The concept of complexity related to the celestial systems is elaborated within the context of distinct revised gravity theories. However, its interpretation in $\textit{f}$($\textit{R}$, $\textit{G}$) gravity is the main idea of our manuscript. We assume that the inner configuration of the system is a cylindrically symmetric geometry comprising the anisotropic configuration of matter. In our case study, we determine the revised equations of motion combined with the orthogonal decomposition of the Riemann tensor. The implications of anisotropic pressure and nonhomogeneous energy density are relevant. Decisive results relating to the Tolman mass, Weyl scalar, and the complexity factor are derived by incorporating dark source terms corresponding to the $\textit{f}$($\textit{R}$, $\textit{G}$) theory. Additionally, the structure scalars calculated in our manuscript are employed to derive the expression for the complexity factor, after considering reducing the complexity constraint to obtain the solutions for the specific models. The compact structures with anisotropic pressure and non-homogeneous energy density claim the maximum complexity. However, these fluids might not demonstrate any complexity if the implications of non-homogeneous energy density and anisotropic pressure are eradicated because of dark source terms corresponding to the $\textit{f}$($\textit{R}$, $\textit{G}$) theory.

Pakistan

A. Rehman

Azerbaijan

M. Yousaf

China

Faisal Javed

Thailand

Phongpichit Channuie

Interpretation of complexity associated with cylindrically symmetric configuration in $\textit{f}$($\textit{R}$, $\textit{G}$) theory

We show that gravitational leptogenesis with dynamical <italic>CPT</italic> breaking in an expanding universe can be reconciled with the exponential <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>R</mi><mo stretchy='false'>)</mo></math> gravity model, which introduces only one additional parameter <italic>&#946;</italic> compared to the standard &#923;CDM cosmology. This model incorporated axions as cold dark matter. For <italic>L</italic> violating interactions, we consider both a non-supersymmetric model with heavy right-handed neutrino decay and a supersymmetric model with sneutrino decay. For both cases, we have shown that the required baryonic asymmetry could be obtained. We have also shown the variation of decoupling temperature for lepton number violating interactions with the <italic>&#946;</italic> parameter in exponential <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>R</mi><mo stretchy='false'>)</mo></math> gravity. Lepton number-violating model parameters are constrained with the <italic>&#946;</italic> through the decoupling temperature. An upper bound on the <italic>&#946;</italic> parameter of the exponential <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>R</mi><mo stretchy='false'>)</mo></math> gravity is also obtained.

India

Suhail Khan

Ajay Bassi

Rathin Adhikari

Leptogenesis in exponential <italic>f</italic>( <italic>R</italic>) gravity model

We report measurements of the ratios of branching fractions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">R</mi><mo stretchy="false">(</mo><msup><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mo>+</mo></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mrow><mover accent="true"><mrow><mi>B</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msup><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mo>+</mo></mrow></msup><msup><mrow><mi>τ</mi></mrow><mrow><mo>−</mo></mrow></msup><msub><mrow><mover accent="true"><mrow><mi>ν</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mi>τ</mi></mrow></msub><mo stretchy="false">)</mo><mo>/</mo><mspace linebreak="goodbreak"></mspace><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mrow><mover accent="true"><mrow><mi>B</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msup><mrow><mi>D</mi></mrow><mrow><mo stretchy="false">(</mo><mo>*</mo><mo stretchy="false">)</mo><mo>+</mo></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>−</mo></mrow></msup><msub><mrow><mover accent="true"><mrow><mi>ν</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mo>ℓ</mo></mrow></msub><mo stretchy="false">)</mo></mrow></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>ℓ</mo></math> denotes either an electron or a muon. These ratios test the universality of the charged-current weak interaction. The results are based on 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> data sample collected with the Belle II detector at the SuperKEKB <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></math> collider, which operates at a center-of-mass energy corresponding to 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> resonance, just above the threshold for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover></math> production. Signal candidates are reconstructed by selecting events in which the companion <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> meson from 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><mo stretchy="false">→</mo><mi>B</mi><mover accent="true"><mi>B</mi><mo stretchy="false">¯</mo></mover></math> decay is identified in semileptonic modes. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>τ</mi></math> lepton is reconstructed via its leptonic decays. We obtain <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">R</mi><mo stretchy="false">(</mo><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><msubsup><mrow><mn>0.418</mn></mrow><mrow><mo>−</mo><mn>0.073</mn></mrow><mrow><mo>+</mo><mn>0.075</mn></mrow></msubsup><msubsup><mrow><mo stretchy="false">(</mo><mi>stat</mi><mo stretchy="false">)</mo></mrow><mrow><mo>−</mo><mn>0.056</mn></mrow><mrow><mo>+</mo><mn>0.049</mn></mrow></msubsup><mrow><mo stretchy="false">(</mo><mi>syst</mi><mo stretchy="false">)</mo></mrow></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">R</mi><mo stretchy="false">(</mo><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo><mo>+</mo></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><msubsup><mrow><mn>0.306</mn></mrow><mrow><mo>−</mo><mn>0.033</mn></mrow><mrow><mo>+</mo><mn>0.035</mn></mrow></msubsup><msubsup><mrow><mo stretchy="false">(</mo><mi>stat</mi><mo stretchy="false">)</mo></mrow><mrow><mo>−</mo><mn>0.018</mn></mrow><mrow><mo>+</mo><mn>0.016</mn></mrow></msubsup><mrow><mo stretchy="false">(</mo><mi>syst</mi><mo stretchy="false">)</mo></mrow></mrow></math>, which are consistent with world average values. Accounting for the correlation between them, these values differ from the Standard Model expectation by a collective significance of 1.7 standard deviations.

I. Adachi

K. Adamczyk

L. Aggarwal

H. Ahmed

H. Aihara

N. Akopov

S. Alghamdi

M. Alhakami

A. Aloisio

N. Althubiti

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

S. Bansal

M. Barrett

M. Bartl

J. Baudot

A. Beaubien

F. Becherer

J. Becker

J.V. Bennett

F.U. Bernlochner

V. Bertacchi

M. Bertemes

E. Bertholet

M. Bessner

S. Bettarini

V. Bhardwaj

B. Bhuyan

F. Bianchi

T. Bilka

D. Biswas

A. Bobrov

D. Bodrov

A. Bolz

A. Bondar

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

J. Cerasoli

M.C. Chang

P. Chang

R. Cheaib

P. Cheema

B.G. Cheon

K. Chilikin

J. Chin

K. Chirapatpimol

H.E. Cho

K. Cho

S.J. Cho

S.K. Choi

S. Choudhury

J. Cochran

I. Consigny

L. Corona

J.X. Cui

E. De La Cruz-Burelo

S.A. De La Motte

G. De Nardo

G. De Pietro

R. de Sangro

M. Destefanis

S. Dey

R. Dhamija

F. Di Capua

J. Dingfelder

Z. Doležal

I. Domínguez Jiménez

T.V. Dong

M. Dorigo

D. Dossett

S. Dubey

K. Dugic

G. Dujany

P. Ecker

Test of lepton flavor universality with measurements of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi><mo stretchy="false">(</mo><msup><mi>D</mi><mo>+</mo></msup><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>R</mi><mo stretchy="false">(</mo><msup><mi>D</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup><mo stretchy="false">)</mo></math> using semileptonic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> tagging at the Belle II experiment

We explore the non-perturbative aspects of $\textit{c}$ = 1 string with compactified Euclidean time, its 0 + 0 dimensional matrix model duals (at self-dual radius), and 0 + 1 dimensional Matrix Quantum Mechanics (free fermion) description. We calculate the instanton normalizations, disk two-point function, and annulus one-point function in worldsheet formalism using string field theory insights. We further match them with the corresponding predictions from the matrix model descriptions. We also have some results and remarks regarding the multi ZZ instanton normalizations and the general (1, $\textit{n}$) ZZ instanton normalization for $\textit{c}$ = 1 string at both self-dual and generic radius.

Rishabh Kaushik

$\textit{c}$ = 1, $\textit{R}$ = 1 and $\textit{N}$ ≫ 1: ZZ instantons in 2D string theory and matrix integrals

We examine the structure scalars constructed from the orthogonal splitting of the Riemann tensor for the spacetime metric describing the interior of a charged matter configuration undergoing dissipative collapse in the framework of <math altimg='si1.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math> gravity (where <math altimg='si2.svg'><mi>R</mi></math> and <math altimg='si3.svg'><mi>T</mi></math> are the Ricci scalar and the trace of energy-momentum tensor, respectively), and also the way these quantities influence the various physical parameters of the collapsing matter. In absence of dissipation, the energy density inhomogeneity is found to be influenced by the structure scalar <math altimg='si4.svg'><msub><mi>X</mi><mrow><mi>T</mi><mi>F</mi></mrow></msub></math> and the mass-function of the collapsing matter. Further, the presence of charge affects the structure scalars and the total mass-energy content. The dependence of the various physical parameters like heat dissipation, energy density inhomogeneity, evolution of the expansion scalar, the shear scalar, effective homogeneous energy density, and pressure anisotropy on the structure scalars, have been clearly indicated along with a discussion on the complexity factor of the collapsing configuration. The <math altimg='si1.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math> junction conditions have been presented, showing the matching conditions for the matter Lagrangian and their derivatives at the boundary. The energy conditions are also presented and the possibility of violation of the Strong Energy Condition has been discussed.

Uttaran Ghosh

Sarbari Guha

Structure scalars for charged dissipative spherical collapse in <math altimg='si1.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math> gravity

This study explores baryogenesis within a modified gravitational framework where the action incorporates a non-local kernel dependent on the Ricci scalar <italic>R</italic> and its covariant derivative &#8711; <italic>R</italic>. This extension, referred to as <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>R</mi><mo>,</mo><mi mathvariant='normal'>&#8711;</mi><mi>R</mi><mo stretchy='false'>)</mo></math> gravity, generalizes traditional <math altimg='si2.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>R</mi><mo stretchy='false'>)</mo></math> theories by introducing additional derivative terms that may influence early-universe dynamics. Within this framework, we examine four distinct forms of the cosmological scale factor: (i) an intermediate scaling solution, (ii) a conventional power-law expansion, (iii) a generalized hybrid evolution combining both power-law and exponential growth terms and (iv) logamediate scale factor. We introduce a charge-parity (CP) violating interaction term that scales linearly with the spacetime derivative of the combined Ricci scalar and its covariant derivative, expressed as <math altimg='si3.svg'><msub><mrow><mo>&#8706;</mo></mrow><mrow><mi>&#956;</mi></mrow></msub><mo stretchy='false'>(</mo><mi>R</mi><mo linebreak='badbreak' linebreakstyle='after'>+</mo><mi mathvariant='normal'>&#8711;</mi><mi>R</mi><mo stretchy='false'>)</mo></math>. Through numerical computation, we determine the resulting baryon asymmetry by evaluating the dimensionless ratio <math altimg='si4.svg'><mfrac><mrow><msub><mrow><mi>&#951;</mi></mrow><mrow><mi>B</mi></mrow></msub></mrow><mrow><mi>s</mi></mrow></mfrac></math>, where <math altimg='si5.svg'><msub><mrow><mi>&#951;</mi></mrow><mrow><mi>B</mi></mrow></msub></math> represents the baryon number density and <italic>s</italic> denotes the entropy density of the universe. We quantitatively compare our theoretical predictions for the baryon-to-entropy ratio, <math altimg='si4.svg'><mfrac><mrow><msub><mrow><mi>&#951;</mi></mrow><mrow><mi>B</mi></mrow></msub></mrow><mrow><mi>s</mi></mrow></mfrac></math>, with the current observational constraint of <math altimg='si6.svg'><mn>9.42</mn><mo>&#215;</mo><msup><mrow><mn>10</mn></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo><mn>11</mn></mrow></msup></math>. Notably, our numerical results demonstrate remarkable agreement with this empirically established value, supporting the viability of our modified gravitational framework in explaining the observed baryon asymmetry of the universe.

Saudi Arabia

Abdulmohsen Daham Alruwaili

Nadeem Azhar

Abdul Jawad

Investigating baryon to entropy ratio phenomenon in <italic>f</italic>( <italic>R</italic>,&#8711; <italic>R</italic>) gravity

This study explores the structure of compact stars using an extended theory of gravity known as <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi mathvariant='script'>R</mi><mo>,</mo><mi mathvariant='script'>G</mi><mo>,</mo><mi mathvariant='script'>T</mi><mo stretchy='false'>)</mo></math> gravity, where <math altimg='si3.svg'><mi mathvariant='script'>R</mi></math>, is the Ricci scalar, <math altimg='si4.svg'><mi mathvariant='script'>G</mi></math>, the Gauss-Bonnet invariant, and <math altimg='si5.svg'><mi mathvariant='script'>T</mi></math> the trace of the energy-momentum tensor. Focusing on massive radio pulsars, specifically neutron stars with masses greater than 1.8 solar masses, utilize these extreme astrophysical environments to test gravity in regimes unreachable by Earth-based experiments. We adopt a linear form of the theory, <math altimg='si18.svg'><mi>f</mi><mo stretchy='false'>(</mo><mrow><mi mathvariant='script'>R</mi><mo>,</mo><mi mathvariant='script'>G</mi><mo>,</mo><mi mathvariant='script'>T</mi></mrow><mo stretchy='false'>)</mo><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mi mathvariant='script'>R</mi><mo linebreak='goodbreak' linebreakstyle='after'>+</mo><mi>&#945;</mi><mi mathvariant='script'>G</mi><mo linebreak='goodbreak' linebreakstyle='after'>+</mo><mi>&#946;</mi><mi mathvariant='script'>T</mi></math>, with <italic>&#945;</italic>, <cross-ref refid='fn0010' id='crf0390'>1</cross-ref> and <italic>&#946;</italic> are dimensional constants, and derive an exact analytical solution for anisotropic perfect fluid spheres in hydrostatic equilibrium. This model incorporates the compactness factor <math altimg='si7.svg'><mi>C</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mfrac><mrow><mn>2</mn><mi>G</mi><mi>M</mi></mrow><mrow><mi>R</mi><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></math>, to describe all physical properties within the stellar interior. To constrain the model, we employ observational data from the pulsar <italic>U</italic>1724, using its mass and radius to fix the parameters at their upper bounds: <math altimg='si8.svg'><msub><mrow><mi>&#945;</mi></mrow><mrow><mn>1</mn></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mfrac><mrow><mi>&#945;</mi></mrow><mrow><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mo>&#177;</mo><mn>0.023</mn></math> and <math altimg='si9.svg'><msub><mrow><mi>&#946;</mi></mrow><mrow><mn>1</mn></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mfrac><mrow><mi>&#946;</mi></mrow><mrow><msup><mrow><mi>&#954;</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mo>&#177;</mo><mn>0.001</mn></math>. The resulting model is consistent with physical viability and observational constraints. Notably, the squared sound speed in this framework remains below the theoretical limit ( <math altimg='si10.svg'><mmultiscripts><mrow><mtext mathvariant='normal'>c</mtext></mrow><mrow><mi>s</mi></mrow><none /><none /><mrow><mn>2</mn></mrow></mmultiscripts><mo linebreak='goodbreak' linebreakstyle='after'>&lt;</mo><msup><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy='false'>/</mo><mn>3</mn></math>), contrasting with general relativity results. Without assuming a specific equation of state, the model exhibits linear behavior and predicts a core density several times higher than nuclear saturation density ( <math altimg='si11.svg'><msub><mrow><mi>&#961;</mi></mrow><mrow><mtext>nuc</mtext></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>2.6</mn><mo>&#215;</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>14</mn></mrow></msup></math> g/cm 3), with surface density <math altimg='si12.svg'><msub><mrow><mi>&#961;</mi></mrow><mrow><mi>s</mi></mrow></msub></math>, also exceeding this threshold. Additionally, the derived mass-radius relation agrees well with existing astrophysical observations.

Egypt

South Africa

G.G.L. Nashed

Constraining linear form of <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mrow><mi mathvariant='script'>R</mi><mo>,</mo><mi mathvariant='script'>G</mi><mo>,</mo><mi mathvariant='script'>T</mi></mrow><mo stretchy='false'>)</mo></math> gravity from astrophysical observations of the Pulsar U1724

This study examines the structure and stability of dark energy stars within the context of $$R^2$$ gravity, with the gravity model defined by $$f(R) = R + a R^2$$ (the Starobinsky model). Specifically, dark energy is a mysterious force that can prevent the gravitational collapse of compact objects to singularities. To characterize dark energy, we consider modified Chaplygin fluid as an equation of state (EoS) of matter and study its mass-radius relation for different model parameters. By numerically solving the modified Tolman–Oppenheimer–Volkoff (TOV) equations, our primary objective is to examine the influence of variations in the $$R^2$$ gravity parameter $\textit{a}$ on the energy density, pressure, mass-radius and mass-central density relationships of dark energy stars. Our findings reveal that the variation of $\textit{a}$ does not significantly impact on the $$(M-R)$$ relations but comfortably exceeds the 2 $$M_{\odot }$$ limit. Additionally, we examine the dynamical stability of these stars by evaluating the static stability criterion, adiabatic index, and sound speed. Finally, we compare our results with various astrophysical observational data and discuss future observations that could validate the predictions of our model.

Ayan Banerjee

Safiqul Islam

Uzbekistan

Javlon Rayimbaev

Inomjon Ibragimov

Sokhibjan Muminov

Ikram Davletov

Comprehensive analysis of dark energy stars in $\textit{R}$-squared gravity

In this paper, we investigate Friedmann Robertson Walker (FRW) space time filled with a perfect fluid in <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>R</mi><mo>,</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>m</mi></mrow></msub><mo stretchy='false'>)</mo></math> modified theory framework formulated by Harko and Lobo (2010), where <italic>R</italic> is the Ricci scalar curvature, <math altimg='si2.svg'><msub><mrow><mi>L</mi></mrow><mrow><mi>m</mi></mrow></msub></math> is the ideal fluid's Lagrangian. Two specific non-linear <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>R</mi><mo>,</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>m</mi></mrow></msub><mo stretchy='false'>)</mo></math> functional forms are assumed: <math altimg='si3.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>R</mi><mo>,</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>m</mi></mrow></msub><mo stretchy='false'>)</mo><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mfrac><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo linebreak='goodbreak' linebreakstyle='after'>+</mo><mo stretchy='false'>(</mo><mn>1</mn><mo linebreak='badbreak' linebreakstyle='after'>+</mo><mi>&#945;</mi><mi>R</mi><mo stretchy='false'>)</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>m</mi></mrow></msub></math> representing a non-minimal coupling case and <math altimg='si4.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>R</mi><mo>,</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>m</mi></mrow></msub><mo stretchy='false'>)</mo><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mfrac><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo linebreak='goodbreak' linebreakstyle='after'>+</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mi>m</mi></mrow><mrow><mi>n</mi></mrow></msubsup><mo linebreak='goodbreak' linebreakstyle='after'>+</mo><mi>&#946;</mi></math> representing a minimal coupling case. Here, we use a cubic parametrization of the deceleration parameter that produces an accelerating universe to obtain the exact solution for the field equations. We investigate the evolution of cosmological parameters including pressure and energy density. Using <math altimg='si5.svg'><msub><mrow><mi>L</mi></mrow><mrow><mi>m</mi></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mi>&#961;</mi></math> and a cubic parametrization of the deceleration parameter to account for late-time cosmic acceleration. We analyze the evolution of cosmological parameters in terms of both cosmic time and redshift and constrain model parameters using observational datasets from <math altimg='si6.svg'><mi>H</mi><mo stretchy='false'>(</mo><mi>z</mi><mo stretchy='false'>)</mo></math>, Pantheon, BAO, H(z)+Pantheon, H(z)+BAO+Pantheon. The results show a transition of the deceleration parameter from deceleration to acceleration and indicate a possible quintessence-like behavior at the present epoch. The findings suggest that the proposed models can effectively describe the universe's expansion history in agreement with observations.

Kangujam Priyokumar Singh

Syed Sabanam

Anil Kumar Yadav

Asem Jotin Meitei

Modeling through the cubic parametrization of the deceleration parameter in <italic>f</italic>( <italic>R</italic>, <italic>Lm</italic>) gravity with observational constraints

We focus on the inflationary predictions of <italic>&#946;</italic>-exponential potential models, in which the inflaton is associated with a field that determines the size of extra dimensions. This provides a well-motivated starting point for exploring physics at very high energy scales. Consequently, we incorporate an <math altimg='si1.svg'><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math> term within the Palatini formulation of gravity. Additionally, we extend our analysis by examining the effects of reheating on inflationary observables, considering various scenarios for the reheat temperature. We present the inflationary predictions for spectral index <math altimg='si2.svg'><msub><mrow><mi>n</mi></mrow><mrow><mi>s</mi></mrow></msub></math>, tensor-to-scalar ratio <italic>r</italic>, and the running of the spectral index <math altimg='si3.svg'><mi mathvariant='normal'>d</mi><msub><mrow><mi>n</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy='false'>/</mo><mi mathvariant='normal'>d</mi><mi mathvariant='normal'>ln</mi><mo>&#8289;</mo><mi>k</mi></math> in the context of a <italic>&#946;</italic>-exponential potential minimally coupled in Palatini <math altimg='si1.svg'><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math> gravity. Furthermore, we confront our results with observational constraints from BICEP/Keck, Planck 2018, and the most recent Planck+ACT DR6 data released by the ACT collaboration. We also consider the projected sensitivities of upcoming CMB experiments, including CMB-S4, LiteBIRD, and SPIDER. Our findings demonstrate the viability of the model, even in light of the tighter constraints expected from future data.

Türkiye

United States

Nilay Bostan

Rafid H. Dejrah

Inflationary dynamics and observables: <italic>&#946;</italic>-exponential models in Palatini <italic>R</italic> 2 gravity