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

To date, wormholes have not been observed. Dynamic wormholes are difficult to detect due to their transient existence or extremely low spacetime curvature contrast, while static wormholes rely on “exotic matter” that violates the Null Energy Condition and lack direct theoretical support. This study explores the mechanism of dynamic wormhole formation via gravitational collapse of Bose–Einstein Condensate (BEC) dark matter in generalized Vaidya spacetime. Under specific conditions, the gravitational collapse of BEC dark matter interacts with gravitational fields to trigger abrupt changes in spacetime topology. This process depends on special parameters that are more likely to be satisfied in extreme environments. During the collapse, the condensate properties of BEC influence the evolution of spacetime curvature, and its intrinsic oscillatory behavior may facilitate the formation of dynamic wormholes. The research deduces function constraints that satisfy various energy conditions, constructs a dynamic wormhole form adapted to generalized Vaidya spacetime, and derives the Hawking radiation expression and mass function constraints by combining Lorentz-breaking quantum gravity theory. This mechanism confirms the feasibility of dynamic wormhole formation, provides a new perspective for understanding the behavior of dark matter under extreme gravity and the evolution of spacetime topology, and advances wormhole research toward the analysis of dynamic formation processes.

Junjie Wei

Discussion on the feasibility of dynamic wormhole formation based on the gravitational collapse of Bose–Einstein condensed dark matter on generalized Vaidya space-time

We propose a unified model of dark energy and inflation through the Markov–Mukhanov modification of the Einstein–Hilbert action, where the matter sector is coupled to gravity via a scalar coupling function depending only on the energy density of the matter content. We assume that the coupling function encodes the UV corrections to the standard model of cosmology and we determine the form of the coupling that allows for the dark energy component to be dynamical and act as the inflaton field in the early universe. Interestingly we show that our model, in order to account for inflation, prefers a dark energy equation of state with $\textit{w}$ close but not equal to $$-1$$ in agreement with the latest DESI data.

Kazakhstan

Hrishikesh Chakrabarty

Daniele Malafarina

A unified model of dark energy and inflation from the Markov–Mukhanov action

In this paper, we investigate a digitised SU(2) lattice gauge theory in the Hamiltonian formalism. We use partitionings to digitise the gauge degrees of freedom and show how to define a penalty term based on finite element methods to project onto physical states of the system. Moreover, we show for a single plaquette system that in this framework the limit $$g\rightarrow 0$$ can be approached at constant cost.

Germany

Timo Jakobs

Marco Garofalo

United Kingdom

United States

Tobias Hartung

Cyprus

Karl Jansen

Johann Ostmeyer

Switzerland

Simone Romiti

Carsten Urbach

Dynamics in hamiltonian lattice gauge theory: approaching the continuum limit with partitionings of SU(2)

The Regge–Gribov model of the pomeron and odderon in non-trivial transverse space is studied by the renormalization group technique in the single-loop approximation. The pomeron and odderon are taken to have different bare intercepts and slopes. The behaviour when the intercepts move from below to their critical values compatible with the Froissart limitation is studied. The singularities in the form of non-trivial branch points indicating a phase transition are found in the vicinity of five fixed points reported in a previous publication. Since new phases violate the projectile–target symmetry, the model is found non-physical for the bare intercepts above their critical value.

Russia

M. Braun

E. Kuzminskii

M. Vyazovsky

On the reggeon model with the pomeron and odderon: singularities with non-zero masses

We investigate the reconstruction of standard and generalized Rastall gravity inflationary models, using the scalar spectral index and the Rastall parameter expressed as functions of the number of <math altimg='si3.svg'><mrow><mi>e</mi><mo linebreak='goodbreak'>&#8722;</mo></mrow></math>folds <italic>N</italic>. Within a general formalism, we derive the effective potential in terms of the relevant cosmological parameters and the Rastall parameter for these gravity frameworks. As a specific example, we analyze the attractor <math altimg='si4.svg'><mrow><msub><mi>n</mi><mi>s</mi></msub><mrow><mo>(</mo><mi>N</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>&#8722;</mo><mn>1</mn><mo>&#8733;</mo><msup><mi>N</mi><mrow><mo>&#8722;</mo><mn>1</mn></mrow></msup></mrow></math>, first by considering constant values of the Rastall parameter to reconstruct the inflationary stage in standard Rastall gravity, and then by assuming a linear dependence on the number of <math altimg='si3.svg'><mrow><mi>e</mi><mo linebreak='goodbreak'>&#8722;</mo></mrow></math>folds <italic>N</italic> to reconstruct the inflationary model in generalized Rastall gravity. Thus, the reconstruction of the potential <italic>V</italic>( <italic>&#981;</italic>) is obtained for both standard and generalized Rastall gravity inflationary models. In both frameworks, we constrain key parameters of the reconstructed models during inflation using the latest observational data from Planck.

Chile

Ramón Herrera

Carlos Ríos

Reconstructing inflation in a generalized Rastall theory of gravity

It is commonly believed that a unitary supersymmetric quantum field theory (QFT) involving graviton and gravitino fields on fixed 4-dimensional de Sitter spacetime ($\textit{dS}$ ) cannot exist due to known challenges associated with supersymmetry (SUSY) in $\textit{dS}$ . In this paper, we contradict this expectation by presenting a new unitary supersymmetric QFT on $\textit{dS}$ : the free supersymmetric theory of the chiral graviton and chiral gravitino fields. By chiral we mean that the corresponding field strengths are anti-self-dual, and the gauge potentials are complex, each carrying a single complex propagating degree of freedom. The global SUSY transformations are generated by the standard Dirac Killing spinors of $\textit{dS}$ . The theory overcomes the known obstacles to unitary global SUSY on $\textit{dS}$ by closing the commutator between two SUSY transformations on $\textit{so}$(4, 2) ⊕ $\textit{u}$(1) rather than the de Sitter algebra $\textit{so}$(4, 1). Crucially, the $\textit{so}$(4, 2) symmetry is realised through unconventional conformal-like transformations. This free theory cannot become interacting while preserving SUSY in a way that makes the spin-2 sector the true graviton sector of General Relativity, as the three-graviton coupling cannot be $\textit{u}$(1)-invariant.

Atsushi Higuchi

Belgium

Vasileios Letsios

Unitary rigid supersymmetry for the chiral graviton and chiral gravitino in de Sitter spacetime

Given that dark matter and normal matter are nontrivially unified in a grand unified theory, called dark grand unification, we derive novel residual theories at low energy explaining dark matter and neutrino mass. The first chain of which is $\textit{E}$ → SU(3) ⊗ SU(3) ⊗ SU(3) , which contains a matter parity by itself stabilizing a dark matter candidate and producing neutrino mass via a seesaw. The second chain is Trinification → SU(3) ⊗ SU(3) ⊗ U(1) ⊗ U(1) , which results in a novel family-universal 3-3-1-1 model, opposite to the normal 3-3-1-1 (or corresponding 3-3-1) model. Surprisingly, it is a variant of both minimal 3-3-1 model and 3-3-1 model with right-handed neutrinos since both $\textit{e}$ and $\textit{ν}$ are located at the bottoms of lepton triplets. Since this universal 3-3-1-1 model is properly embedded in the trinification, the above matter parity works governing dark matter stability as well as suppressing unwanted fermion mixings. Further, neutrino masses are naturally generated by a canonical seesaw combined with a scotogenic scheme.

Vietnam

Phung Dong

Do Huong

Implications of a dark grand unification

<p>We present a determination of the Cabibbo-Kobayashi-Maskawa matrix element <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>V</mi><mrow><mi>c</mi><mi>b</mi></mrow></msub><mo stretchy="false">|</mo></math> from the decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>D</mi><mo>ℓ</mo><msub><mi>ν</mi><mo>ℓ</mo></msub></math> using a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>365</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy="false">→</mo><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>4</mn><mi>S</mi><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>B</mi><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover></math> data sample recorded by the Belle II experiment at the SuperKEKB collider. The semileptonic decay of one <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> meson is reconstructed in the modes <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>D</mi><mo>−</mo></msup><mo stretchy="false">(</mo><mo stretchy="false">→</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo stretchy="false">)</mo><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><mo stretchy="false">(</mo><mo stretchy="false">→</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><mo stretchy="false">)</mo><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>ℓ</mo></math> denotes either an electron or a muon. Charge conjugation is implied. The second <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> meson in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>4</mn><mi>S</mi><mo stretchy="false">)</mo></math> event is not reconstructed explicitly. Using an inclusive reconstruction of the unobserved neutrino momentum, we determine the recoil variable <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>w</mi><mo>=</mo><msub><mi>v</mi><mi>B</mi></msub><mo>·</mo><msub><mi>v</mi><mi>D</mi></msub></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>v</mi><mi>B</mi></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>v</mi><mi>D</mi></msub></math> are the four-velocities of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math> mesons. We measure the total decay branching fractions to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msup><mrow><mi>D</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub><mo stretchy="false">)</mo><mo>=</mo><mrow><mo stretchy="false">(</mo><mn>2.06</mn><mo>±</mo><mn>0.05</mn><mo stretchy="false">(</mo><mrow><mi>stat</mi></mrow><mo stretchy="false">)</mo><mo>±</mo><mn>0.10</mn><mo stretchy="false">(</mo><mrow><mi>sys</mi></mrow><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>%</mo></mrow></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mn>0</mn></msup><msup><mo>ℓ</mo><mo>+</mo></msup><msub><mi>ν</mi><mo>ℓ</mo></msub><mo stretchy="false">)</mo><mo>=</mo><mrow><mo stretchy="false">(</mo><mn>2.31</mn><mo>±</mo><mn>0.04</mn><mo stretchy="false">(</mo><mrow><mi>stat</mi></mrow><mo stretchy="false">)</mo><mo>±</mo><mn>0.09</mn><mo stretchy="false">(</mo><mrow><mi>sys</mi></mrow><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>%</mo></mrow></math>. We probe lepton flavor universality by measuring <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><mi>B</mi><mo stretchy="false">→</mo><mi>D</mi><mi>e</mi><msub><mi>ν</mi><mi>e</mi></msub><mo stretchy="false">)</mo><mo>/</mo><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><mi>B</mi><mo stretchy="false">→</mo><mi>D</mi><mi>μ</mi><msub><mi>ν</mi><mi>μ</mi></msub><mo stretchy="false">)</mo><mo>=</mo><mrow><mn>1.020</mn><mo>±</mo><mn>0.020</mn><mo stretchy="false">(</mo><mrow><mi>stat</mi></mrow><mo stretchy="false">)</mo><mo>±</mo><mn>0.022</mn><mo stretchy="false">(</mo><mrow><mi>sys</mi></mrow><mo stretchy="false">)</mo></mrow></math>. Fitting the partial decay branching fraction as a function of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>w</mi></math> and using the average of lattice QCD calculations of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>D</mi></math> form factor, we obtain <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>V</mi><mrow><mi>c</mi><mi>b</mi></mrow></msub><mo stretchy="false">|</mo><mo>=</mo><mrow><mo stretchy="false">(</mo><mn>39.2</mn><mo>±</mo><mn>0.4</mn><mo stretchy="false">(</mo><mrow><mi>stat</mi></mrow><mo stretchy="false">)</mo><mo>±</mo><mn>0.6</mn><mo stretchy="false">(</mo><mrow><mi>sys</mi></mrow><mo stretchy="false">)</mo><mo>±</mo><mn>0.5</mn><mo stretchy="false">(</mo><mrow><mi>th</mi></mrow><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math>.</p>

I. Adachi

K. Adamczyk

L. Aggarwal

H. Ahmed

Y. Ahn

H. Aihara

N. Akopov

S. Alghamdi

M. Alhakami

A. Aloisio

K. Amos

M. Angelsmark

N. Anh Ky

C. Antonioli

D.M. Asner

H. Atmacan

T. Aushev

V. Aushev

M. Aversano

R. Ayad

V. Babu

H. Bae

N.K. Baghel

S. Bahinipati

P. Bambade

Sw. Banerjee

M. Barrett

M. Bartl

J. Baudot

A. Baur

A. Beaubien

F. Becherer

J. Becker

J.V. Bennett

F.U. Bernlochner

V. Bertacchi

M. Bertemes

E. Bertholet

M. Bessner

S. Bettarini

B. Bhuyan

F. Bianchi

T. Bilka

D. Biswas

A. Bobrov

D. Bodrov

A. Bondar

G. Bonvicini

J. Borah

A. Boschetti

A. Bozek

M. Bračko

P. Branchini

R.A. Briere

T.E. Browder

A. Budano

S. Bussino

Q. Campagna

M. Campajola

L. Cao

G. Casarosa

C. Cecchi

M.C. Chang

P. Cheema

L. Chen

B.G. Cheon

K. Chilikin

J. Chin

K. Chirapatpimol

H.E. Cho

K. Cho

S.J. Cho

S.K. Choi

S. Choudhury

I. Consigny

L. Corona

J.X. Cui

E. De La Cruz-Burelo

S.A. De La Motte

G. De Pietro

R. de Sangro

M. Destefanis

A. Di Canto

J. Dingfelder

Z. Doležal

I. Domínguez Jiménez

T.V. Dong

X. Dong

K. Dugic

G. Dujany

P. Ecker

J. Eppelt

R. Farkas

P. Feichtinger

T. Ferber

T. Fillinger

C. Finck

G. Finocchiaro

F. Forti

A. Frey

Determination of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>V</mi><mrow><mi>c</mi><mi>b</mi></mrow></msub><mo stretchy="false">|</mo></math> using <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo stretchy="false">→</mo><mi>D</mi><mo>ℓ</mo><msub><mi>ν</mi><mi>l</mi></msub></math> decays at Belle II

<p>We present a detailed numerical and analytical study of the out-of-equilibrium dynamics of Model G, the dynamical universality class relevant to the chiral phase transition. We perform numerical 3D stochastic (Langevin) simulations of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>O</mi><mo stretchy="false">(</mo><mn>4</mn><mo stretchy="false">)</mo></mrow></math> critical point for large lattices in the chiral limit. We quench the system from the high-temperature unbroken phase to the broken phase and study the nonequilibrium dynamics of pion fields. Strikingly, the nonequilibrium evolution of the two-point functions exhibits a regime of growth, a parametrically large enhancement, and a subsequent slow relaxation to equilibrium. We analyze our numerical results using dynamic critical scaling and mean-field theory. The growth of the two-point functions is determined by the nonlinear dynamics of an ideal non-Abelian superfluid, which is a limit of Model G that reflects the broken chiral symmetry. We also relate the nonequilibrium two-point functions to a long-lived parametric enhancement of soft pion yields relative to thermal equilibrium following a quench.</p>