parameters and inflationary observables using a perturbative expansion in the non-minimal coupling $$\xi $$ , and validate these results through numerical calculations. In the minimally coupled case, the model predicts $$ n_s \simeq 0.976 $$ and $$ r \simeq 0.035 $$ for $$N=50$$ and moderate values of $$\beta $$ , remaining compatible with ACT+DESI (P-ACT-LB) constraints at the $$1\sigma $$ level while yielding a spectral tilt larger than the universal attractor prediction. Introducing a small non-minimal coupling significantly improves agreement with observations by suppressing the tensor-to-scalar ratio while preserving the enhanced scalar tilt. For $$N=60 $$ , $$ \lambda \sim 0.3\!-\!0.5 $$ , and $$ \beta \sim \mathcal {O}(1\!-\!5) $$ , the non-minimally coupled model yields $$ n_s \simeq 0.974\!-\!0.976 $$ and $$ r \lesssim 0.03 $$ , comfortably consistent with ACT, DESI, and BICEP/Keck bounds. Our results show that the $$\beta $$ -exponential potential, especially when implemented with a non-minimal coupling, exhibits good agreement with the latest CMB observations. Our inflationary predictions of the non-minimal model of $$n_s$$ and $\textit{r}$ confirming the leading-order contributions in $$\xi $$ are sufficient to capture the essential features of both $\textit{r}$ and $$n_s$$ in observationally relevant regimes.

Jureeporn Yuennan

Uzbekistan

Farruh Atamurotov

Phongpichit Channuie

Constraining $$\beta $$ -exponential inflation with the latest ACT observations

We investigate exact charged and uncharged black hole solutions in a (2+1)-dimensional spacetime within the framework of quadratic form of <math altimg='si2.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='double-struck'>Q</mi><mo>)</mo></mrow></math> symmetric teleparallel gravity, where <math altimg='si15.svg'><mi mathvariant='double-struck'>Q</mi></math> is the non-metricity scalar. By adopting spherical symmetry and considering both vanishing and non-vanishing electromagnetic fields, we derive new classes of black hole solutions and analyze their geometric and physical properties. The study demonstrates that the inclusion of quadratic corrections in the gravitational Lagrangian significantly modifies the structure of solutions, producing deviations from the standard BTZ geometry. Invariants such as curvature and non-metricity scalars are calculated to classify the singularity structure and spacetime behavior. Thermodynamic quantities, including Hawking temperature, entropy, and heat capacity, are computed, showing consistency with the first law of black hole thermodynamics. Furthermore, we examine the geodesic motion of test particles and derive the effective potential to explore the stability of photon orbits. A notable outcome is the identification of weaker black hole singularities in comparison to General Relativity, attributed to the non-metricity corrections. The possibility of multi-horizon configurations is also explored. This study provides a comprehensive analysis of the gravitational, thermodynamic, and dynamical features of lower-dimensional black holes in <math altimg='si2.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='double-struck'>Q</mi><mo>)</mo></mrow></math> gravity and highlights their distinct characteristics with respect to General Relativity.

Egypt

Gamal G.L. Nashed

Stable black holes in lower dimensional <math altimg='si2.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='double-struck'>Q</mi><mo>)</mo></mrow></math> non-metric gravity

We discuss the conversion mechanism from scalar field to gravitational waves in magnetic background in <italic>f</italic>( <italic>R</italic>) gravity minimal coupled to the Maxwell electrodynamics. Applying the conversion in early universe with primordial magnetic field and the neutron star with strong magnetosphere, the generated gravitational waves, converted from the scalar field, exhibit distinct power spectra which can be potentially probed by future experiments such as DECIGO, BBO, CE and ET.

Gravitational waves in minimal Maxwell <italic>f</italic>( <italic>R</italic>) gravity