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

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

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

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

We investigate the sensitivity of a companion neutrino detector situated in the plane of a high-energy, high-intensity muon storage ring to elastic $\textit{ν}$ and $\textit{ν}$ scattering on electrons (E$\textit{ν}$ES). Assuming a muon collider with center-of-mass energies of up to 10 TeV, we report sensitivity to the weak couplings $\textit{g}$ and $\textit{g}$ up to around 0.05% relative error, and sensitivity to the weak mixing angle in the momentum transfer $\textit{Q}$ ∈ [10 , 2] GeV range up to around 0.03% relative error. E$\textit{ν}$ES measurements with high-energy muon storage rings allow one to directly interrogate the momentum-transfer regime associated with the NuTeV anomaly. This level of precision allows unique sensitivity to the momentum-dependence of sin θ . We estimate that with the neutrinos from a $\textit{E}$ = 1.5 TeV (or higher) muon collider, the hypothesis that sin $\textit{θ}$ does not “run” can be safely ruled out.

United States

André Gouvêa

Adrian Thompson

Electroweak observables in neutrino-electron scattering from a muon storage ring

We present a fully backreacted Einstein-Maxwell-Dilaton–flavor model with dynamical light and strange sectors, calibrated to lattice QCD using a machine-learning–assisted spectral method. The model reproduces the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>-flavor equation of state and chiral dynamics with quantitative accuracy, and maps the Columbia plot with a tricritical point at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>m</mi></mrow><mrow><mi>s</mi></mrow><mrow><mi>tri</mi></mrow></msubsup><mo>≃</mo><mn>21</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math> and a critical mass <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>c</mi></msub><mo>≃</mo><mn>0.785</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, consistent with lattice results. At finite density, it yields a crossover-to-first-order transition and predicts a critical endpoint at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mi>C</mi></msub><mo>=</mo><mn>75.4</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>μ</mi><mi>C</mi></msub><mo>=</mo><mn>768</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>, within the reach of heavy-ion experiments. These findings establish a unified holographic framework for the QCD phase structure across quark masses and baryon density, providing the first consistent and quantitative description of both deconfinement and chiral transitions within a single holographic model.

Jin-Yang Shen

Xin-Yi Liu

Jin-Rui Wu

Yue-Liang Wu

Zhen Fang

Toward a holographic realization of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>-flavor QCD phase structure

Dark photons with kinetic mixing are compelling mediators for the interactions between dark matter and Standard Model particles. While most experimental searches focus on fully visible or fully invisible decays of dark photons, we explore processes that involve dark Higgs-strahlung, i.e. the emission of a dark Higgs boson connected to the mass generation of the dark photon. If the dark Higgs boson is the lightest dark sector particle, it is expected to be long-lived and decay into Standard Model particles via Higgs mixing. At electron-positron colliders, dark Higgs-strahlung may occur either in isolation (leading to a single displaced vertex and missing energy) or accompanied by a photon from initial-state radiation. Both signatures offer distinctive kinematic features, such as peaks in photon energy or missing invariant mass, which enable efficient background suppression and enhance sensitivity beyond existing searches. Our study suggests that Belle II could significantly improve coverage of dark sector models by targeting this previously unexplored final state and that combining dark Higgs-strahlung events with and without additional photon offers great potential for reconstructing the properties of the dark sector.

Germany

Francesca Acanfora

Felix Kahlhoefer

Dark Higgs-strahlung at Belle II: a distinctive dark sector signature with displaced vertices and missing energy

We interpret the Euclidean solution of JT de Sitter gravity as the Coleman-de Luccia instanton for the decay of the low-entropy horizon of its static patch solution into either a Big Crunch or an infinite-entropy Lorentzian de Sitter cosmology. As in previous work by one of the authors, the Big Crunch is interpreted as bounding the entropy of the static state. The principle of detailed balance then guarantees it will transition back to a higher entropy causal diamond in the expanding cosmology. We then construct a family of explicit quantum mechanical models and appropriate metastable states, with transition probabilities well approximated by the semi-classical calculations in JT de Sitter gravity.

Tom Banks

Sidan A

JT de Sitter gravity as a model of Coleman-de Luccia tunneling

We revisit sterile neutrino production enabled by nonstandard interactions (NSIs) among active neutrinos mediated by new bosons. We focus on vector mediators, including neutrinophilic, gauged <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>L</mi></mrow><mrow><mi>μ</mi></mrow></msub><mo>−</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>τ</mi></mrow></msub></mrow></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></math> realizations, that modify in-medium dispersion and scattering, thereby altering the active-sterile conversion history. Building on a novel production framework with NSI thermal potentials and collision integrals, we compute nonthermal phase-space distributions across sterile neutrino mixing and NSI parameters and map each point to an equivalent thermal warm dark matter particle mass <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>th</mi></msub></math> via linear theory transfer function fitting with the cosmological structure formation Boltzmann solver. This enables a direct reinterpretation of state-of-the-art structure formation limits from Milky Way satellites, strong lensing, and the Lyman-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>α</mi></math> forest. These limits, in conjunction with x-ray decay searches, as well as results from a wide variety of particle physics experiments allow for a more complete examination of these models. We find that these vector-mediated models are ruled out when the full combination of current constraints, listed above, are taken into account. NSI scalar-mediated models and models with low reheating temperatures remain viable.

Cannon M. Vogel

Helena García Escudero

Kevork N. Abazajian

Cosmic structure strikes back: The elimination of vector-mediated nonstandard interaction models as a mechanism for sterile neutrino dark matter production

We consider an abelian extension of the Standard Model (SM) comprising a new gauge group U(1)$\textit{′}$, with the neutral gauge boson $\textit{Z′}$ having flavour violating couplings to quarks and leptons. The fermion content is the same as in SM except for the addition of three right-handed neutrinos. The model, proposed in [1], describes the couplings of $\textit{Z′}$ to fermions in terms of three rational parameters $\textit{ϵ}$ that sum to zero imposing the cancellation of the gauge anomalies. Each $\textit{ϵ}$ is common to all fermions in a generation, a feature producing correlations among quark and lepton observables. We focus on $$b\to s{{\ell}}_{1}^{-}{{\ell}}_{2}^{+}$$ transitions for the lepton flavour conserving $\textit{ℓ}$ = $\textit{ℓ}$ and lepton flavour violating case $\textit{ℓ}$ ≠ $\textit{ℓ}$ . Small deviations with respect to the SM predictions are found in the first case, which reflects a feature of the model where quark and lepton sectors prevent each other to manifest large discrepancies with respect to SM. We investigate the correlations between rare $\textit{B}$ and $\textit{B}$ decays and the leptonic processes $\textit{τ}$ → $\textit{μ}$ $\textit{μ}$ $\textit{μ}$ , $\textit{μ}$ → $\textit{e}$ $\textit{γ}$, $\textit{μ}$ → $\textit{e}$ $\textit{e}$ $\textit{e}$ and the $\textit{μ}$ → $\textit{e}$ conversion in nuclei. We show that the current experimental upper bounds on these four channels play an increasingly important role in constraining the branching fractions of lepton flavour violating $\textit{B}$ and $\textit{B}$ decays. While the present bound on $\textit{τ}$ → $\textit{μ}$ $\textit{μ}$ $\textit{μ}$ does not impose significant restrictions, the other three modes set progressively more stringent limits, an important information for the planned new experimental facilities.

Italy

P. Colangelo

F. Fazio

D. Milillo

Correlating lepton flavour violating $\textit{b}$ → $\textit{s}$ and leptonic decay modes in a minimal abelian extension of the Standard Model