We examine whether nonlinear matter dependence in <math altimg='si24.svg'><mrow><mi>f</mi><mo>(</mo><mrow><mi>Q</mi><mo>,</mo><msub><mi>L</mi><mi>m</mi></msub></mrow><mo>)</mo></mrow></math>gravity can account for the observed late-time acceleration of the Universe. For this purpose, we consider <math altimg='si25.svg'><mrow><mi>f</mi><mrow><mo>(</mo><mrow><mi>Q</mi><mo>,</mo><msub><mi>L</mi><mi>m</mi></msub></mrow><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mi>a</mi><mi>Q</mi><mo linebreak='goodbreak'>+</mo><mn>2</mn><msubsup><mi>L</mi><mi>m</mi><mi>n</mi></msubsup><mo linebreak='goodbreak'>+</mo><mi>b</mi></mrow></math> and reconstruct the expansion history using <math altimg='si26.svg'><mrow><mi>H</mi><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><msub><mi>H</mi><mn>0</mn></msub><mtext>exp</mtext><mi>&#8289;</mi><mrow><mo>(</mo><mrow><mi>&#945;</mi><mi>z</mi><mo linebreak='badbreak'>+</mo><mi>&#946;</mi><msup><mrow><mi>z</mi></mrow><mn>2</mn></msup></mrow><mo>)</mo></mrow></mrow></math>. The parameters of the Hubble parametrization are constrained through Bayesian analysis using the joint Cosmic Chronometer and DESI BAO datasets. The reconstructed evolution is consistent with the observational measurements and describes a smooth transition from past deceleration to the present accelerated phase. The model produces positive energy density and negative pressure at late times, leading to a quintessence-like cosmic evolution without entering the phantom regime. Its dynamical behaviour also provides testable departures from the spatially flat <math altimg='si12.svg'><mstyle mathvariant='normal'><mi>&#923;</mi></mstyle></math>CDM expansion history. These findings support nonlinear <math altimg='si24.svg'><mrow><mi>f</mi><mo>(</mo><mrow><mi>Q</mi><mo>,</mo><msub><mi>L</mi><mi>m</mi></msub></mrow><mo>)</mo></mrow></math> gravity as a viable framework for describing late-time cosmic acceleration.

India

S.N. Bayaskar

A.D. Vishwakarma

S.A.A. Qadeer

Azerbaijan

J. Praveen

S.C. Darunde

Dark energy in non-linear <math altimg='si23.svg'><mrow><mi>f</mi><mo>(</mo><mrow><mi>Q</mi><mo>,</mo><msub><mi>L</mi><mi>m</mi></msub></mrow><mo>)</mo></mrow></math> gravity with exponential parametrization of Hubble parameter

We present a theory-constrained hierarchical Bayesian analysis of primordial black holes (PBHs) generated by inflationary perturbations in <italic>f</italic>( <italic>Q, T</italic>) gravity, and confront the resulting PBH population with the gravitational-wave catalog GWTC-3. In this framework, the parameters ( <italic>&#945;, &#946;, &#955;</italic>) characterize the effective inflationary dynamics, with <italic>&#945;</italic> and <italic>&#946;</italic> specifying the adopted <italic>f</italic>( <italic>Q, T</italic>) gravitational sector and <italic>&#955;</italic> parameterizing the local behavior of the specified inflaton potential near its quasi-inflection-point region. Starting from the modified background dynamics in <italic>f</italic>( <italic>Q, T</italic>) gravity, we compute the curvature power spectrum and determine the resulting PBH mass distribution through gravitational collapse at horizon re-entry. Within the adopted analytic approximation and Gaussian-modulated potential, the inflationary dynamics determine the PBH mass-function parameters through the background evolution and the curvature power spectrum. Using posterior samples of detected binary black-hole events, we construct a theory-constrained hierarchical likelihood and explore the corresponding hyperparameter space with Markov Chain Monte Carlo, obtaining constraints on the effective inflationary parameters of the adopted model. Our analysis demonstrates how gravitational-wave population data can be used to constrain an inflationary modified-gravity model through its predicted PBH population. This provides a statistical framework linking early-Universe modified gravity to late-time compact-binary observations and offers a new observational probe of the inflationary sector of alternative gravity theories.

Iran

S. Davood Sadatian

S. Mohamad Reza Hosseini

Theory-constrained hierarchical inference of primordial black holes in <italic>f</italic>( <italic>Q, T</italic>) gravity with GWTC-3

Galaxy clusters are the largest virialized structures in the universe, and the discrepancy between their hydrostatic mass and their observed baryonic content remains one of the principal motivations for both dark matter and modified gravity. We confront three <italic>f</italic>( <italic>R</italic>) gravity models; the Yukawa-like model, the Hu&#8211;Sawicki model, and the <italic>Rn</italic> model directly against the baryonic mass of ten galaxy clusters drawn from archival X-ray data, using a linear regression between baryonic mass <italic>M</italic> <inf>bar</inf> and theoretical modified mass <italic>M</italic> <inf>mod</inf>, together with a relative likelihood analysis of the mass ratio <italic>M</italic> <inf>bar</inf>/ <italic>M</italic> <inf>mod</inf>, as complementary diagnostics. Model-specific free parameters; the Yukawa coupling <italic>&#945;</italic> and the <italic>Rn</italic> scale factor <italic>k<inf>fR</inf></italic> are constrained via Markov Chain Monte Carlo (MCMC) sampling against the cluster sample itself. We find that none of the three models, in their classical form, fully reconciles the modified mass with the observed baryonic mass. The Yukawa model with a free coupling constrained at cluster scales ( <math altimg='si7.svg'><mrow><mi>&#945;</mi><mo linebreak='goodbreak'>=</mo><mn>10</mn><mo>.</mo><msubsup><mn>304</mn><mrow><mo>&#8722;</mo><mn>0.470</mn></mrow><mrow><mo>+</mo><mn>0.527</mn></mrow></msubsup></mrow></math>) comes closest to the ideal 1:1 relation, with a regression slope of 0.841&#8239;&#177;&#8239;0.085. The power-law <italic>Rn</italic> model, with <math altimg='si8.svg'><mrow><msub><mi>k</mi><mrow><mi>f</mi><mi>R</mi></mrow></msub><mo linebreak='goodbreak'>=</mo><mn>0</mn><mo>.</mo><msubsup><mn>0367</mn><mrow><mo>&#8722;</mo><mn>0.0027</mn></mrow><mrow><mo>+</mo><mn>0.0029</mn></mrow></msubsup></mrow></math> consistent with the value found at galactic scales, yields a slope of 0.524&#8239;&#177;&#8239;0.146. The Hu&#8211;Sawicki model, despite confirming the theoretically predicted 4/3 enhancement of the Newtonian mass in the unscreened regime, yields the most discrepant regression slope of 0.158&#8239;&#177;&#8239;0.019, indicating that this enhancement alone closes only a small fraction of the mass gap. The Yukawa model with the fixed coupling calibrated at spherical galaxy scales ( <math altimg='si9.svg'><mrow><mi>&#948;</mi><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mn>0.98</mn></mrow></math>) performs worst of all, overshooting unity with a slope of 2.475&#8239;&#177;&#8239;0.355. These results indicate that classical <italic>f</italic>( <italic>R</italic>) gravity, evaluated with parameters constrained directly from cluster data, substantially reduces but does not eliminate the cluster mass discrepancy, motivating the search for additional physical mechanisms operating on top of the geometric modification.

Indonesia

Syifarani Cahya Anwar

Feri Apryandi

Muhammad Lawrence Pattersons

Judhistira Aria Utama

Rillya Arundaa

Megastin Massang Lumembang

Impact of f(R) gravity models on hydrostatic mass of galaxy clusters

In this work we explore the non-singular bouncing scenarios in the framework of <math altimg='si9.svg'><mrow><mi>f</mi><mo>(</mo><mi>Q</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>)</mo></mrow></math> gravity, where the gravitational action depends on the non-metricity scalar ( <italic>Q</italic>) and matter Lagrangian density <math altimg='si10.svg'><mrow><mo>(</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>)</mo></mrow></math>. Using the functional form <math altimg='si11.svg'><mrow><mi>f</mi><mrow><mo>(</mo><mi>Q</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mi>&#945;</mi><mi>Q</mi><mo linebreak='goodbreak'>+</mo><mn>2</mn><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo linebreak='goodbreak'>+</mo><mi>&#946;</mi></mrow></math>, two different bouncing scenario models are analyzed in a homogeneous, isotropic and flat FLRW universe. The cosmological evolution is analyzed through the behavior of the Hubble parameter, deceleration parameter, energy density, pressure, and equation of state parameter. Both models exhibit a successful bounce characterized by a smooth transition from a contracting universe ( <italic>H</italic>&#8239;&lt;&#8239;0) to an expanding phase ( <italic>H</italic>&#8239;&gt;&#8239;0) without encountering any initial singularity <math altimg='si12.svg'><mrow><mo>(</mo><mi>H</mi><mo linebreak='goodbreak'>=</mo><mn>0</mn><mo>)</mo></mrow></math>. The EOS parameter exhibits phantom crossing behavior, while the energy conditions reveal NEC and SEC violation around the bounce, consistent with bouncing cosmology requirements. Stability analysis through metric perturbations and adiabatic index confirms stable late-time cosmic evolution. The study suggests that <math altimg='si9.svg'><mrow><mi>f</mi><mo>(</mo><mi>Q</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>)</mo></mrow></math> theory offers a promising geometrical background for understanding non-singular early universe dynamics and bouncing scenarios.

Vinod Kumar Bhardwaj

Saudi Arabia

Meraj Ali Khan

Shyam Das

Saibal Ray

Exploring the scenarios of non-singular bouncing cosmology in <math altimg='si9.svg'><mrow><mi>f</mi><mo>(</mo><mi>Q</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>)</mo></mrow></math> gravity

Using a dataset corresponding to an integrated luminosity of 9 fb collected in proton-proton collisions between 2011 and 2018 by the LHCb experiment, evidence is found for the decay $$ {B}_s^0\to {\phi \eta}^{\prime } $$ with 3$\textit{.}$5$\textit{σ}$ significance. The branching ratio relative to the $$ {B}_s^0\to \phi \phi $$ decay is determined to be ℛ = (3$\textit{.}$56 ± 0$\textit{.}$79 ± 0$\textit{.}$18 ± 0$\textit{.}$06) × 10 . This corresponds to a branching fraction, $$ \mathcal{B}\left({B}_s^0\to {\phi \eta}^{\prime}\right)=\left(0.66\pm 0.15\pm 0.03\pm 0.02\right)\times {10}^{-6} $$ where, in both cases, the first uncertainty is statistical, the second systematic, and the third due to external branching fractions.

Netherlands

R. Aaij

United States

M. Abdelfatah

United Kingdom

A. Abdelmotteleb

Switzerland

C. Abellan Beteta

F. Abudinén

T. Ackernley

A. Adefisoye

Spain

B. Adeva

M. Adinolfi

Sweden

P. Adlarson

France

C. Agapopoulou

C. Aidala

S. Akar

K. Akiba

Italy

P. Albicocco

Germany

J. Albrecht

Lithuania

R. Aleksiejunas

F. Alessio

P. Alvarez Cartelle

Brazil

S. Amato

J. Amey

Y. Amhis

China

L. An

L. Anderlini

M. Andersson

P. Andreola

M. Andreotti

S. Andres Estrada

A. Anelli

D. Ao

C. Arata

F. Archilli

Z. Areg

M. Argenton

Costa Rica

S. Arguedas Cuendis

L. Arnone

M. Artuso

E. Aslanides

R. Ataíde Da Silva

M. Atzeni

B. Audurier

J. Authier

D. Bacher

I. Bachiller Perea

S. Bachmann

M. Bachmayer

J. Back

Z. Bai

V. Balagura

A. Balboni

W. Baldini

Z. Baldwin

L. Balzani

H. Bao

J. Baptista de Souza Leite

C. Barbero Pretel

M. Barbetti

I. Barbosa

R. Barlow

M. Barnyakov

S. Barsuk

W. Barter

J. Bartz

Poland

S. Bashir

Mongolia

B. Batsukh

P. Battista

Hungary

A. Bavarchee

A. Bay

A. Beck

M. Becker

F. Bedeschi

I. Bediaga

N. Behling

S. Belin

A. Bellavista

I. Belov

I. Belyaev

E. Ben-Haim

G. Bencivenni

R. Bernet

A. Bertolin

F. Betti

J. Bex

Ukraine

O. Bezshyyko

S. Bhattacharya

M. Bieker

N. Biesuz

A. Biolchini

M. Birch

F. Bishop

A. Bitadze

A. Bizzeti

T. Blake

F. Blanc

J. Blank

S. Blusk

J. Boelhauve

O. Boente Garcia

T. Boettcher

A. Bohare

Evidence for the decay $$ {B}_s^0\to {\phi \eta}^{\prime } $$

In this work, we examine Big Bang Nucleosynthesis (BBN) within the framework of <italic>f</italic>( <italic>Q, C</italic>) gravity by considering three representative functional forms of the gravitational Lagrangian. The first model is constructed from quadratic contributions involving the nonmetricity scalar <italic>Q</italic> and the boundary term <italic>C</italic>. The second employs a separable form containing the standard linear dependence on <italic>Q</italic> together with a logarithmic correction associated with <italic>C</italic>, whereas the third model introduces a multiplicative coupling between <italic>Q</italic> and <italic>C</italic>. For each scenario, we investigate the background dynamics during the radiation-dominated phase and assess whether the resulting expansion history is compatible with the requirements of successful BBN. We subsequently derive constraints on the corresponding model parameters by confronting the predicted primordial abundances of the principal light elements, with particular emphasis on helium-4 and deuterium. Among the three cases considered, the second model yields the most favorable agreement with the observationally inferred primordial abundances of helium-4 and deuterium, thereby identifying a viable region of its parameter space.

Subhajit Sarkar

Ujjal Debnath

Big Bang nucleosynthesis constraints on f(Q,C) gravity

A measurement of the ratio of semileptonic branching fractions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">R</mi><mo stretchy="false">(</mo><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow><mo stretchy="false">)</mo></math>, defined as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">R</mi><mo stretchy="false">(</mo><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow><mo stretchy="false">)</mo><mo>≡</mo><mspace linebreak="goodbreak"></mspace><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow><msup><mrow><mi>τ</mi></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mi>τ</mi></mrow></msub><mo stretchy="false">)</mo></mrow><mo>/</mo><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mi>μ</mi></mrow></msub><mo stretchy="false">)</mo></mrow></mrow></math>, is reported using a sample of proton-proton collision data corresponding to an integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>5.4</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> recorded by the LHCb experiment in 2016–2018 at a center-of-mass energy of 13 TeV. The measured value is found to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">R</mi><mo stretchy="false">(</mo><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow><mo stretchy="false">)</mo><mo>=</mo><mspace linebreak="goodbreak"></mspace><mn>0.51</mn><mo>±</mo><mn>0.12</mn><mrow><mo stretchy="false">(</mo><mi>stat</mi><mo stretchy="false">)</mo></mrow><mo>±</mo><mn>0.08</mn><mrow><mo stretchy="false">(</mo><mi>syst</mi><mo stretchy="false">)</mo></mrow></math>, which is within 1.8 standard deviations of the predictions from the standard model assuming lepton flavor universality.

A.S.W. Abdelmotteleb

A.A. Adefisoye

C.A. Aidala

H. Al Saleh

CERN

J.L. Amey

J.A. Authier

J.J. Back

Z.B. Bai

I.R. Barbosa

R.J. Barlow

S. Baron

P.B. Battista

I.B. Bediaga

N.A. Behling

J.L.M. Berkey

M.S. Bieker

N.V. Biesuz

F.C.R. Bishop

J.E. Blank

J.A. Boelhauve

Measurement of the Ratio of Branching Fractions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>τ</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>τ</mi></msub><mo stretchy="false">)</mo><mo>/</mo><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msubsup><mi>B</mi><mi>c</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>μ</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>μ</mi></msub><mo stretchy="false">)</mo></math>

Flux quantization is subtle when divisor products do not determine the intrinsic vertical lattice. On a fixed smooth resolved nonflat cubic Calabi-Yau fourfold, a saturation-independent finite-index analysis determines residue sectors and proves every shifted-quantized free vertical class pairs evenly with a selected tenplet cycle. Under the gauge-preserving matter-surface interpretation, odd net tenplet chirality is excluded in that sector. An arithmetic cover yields exact flux-charge recurrences and intrinsic minima on four progressions; neutral minima exceed the tadpole bound. Every nonzero tadpole-bounded uplifted class in the cover fails primitivity throughout the Kähler cone. A coefficient-degree theorem obstructs flat sectionless completions of ten rooted cubic presentations and extends conditionally to nef bases. The results concern the free-vertical sector, not compactifications or stabilized vacua.

Owais Ahmad

Canada

Arshid Shabir

Belgium

Mir Faizal

A finite-index theorem for discrete-symmetric flux data in F-theory

This paper presents a comprehensive analysis of junction conditions for gluing different $\textit{f}$($\textit{R}$) gravitational theories across a non-null hypersurface. Using the variational approach, we systematically derive the junction conditions for both general $\textit{f}$($\textit{R}$) theories and the special case of Einstein gravity, for comparison. We demonstrate that when joining two distinct $\textit{f}$($\textit{R}$) theories, the junction conditions require continuity of $$\partial f(R)/\partial R$$ , the extrinsic curvature $$K_{\mu \nu }$$ , while allowing for discontinuities in the Ricci Scalar $\textit{R}$. Furthermore, we establish the equivalence between Jordan and Einstein frame formulations through careful treatment of conformal transformations; Our results reveal that different $\textit{f}$($\textit{R}$) theories can be consistently matched provided specific relations between their functional forms and geometric quantities are satisfied at the interface.

Amin Aalipour

Nima Khosravi

Gluing different gravitational models: $\textit{f}$($\textit{R}$) case

QCD-like theories with $\textit{N}$ = 2 fermion flavours in real and pseudoreal representations are studied within Chiral Perturbation Theory. For the pseudoreal symmetry-breaking pattern $\textit{SU}$ (4)/$\textit{Sp}$(4), the reduced NLO Lagrangian is derived. The NLO and NNLO corrections to the pion masses, decay constants, and vacuum condensates are calculated for non-degenerate fermion masses, extending previous results obtained for degenerate masses and for the non-degenerate case at NLO. Using the available spectroscopic and scattering lattice data for the $\textit{Sp}$($\textit{N}$ = 4) gauge theory with two fermion flavours, fits of the NLO low-energy constants are performed at NNLO precision. It is found that higher-order corrections are important for reproducing lattice observables and have a significant impact on the phenomenology of strongly interacting pionic dark matter, particularly in the regime of big $\textit{M}$ /$\textit{F}$ .

Johan Bijnens

Norway

Daniil Krichevskiy

QCD-like theories at next-to-next-to-leading order with $\textit{N}$ $\textit{F}$ = 2 non-degenerate fermions