We investigate a quantum cosmological model within the framework of Einstein–Aether gravity. The model consists of a positively curved FLRW Universe whose matter content is described by a radiation fluid, in the presence of a positive cosmological constant $$\Lambda $$ . We first perform a classical Hamiltonian analysis, constructing the phase space and deriving the dynamics of the scale factor. Notably, we identify specific initial conditions that lead to an inflationary expansion. Subsequently, we quantize the model following Dirac’s formalism, obtaining the Wheeler-DeWitt equation for the wave function of the Universe. We solve this equation numerically and compare our results to those of the WKB approximation, computing quantum tunneling probabilities and the expectation value of the scale factor, along with its standard deviation. Finally, we analyze how these tunneling probabilities are influenced by variations in the fundamental parameters of the theory ( $$\Lambda $$ , $$\sigma $$ , $$\beta $$ ) and the energy of the fluid $\textit{E}$. Our results indicate a higher probability for the quantum birth of the Universe in a parameter regime characterized by larger values of $$\Lambda $$ , $$\sigma $$ , and fluid energy $\textit{E}$, together with a smaller value of $$\beta $$ .

Brazil

A. Castro Junior

G. Monerat

G. Oliveira-Neto

E. Corrêa Silva

Einstein–Aether primordial universe with radiation and dark energy

A numerical framework for approximating G <inf>2</inf>-structure 3-forms on contact Calabi&#8211;Yau manifolds is presented. The approach proceeds in three stages: first, existing neural network models are employed to compute an approximate Ricci-flat metric on a Calabi&#8211;Yau threefold. Second, using this metric and the explicit construction of a G <inf>2</inf>-structure on the associated 7-dimensional Calabi&#8211;Yau link in the 9-sphere, numerical approximations of the 3-form are generated on a large set of sampled points. Finally, a dedicated neural architecture is trained to learn the 3-form and its induced Riemannian metric directly from data, validating the learned structure and its torsion via a numerical implementation of the exterior derivative, which may be of independent interest.

United Kingdom

Elli Heyes

Edward Hirst

Henrique N. Sá Earp

Tomás S.R. Silva

Neural and numerical methods for G <inf>2</inf>-structures on contact Calabi&#8211;Yau 7&#8211;manifolds

We explore 3d $$ \mathcal{N} $$ = 4 theories arising from twisted compactification of 4d $$ \mathcal{N} $$ = 2 ($\textit{G}$, $\textit{G}$ ) Argyres-Douglas superconformal field theories (SCFTs), together with the 2d vertex operator algebras (VOAs) supported on the holomorphic boundary of their topologically twisted sector. Starting from the Coulomb branch BPS spectra of the ($\textit{G}$, $\textit{G}$ ) Argyres-Douglas theories, we develop a systematic and efficient method to obtain the ellipsoid partition functions of associated 3d theories using quiver mutations and wall-crossing invariants. This allows us to extract the modular data of the boundary VOAs, which are related to the Schur sectors of the 4d theories through the 4d SCFT/2d VOA correspondence. Our results provide a useful computational bridge between 4d SCFTs and 2d VOAs through interpolating 3d topological field theories.

South Korea

Minsung Kim

Sungjoon Kim

3D TFTs and boundary VOAs from BPS spectra of ($\textit{G}$, $\textit{G}$ ′) Argyres-Douglas theories

A modified gravitational model whose action is given by an arbitrary function of the Ricci scalar, the matter Lagrangian density, a scalar field, and its kinetic term is investigated as an extension of the gravitational sector including an additional dynamical degree of freedom. Within this framework, the causal structure of rotating cosmological solutions is analyzed by considering Gödel and Gödel-type spacetimes as background geometries used as theoretical probes of the model consistency. Different matter sources are examined, including a perfect fluid and scalar-field configurations. It is found that the standard Gödel metric is not compatible with the scalar sector of the theory unless the model reduces to the General Relativity limit. In contrast, Gödel-type geometries admit a wider class of solutions whose causal properties depend on the model parameters and on the matter content. In particular, perfect-fluid sources may lead to either causal or noncausal configurations, whereas scalar-field configurations constrain the geometry to the causal limit, preventing the formation of closed timelike curves, highlighting that the scalar field plays a nontrivial dynamical role distinct from that of a cosmological constant.

L. Evangelista

M. Silva

J. Moretti

A. Santos

Causality and its violation in $$f(R,\mathcal {L}_m,\phi ,g^{\mu \nu }\nabla _\mu \phi \nabla _\nu \phi )$$ gravity

The novel proposal to invoke the split of the Ricci scalar into bulk and boundary terms in the gravitational action, opens up a new avenue of investigation into stellar dynamics. The Lagrangian contains functional forms of the bulk term while the boundary term do not contribute to the dynamics. The advantage of the proposition is that the stellar structure equations are up to order two, thus the theory is not haunted by ghosts. We obtain explicitly the defining equations for the thermodynamical variables and the geometry for the pure quadratic case, since the linear case amounts to general relativity. In trying to establish the vacuum geometry associated with the theory it turns out that two possible metrics emerge through the vanishing of the energy-momentum tensor. Next, we analyse the isotropy equation and make the observation that it is autonomous. It is rare that this happens in astrophysical modelling. This behaviour prompted the use of dynamical systems to understand the stability properties of fixed points or invariant submanifolds. It was necessary to choose a gauge in order to split the autonomous equation into a system from which we could plot a phase portrait and deduce the stability of solution trajectories. We find that the invariant submanifolds were generally stable with nearby paths approaching them.

South Africa

Sudan Hansraj

Christian Boehmer

Ndumiso Buthelezi

Dynamical systems approach to stellar modelling in $\textit{f}$($\textit{G}$, $\textit{B}$) gravity

We present quantitative results on the single-mass heavy-flavor contributions in the region of large virtualities <italic>Q</italic> 2 up to three-loop order to the unpolarized structure function <italic>F</italic> <inf>2</inf>( <italic>x, Q</italic> 2) and the polarized structure function <italic>g</italic> <inf>1</inf>( <italic>x, Q</italic> 2) for the first time. These results are relevant for precision QCD analyses of the World deep-inelastic data and the data taken at future colliders, such as the Electron&#8211;Ion Collider, since the scaling violations due to massless and massive Wilson coefficients are significantly different. In order to measure the strong coupling constant <math altimg='si19.svg'><mrow><msub><mi>&#945;</mi><mi>s</mi></msub><mrow><mo>(</mo><msubsup><mi>M</mi><mi>Z</mi><mn>2</mn></msubsup><mo>)</mo></mrow></mrow></math> and the twist-2 parton distribution functions consistently at highest precision, the next-to-next-to-leading order corrections have to be taken into account. We also provide a fast and precise public numerical code for the unpolarized and polarized massive Wilson coefficients in the asymptotic region.

Austria

J. Ablinger

Germany

A. Behring

J. Blümlein

A. De Freitas

A. von Manteuffel

C. Schneider

Switzerland

K. Schönwald

The three-loop single-mass heavy-flavor corrections to the structure functions <italic>F</italic> <inf>2</inf>( <italic>x, Q</italic> 2) and <italic>g</italic> <inf>1</inf>( <italic>x, Q</italic> 2)

We study finite-volume (FV) corrections to determinations of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>g</mi><mi>A</mi></msub></math> via lattice quantum chromodynamics (QCD) using analytic results and numerical analysis. We observe that <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><mo>)</mo></mrow></math> heavy Baryon chiral perturbation theory does not provide an unambiguous prediction for the sign of the FV correction, which is not surprising when one also considers large-<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>N</mi><mi>c</mi></msub></math> constraints on the axial couplings. We further show that nonmonotonic FV corrections are naturally allowed when one considers either including explicit <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Δ</mi></math>-resonance degrees of freedom or one works to higher orders in the chiral expansion. We investigate the potential impact of these FV corrections with a precision study of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>g</mi><mi>A</mi></msub></math> using models of FV corrections that are monotonic and nonmonotonic. Using lattice QCD data that is approximately at the 1% level of precision, we do not see significant evidence of nonmonotonic corrections. Looking forward to the next phase of lattice QCD calculations, we estimate that calculations that are between the 0.1% and 1% level of precision may be sensitive to these FV artifacts. Finally, we present an update of the CalLat prediction of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>g</mi><mi>A</mi></msub></math> in the isospin limit with subpercent precision, <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msubsup><mi>g</mi><mi>A</mi><mi>QCD</mi></msubsup><mo>=</mo><mn>1.2674</mn><mrow><mo>(</mo><mn>96</mn><mo>)</mo></mrow></mrow></math>.

United States

Zack Hall

Dimitra A. Pefkou

Aaron S. Meyer

Thomas R. Richardson

Raúl A. Briceño

M.A. Clark

Martin Hoferichter

Emanuele Mereghetti

Henry Monge-Camacho

Colin Morningstar

Amy Nicholson

Pavlos Vranas

André Walker-Loud

Signs of nonmonotonic finite-volume corrections to <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>g</mi><mi>A</mi></msub></math>

The Standard Model prediction of the muon $$g-2$$ increasingly depends on lattice QCD computations of the hadronic vacuum polarization (HVP), where the isospin-breaking (IB) effects remain a significant source of uncertainty. To complement the lattice QCD evaluations, the data-driven approach to HVP has been used to assess some of the electromagnetic IB effects, in particular from the channels with a photon in the final state, e.g., $$e^+e^-\rightarrow \pi ^0 \gamma $$ . Here we argue that such contributions are largely canceled by virtual electromagnetic corrections to the purely hadronic channels: $$\pi ^+ \pi ^-$$ , $$\pi ^+ \pi ^- \pi ^0$$ , etc. We identify these leading corrections by performing a field-theoretic calculation in a vector-meson dominance model, thereby reconciling the timelike and spacelike approaches to electromagnetic effects. Although these virtual corrections are more difficult to extract in a systematic manner, addressing them is essential for the data-driven method to consistently complement the lattice QCD program.

France

Volodymyr Biloshytskyi

Dominik Erb

Harvey Meyer

Julian Parrino

Vladimir Pascalutsa

Field-theoretic versus data-driven evaluations of electromagnetic corrections to hadronic vacuum polarization in $$(g-2)_\mu $$

In this work, we investigate the internal structure and physical features of compact stars in the background of modified gravity, specifically within <italic>f</italic>( <italic>R, G</italic>) gravity, where <italic>R</italic> represents the Ricci scalar and <italic>G</italic> denotes the Gauss&#8211;Bonnet invariant. The interior spacetime of the stellar configuration is described by the Kohler&#8211;Chao metric, which provides a suitable geometric representation for dense compact objects. Our analysis considers ten well-known compact star candidates, namely Her X-1, SAX J1808.4-3658, SMC X-1, LMC X-4, Cen X-3, 4U 1820-30, PSR J1903+327, 4U 1608-52, Vela X-1, and PSR J1614-2230. To incorporate higher-curvature effects, the functional form of <italic>f</italic>( <italic>R, G</italic>) is decomposed into two independent contributions, <italic>f</italic> <inf>1</inf>( <italic>R</italic>) and <italic>f</italic> <inf>2</inf>( <italic>G</italic>), representing the Ricci scalar and Gauss&#8211;Bonnet sectors, respectively. For the <italic>R</italic>-dependent part, we adopt the Hu&#8211;Sawicki type model, while three different models, namely logarithmic and power-law models, are considered for the Gauss&#8211;Bonnet contribution. This reconstruction gives three distinct modified gravity models used to study the different features of compact stellar configurations. Using these models, we study the physical viability of the stellar structures by examining anisotropic pressure content, equilibrium scenario through the Tolman&#8211;Oppenheimer&#8211;Volkoff equation, energy conditions, and stability conditions. The obtained results demonstrate that the energy density, radial pressure, tangential pressure, and anisotropy remain well-behaved throughout the stellar interior for all considered stars. The analysis indicates that the proposed <italic>f</italic>( <italic>R, G</italic>) models together with the Kohler&#8211;Chao interior solution provide physically consistent and stable configurations for compact stars within the modified gravity framework.

Saudi Arabia

Ahdab K. Althukair

Azerbaijan

Pakistan

M. Ilyas

Greece

Russia

Euaggelos E. Zotos

Kohler-Chao interior solutions for compact stellar objects in <italic>f</italic>( <italic>R, G</italic>) gravity

Gauss–Bonnet inflation typically affects the dynamics over an extended portion of the trajectory, making it difficult to isolate a controlled imprint at CMB scales. We consider a trajectory-selective coupling $$\mu (\phi ,X)$$ that gates the Gauss–Bonnet sector in phase space, enabling the higher-curvature contribution to be localized within a finite e-fold window while remaining negligible elsewhere. We identify stable inflationary solutions consistent with this localization and enforce standard ghost and gradient stability conditions for both scalar and tensor perturbations. For these viable backgrounds we compute pivot-scale observables and examine their dependence on the overall Gauss–Bonnet strength and on the kinetic gating. The framework offers a controlled route for realizing localized higher-curvature effects with predictable consequences for CMB-scale measurements.

Iran

Ali Seidabadi

Sara Saghafi

Kourosh Nozari

Beyond $$f(\phi ){\mathcal {G}}$$ : Gauss–Bonnet inflation with $$\mu (\phi ,X)$$