The aim of this paper is to investigate the stability and existence of the closed Einstein Universe (EU) under linear homogeneous perturbations within the framework of $$ f(\mathcal {R}, \phi , \chi ) $$ gravity. For this, we consider a closed Friedmann–Roberson–Walker universe filled with isotropic matter. Perturbations are imposed on the matter parameters and on the scale factor. We systematically derive the static and perturbed field equations for scenarios with and without conservation of the energy–momentum tensor and examine the associated stability regions through selected models in $$f(\mathcal {R},\phi ,\chi )$$ gravity. The graphical analysis shows that for suitable choices of model parameters such as $$ \alpha $$ , $\textit{b}$ and scalar field $$\phi _o$$ , the stable regions of the Einstein universe can be obtained in this theory of gravity. Significant differences in stability regions are observed for scalar fields governed by standard kinetic energy and for those characterized by negative kinetic energy. The scalar field and coupling parameters play a key role in the existence of stable regions of the Einstein universe.

Pakistan

 Muhammad

M. Azam

A perturbative approach on the stability of the Einstein universe in $$f(\mathcal {R},\phi ,\chi )$$ gravity

<p>The Deep Underground Neutrino Experiment (DUNE) is a next-generation neutrino experiment with a rich physics program that includes searches for the hypothetical phenomenon of proton decay. Utilizing liquid-argon time-projection chamber technology, DUNE is expected to achieve world-leading sensitivity in the proton decay channels that involve charged kaons in their final states. The first DUNE demonstrator, ProtoDUNE Single-Phase, was a 0.77 kt detector that operated from 2018 to 2020 at the CERN Neutrino Platform, exposed to a mixed hadron and electron test-beam with momenta ranging from 0.3 to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>7</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>/</mo><mi mathvariant="normal">c</mi></mrow></math>. We present a selection of low-energy kaons among the secondary particles produced in hadronic reactions, using data from the 6 and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>7</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>/</mo><mi mathvariant="normal">c</mi></mrow></math> beam runs. The selection efficiency is 1% and the sample purity 92%. The initial energies of the selected kaon candidates encompass the expected energy range of kaons originating from proton decay events in DUNE (below <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∼</mo><mn>200</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>). In addition, we demonstrate the capability of this detector technology to discriminate between kaons and other particles such as protons and muons, and provide a comprehensive description of their energy loss in liquid argon, which shows good agreement with the simulation. These results pave the way for future proton decay searches at DUNE.</p>

Iran

S. Abbaslu

United States

F. Abd Alrahman

CERN

A. Abed Abud

R. Acciarri

Brazil

L.P. Accorsi

Colombia

M.A. Acero

M.R. Adames

Georgia

G. Adamov

M. Adamowski

C. Adriano

F. Akbar

Italy

F. Alemanno

N.S. Alex

K. Allison

M. Alrashed

A. Alton

Spain

R. Alvarez

United Kingdom

T. Alves

A. Aman

H. Amar

P. Amedo

J. Anderson

D.A. Andrade

C. Andreopoulos

M. Andreotti

M.P. Andrews

Madagascar

F. Andrianala

Portugal

S. Andringa

F. Anjarazafy

S. Ansarifard

D. Antic

M. Antoniassi

Mexico

A. Aranda-Fernandez

Chile

T. Araya-Santander

L. Arellano

E. Arrieta Diaz

M.A. Arroyave

M. Artero Pons

J. Asaadi

M. Ascencio

Israel

A. Ashkenazi

D. Asner

L. Asquith

E. Atkin

France

D. Auguste

A. Aurisano

Ukraine

V. Aushev

D. Autiero

D. Ávila Gómez

M.B. Azam

F. Azfar

A. Back

J.J. Back

Y. Bae

I. Bagaturia

L. Bagby

Kazakhstan

D. Baigarashev

S. Balasubramanian

A. Balboni

P. Baldi

W. Baldini

J. Baldonedo

B. Baller

India

B. Bambah

F. Barao

Romania

D. Barbu

G. Barenboim

P. Barham Alzás

G.J. Barker

W. Barkhouse

G. Barr

A. Barros

N. Barros

D. Barrow

J.L. Barrow

A. Basharina-Freshville

A. Bashyal

V. Basque

M. Bassani

D. Basu

C. Batchelor

L. Bathe-Peters

J.B.R. Battat

F. Battisti

J. Bautista

Türkiye

F. Bay

J.L.L. Bazo Alba

J.F. Beacom

E. Bechetoille

B. Behera

E. Belchior

B. Bell

G. Bell

L. Bellantoni

G. Bellettini

V. Bellini

O. Beltramello

Armenia

A. Belyaev

Paraguay

C. Benitez Montiel

D. Benjamin

Identification of low-energy kaons in the ProtoDUNE-SP detector

Phantom divide line transitions are not possible in the context of single scalar field scalar-tensor theories. In this article we study a combined framework of a tachyonic minimally coupled single scalar field theory in the presence of an <math altimg='si1.svg'><msup><mi mathvariant='script'>R</mi><mn>2</mn></msup></math> correction term and with a rescaled Einstein-Hilbert term of the form <math altimg='si6.svg'><mrow><mo>&#8764;</mo><mi>&#955;</mi><mfrac><mi mathvariant='script'>R</mi><mrow><mn>16</mn><mi>&#960;</mi><mi>G</mi></mrow></mfrac></mrow></math>. Such terms can be part of an <math altimg='si7.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>R</mi><mo>)</mo></mrow></math> gravity which in the large curvature regime yields such correction terms effectively. Alternatively, such terms can simply be quantum corrections to the scalar field action. We aim to answer two questions, firstly if this framework can lead to phantom divide line transitions and secondly whether the resulting model can be compatible with the ACT data. The model we studied is an inverse square power-law model, well known from tachyon inflation models. As we show, the field equations can be cast in terms of the scalar field solely, however the resulting theory is distinct from a single scalar field theory, because the phantom divide line is crossed during inflation. Thus initially the tachyonic nature of the scalar field generates a phantom equation of state parameter, and during inflation the phantom divide line is crossed, with the effective equation of state parameter at the end of inflation being <math altimg='si8.svg'><mrow><mi>w</mi><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mn>1</mn><mo linebreak='goodbreak'>/</mo><mn>3</mn></mrow></math> which corresponds to the non-accelerating state of the Universe. The model is proved to be compatible with the ACT data, only when the gravity during inflation is stronger than Einstein-Hilbert gravity, with the effective gravitational constant during inflation being <math altimg='si9.svg'><mfrac><mi>G</mi><mi>&#955;</mi></mfrac></math>. The effective theory is valid only during inflation, thus Big-Bang nucleosynthesis is not affected by the rescaling of the Einstein-Hilbert gravity. The feature of a phantom crossing in <math altimg='si10.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>R</mi><mo>,</mo><mi>&#981;</mi><mo>)</mo></mrow></math> frameworks is new in the literature.

S.D. Odintsov

Greece

Azerbaijan

V.K. Oikonomou

<math altimg='si1.svg'><msup><mi mathvariant='script'>R</mi><mn>2</mn></msup></math>-corrected Tachyon Scalar Field Inflation, the ACT Data, and Phantom Transition

In this work, we investigate the relativistic structure of white dwarfs (WDs) within the framework of modified gravity theory <math altimg='si3.svg'><mrow><mi>f</mi><mrow><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>,</mo><msub><mi>L</mi><mi>m</mi></msub><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><mi>R</mi><mo linebreak='goodbreak'>+</mo><mi>&#945;</mi><mi>T</mi><msub><mi>L</mi><mi>m</mi></msub></mrow></math>, which introduces a non-minimal coupling between matter and curvature. Using a realistic equation of state (EoS) that includes contributions from a relativistic degenerate electron gas and ionic lattice effects, we solve the modified Tolman-Oppenheimer-Volkoff (TOV) equations for two standard choices of the matter Lagrangian density: <math altimg='si9.svg'><mrow><msub><mi>L</mi><mi>m</mi></msub><mo linebreak='goodbreak'>=</mo><mi>p</mi></mrow></math> and <math altimg='si6.svg'><mrow><msub><mi>L</mi><mi>m</mi></msub><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mi>&#961;</mi></mrow></math>. We show that the extra <italic>&#945;TL<inf>m</inf></italic> term significantly alters the mass-radius relation of WDs, especially at high central densities <math altimg='si11.svg'><mrow><mo>(</mo><msub><mi>&#961;</mi><mi>c</mi></msub><mo>&#8819;</mo><msup><mn>10</mn><mn>8</mn></msup><mo linebreak='goodbreak'>&#8722;</mo><msup><mn>10</mn><mn>9</mn></msup><mspace width='0.16em' /><mrow><mi mathvariant='normal'>g</mi></mrow><mo linebreak='goodbreak'>/</mo><mi>c</mi><msup><mi>m</mi><mn>3</mn></msup><mo>)</mo></mrow></math>, allowing for stable super-Chandrasekhar configurations. In particular, depending on the sign and magnitude of the parameter <italic>&#945;</italic>, the maximum mass can increase or decrease, and in some regimes, the usual critical point indicating the transition from stability to instability disappears. Our findings suggest that <italic>f</italic>( <italic>R, T, L<inf>m</inf></italic>) gravity provides a viable framework to explain the existence of massive WDs beyond the classical Chandrasekhar limit. Using Bayesian inference with WD observational data, we further constrain the coupling parameter <italic>&#945;</italic> for the two choices of the Lagrangian density <italic>L<inf>m</inf></italic>.

Edson Otoniel

Juan M.Z. Pretel

Clésio E. Mota

César O.V. Flores

Victor B.T. Alves

Germany

Franciele M. da Silva

White dwarf structure in <italic>f</italic>( <italic>R, T, L<inf>m</inf></italic>) gravity: Beyond the Chandrasekhar mass limit

In this work, we examine the influence of nonlinear electrodynamics (NED) and <italic>f</italic>( <italic>R, T</italic>) gravity on quasi-periodic oscillations (QPOs) around a magnetically charged black hole. By analyzing the effective potential, specific energy, and angular momentum of circular orbits, we study how the NED parameter <italic>&#945;</italic> and the gravitational coupling parameter <italic>&#946;</italic> affect orbital dynamics. Increasing <italic>&#945;</italic> leads to systematic deviations from the Reissner-Nordstr&#246;m behavior, reflected in shifts in the ISCO radius and orbital frequencies. We further explore QPO-generating radii using the Relativistic Precession (RP), Warped Disk (WD), and Epicyclic Resonance (ER2-ER4) models. We further extend our analysis by performing an MCMC-based parameter estimation using QPO data from black holes spanning a wide range of mass scales. This approach yields consistent observational constraints on the model parameters.

Bidyut Hazarika

Abhishek Baruah

Prabwal Phukon

Observational constraints on <italic>f</italic>( <italic>R, T</italic>) gravity coupled with NED from black hole quasi periodic oscillations

Inspired by the observation of the ${\eta}_{t}$ meson at the LHC and the promising prospect of the ${\eta}_{t}$ meson available at the approaching HL-LHC, branching ratios for the ${\eta}_{t}$ ${\to}$ $f\bar{f}$ , $gg$ , ${\gamma}{\gamma}$ , $W^{+}W^{-}$ , $Z^{0}Z^{0}$ , $Z^{0}{\gamma}$ , and $Z^{0}H$ decays are roughly estimated. It is found that tens of opposite-charge dilepton events from the ${\eta}_{t}$ ${\to}$ $W^{+}W^{-}$ decay and hundreds of events from the ${\eta}_{t}$ ${\to}$ $Z^{0}H$ ${\to}$ ${\ell}^{+}{\ell}^{-}H$ decay using the single $Z^{0}$ boson tagging method are expected to be accessible. This estimation provides a reference for future experimental study on the ${\eta}_{t}$ meson.

China

Yueling Yang

Bingbing Yang

Jiazhi Li

Zhaojie Lü

Junfeng Sun

Searching for the toponium ${{\boldsymbol\eta}_{\boldsymbol t}}$ with the ${{\boldsymbol\eta}_{\boldsymbol t}}$ ${\boldsymbol\to}$ ${{\boldsymbol W}^{\bf +}{\boldsymbol W}^{\bf -}}$ decay * Supported by the National Natural Science Foundation of China (12275068, 12275067), the National Key R&D Program of China (2023YFA1606000), the Natural Science Foundation of Henan Province (252300421491, 242300420250), and the Science and Technology R&D Program Joint Fund Project of Henan Province (225200810030), as well as the Science and Technology Innovation Leading Talent Support Program of Henan Province (254200510039)

Neutrino oscillation experiments have confirmed that neutrinos are massive particles and that lepton flavors are mixed. To explain the observed lepton mass spectra and flavor mixing patterns, flavor symmetry plays a crucial and unique role. In this paper, we propose a useful symmetry-breaking scheme by applying $S_{3L} \times S_{3R} \rightarrow $ $ S_{2L} \times S_{2R} \rightarrow \emptyset$ within both charged-lepton and neutrino sectors at the mass-matrix level. For the three distinct residual subgroups $S_{2L}^{(23)} \times S_{2R}^{(23)}$ , $S_{2L}^{(13)} \times S_{2R}^{(13)}$ , and $S_{2L}^{(12)} \times S_{2R}^{(12)}$ that are under consideration, we systematically analyze the various parameterizations of the lepton mass matrices. It is shown that all three scenarios are in good agreement with current neutrino oscillation data. Notably, within the latest best-fit values of neutrino oscillation parameters, the predicted values of the Dirac CP-violating phase $\textit{δ}$ are $294.6^\circ$ , $302.3^\circ$ , and $287.0^\circ$ , respectively. To further assess the viability of the model, a comprehensive numerical analysis is performed by utilizing neutrino oscillation parameters at the $3\sigma$ level. It is found that the allowed ranges of $\textit{δ}$ are $281.2^\circ \rightarrow 338.7^\circ$ , $287.0^\circ \rightarrow 342.2^\circ$ , and $282.7^\circ \rightarrow 297.0^\circ$ , which all fall within its $3\sigma$ range. These results indicate that the proposed symmetry-breaking scheme $S_{3L} \times S_{3R} \rightarrow S_{2L} \times S_{2R} \rightarrow \emptyset$ can naturally explain the realistic lepton mass hierarchy and mixing pattern, thereby providing valuable theoretical perspectives for future research.

Chang-Qi Hu

Chun-Yuan Li

Xiao Liang

Xing-Hua Yang

Dai-Xing Zhang

Further study on lepton mass spectra and flavor mixing with $\textit{S}$ 3$\textit{L}$ × $\textit{S}$ 3$\textit{R}$ flavor symmetry * Supported in part by the National Natural Science Foundation of China (12105162, 12305106), the Natural Science Foundation of Shandong Province (ZR2021QA058, ZR2021QA040) and the Youth Innovation Technology Project of Higher School in Shandong Province (2023KJ146)

We explore a supergravity model based on the modified Kähler potential $$\hat{K} = -3 \ln \left( \Phi + \Phi ^\dagger - \beta \, \mathcal {R} \bar{\mathcal {R}} -\right. \left. \gamma \, (\mathcal {R}\bar{\mathcal {R}})^2 \right) $$ ,where $$\Phi $$ is a chiral superfield containing the dilaton and $$\mathcal {R}$$ is the chiral curvature superfield. The quartic term $$-\gamma (\mathcal {R}\bar{\mathcal {R}})^2$$ ensures stabilization of the curvature sector, in line with recent proposals in modified supergravity, while the linear term $$-\beta \mathcal {R}\bar{\mathcal {R}}$$ yields a dilaton-modulated contribution to the effective $$R^2$$ coefficient. As clarified via the superfield Legendre transform, the model is equivalent to Einstein supergravity coupled to three chiral superfields ( $$\Phi $$ , $\textit{S}$, $\textit{T}$), yielding six physical scalars. Full stability requires both the curvature–sector stabilization (via $$\gamma $$ ) and a non-vanishing dilaton VEV. When the extra scalars are stabilized and $$\langle \phi \rangle = \mathcal {O}(M_P)$$ , the kinetic mixing is exponentially suppressed during inflation ( $$Z \propto e^{-\sigma /\sqrt{6}}$$ ), reducing the dynamics to an effectively single-field Starobinsky model. Thus, cosmological viability is inherited conditionally from the established success of Starobinsky inflation. To the best of our knowledge, this represents the first explicit realization of $\textit{dilaton-coupled modified supergravity}$, where a physical scalar (the dilaton) directly influences the curvature sector through the Kähler geometry. While chiral matter couplings to modified supergravity have been studied in the literature, the explicit coupling of the dilaton remains unexplored. The framework is presented as a phenomenological ansatz for exploring scalar–curvature unification in supersymmetry, with the understanding that a UV completion remains an open challenge.

Reza Baghbani

Dilaton coupling to $\textit{R}$

Pulsars, with their extreme densities and precise measurements, offer an exceptional probe of matter under intense gravity. We examined compact star structures within the extended <math altimg='si1.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>,</mo><mi mathvariant='script'>T</mi><mo>)</mo></mrow></math> gravity framework, incorporating the Ricci scalar, matter Lagrangian, and energy-momentum trace. Introducing coupling constants <italic>&#955;</italic> <inf>1</inf> and <italic>&#955;</italic> <inf>2</inf> enabled a realistic description beyond general relativity. Using the Durgapal-Bannerji-type metric, we derived modified field and TOV equations, obtaining expressions for energy density and anisotropic pressures. With the transformation <math altimg='si165.svg'><mrow><msup><mi>e</mi><mrow><mi mathvariant='script'>B</mi><mo>(</mo><mi>r</mi><mo>)</mo></mrow></msup><mo linebreak='goodbreak'>=</mo><msup><mstyle mathvariant='normal'><mi>&#934;</mi></mstyle><mn>2</mn></msup><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow></mrow></math> and a chosen anisotropy function &#916;( <italic>r</italic>), regular stellar models were integrated and matched smoothly to the exterior Schwarzschild-de Sitter spacetime. All physical conditions are satisfied: density and pressures are positive and finite; &#916;( <italic>r</italic>)&#8239;&gt;&#8239;0 implies an outward-directed force; sound speeds remain subluminal; and the adiabatic index &#915;&#8239;&gt;&#8239;4/3 ensures dynamical stability. The generalized TOV equation confirms equilibrium among gravitational, hydrostatic, anisotropic, and curvature-matter coupling forces. The <math altimg='si166.svg'><mrow><mi>M</mi><mo linebreak='goodbreak'>&#8722;</mo><mi>R</mi></mrow></math> relations exhibit clear trends. For <math altimg='si167.svg'><mrow><msub><mi>&#955;</mi><mn>1</mn></msub><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mn>4</mn><mo>,</mo><msub><mi>&#955;</mi><mn>2</mn></msub><mo linebreak='goodbreak'>=</mo><mn>0.4</mn></mrow></math>: PSR J2215+5135 (2.28, <italic>M</italic> <inf>&#8857;</inf>) has <math altimg='si168.svg'><mrow><mi>R</mi><mo linebreak='goodbreak'>=</mo><mn>13</mn><mo>.</mo><msubsup><mn>05</mn><mrow><mo>&#8722;</mo><mn>0.20</mn></mrow><mrow><mo>+</mo><mn>0.13</mn></mrow></msubsup></mrow></math> km (GR: 12.33&#8239;km); PSR J0740+6620 (2.08, <italic>M</italic> <inf>&#8857;</inf>): 12.68 &#8239;&#8594;&#8239; 13.32&#8239;km; PSR J0348+0432 (2.01, <italic>M</italic> <inf>&#8857;</inf>): 12.76 &#8239;&#8594;&#8239; 13.39&#8239;km; PSR J0030+0451 (1.44, <italic>M</italic> <inf>&#8857;</inf>): 13.19 &#8239;&#8594;&#8239; 13.77&#8239;km. Positive <italic>&#955;</italic> <inf>1</inf> compresses stars <math altimg='si169.svg'><mrow><mo>(</mo><mi>R</mi><mo linebreak='goodbreak'>=</mo><mn>11</mn><mo>.</mo><msup><mn>26</mn><mrow><mo>+</mo><mn>0.33</mn></mrow></msup></mrow></math> km for <math altimg='si170.svg'><mrow><msub><mi>&#955;</mi><mn>1</mn></msub><mrow><mo>=</mo><mn>5</mn><mo>)</mo></mrow></mrow></math>, while <math altimg='si171.svg'><mrow><msub><mi>&#955;</mi><mn>1</mn></msub><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mn>5</mn></mrow></math> expands to <math altimg='si27.svg'><mrow><mn>13</mn><mo>.</mo><msubsup><mn>07</mn><mrow><mo>&#8722;</mo><mn>0.20</mn></mrow><mrow><mo>+</mo><mn>0.14</mn></mrow></msubsup></mrow></math> km. At <math altimg='si5.svg'><mrow><msub><mi>&#955;</mi><mn>1</mn></msub><mo linebreak='goodbreak'>=</mo><mn>3</mn></mrow></math>, varying <italic>&#955;</italic> <inf>2</inf> shifts <italic>R</italic> from <math altimg='si86.svg'><mrow><mn>12</mn><mo>.</mo><msubsup><mn>32</mn><mrow><mo>&#8722;</mo><mn>0.29</mn></mrow><mrow><mo>+</mo><mn>0.18</mn></mrow></msubsup></mrow></math> km <math altimg='si172.svg'><mrow><mo>(</mo><msub><mi>&#955;</mi><mn>2</mn></msub><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mn>5</mn><mo>)</mo></mrow></math> to <math altimg='si173.svg'><mrow><mn>11</mn><mo>.</mo><msup><mn>23</mn><mrow><mo>+</mo><mn>0.35</mn></mrow></msup></mrow></math> km <math altimg='si174.svg'><mrow><mo>(</mo><msub><mi>&#955;</mi><mn>2</mn></msub><mo linebreak='goodbreak'>=</mo><mn>5</mn><mo>)</mo></mrow></math>. Overall, including <math altimg='si175.svg'><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub></math> or <math altimg='si176.svg'><mi mathvariant='script'>T</mi></math> slightly enlarges radii, showing that tuning <italic>&#955;</italic> <inf>1</inf>,&#8201; <italic>&#955;</italic> <inf>2</inf> precisely controls compactness and maximum mass&#8212;consistent with observations and testable by future data.

Oman

S.K. Maurya

South Africa

A. Errehymy

K.N. Singh

Kuwait

O. Donmez

Uzbekistan

J. Rayimbaev

S. Otaboyev

Y. Turaev

Constraining <math altimg='si1.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='script'>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>,</mo><mi mathvariant='script'>T</mi><mo>)</mo></mrow></math> gravity with millisecond pulsar observations

We confront the ghost-free non-local <italic>F</italic>( <italic>R</italic>) gravity theories with the latest Atacama Cosmology Telescope (ACT) constraints on the spectral index of the scalar perturbations and the updated constraints of Planck/BICEP on the tensor-to-scalar ratio. After reviewing how the ghost-free non-local version of <italic>F</italic>( <italic>R</italic>) gravity can be obtained, we show that the de Sitter solution can be obtained in this framework. Also, we show that the resulting theory can be cast in terms of an <italic>F</italic>( <italic>R, &#981;</italic>) theory of gravity. We analyze two models of non-local <italic>F</italic>( <italic>R</italic>) gravity, one power-law and the <italic>R</italic> <sup>2</sup> model, and we show that both models can be compatible with the ACT and updated Planck/BICEP constraints.

Japan

Shin’ichi Nojiri

Sergei Odintsov

Ghost-free non-local <italic>F</italic>( <italic>R</italic>) gravity compatible with ACT