Big Bang nucleosynthes describes a significant process in the early universe, responsible for the formation of light nuclei a while after the Big Bang explosion. Its sensitivity to the expansion rate makes BBN an effective probe for testing deviations from standard cosmology, particularly within the framework of modified theories of gravity. In this article, we investigate the evolution of the Universe through Big Bang nucleosynthesis within the framework of <math altimg='si2.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>T</mi><mo>,</mo><mspace width='0.25em' /><mi>B</mi><mo>,</mo><mspace width='0.25em' /><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant='script'>G</mi></mrow></msub><mo>,</mo><mspace width='0.25em' /><msub><mrow><mi>B</mi></mrow><mrow><mi mathvariant='script'>G</mi></mrow></msub><mo stretchy='false'>)</mo></math> gravity. Here, <math altimg='si3.svg'><mi>T</mi><mo>,</mo><mspace width='0.25em' /><mi>B</mi><mo>,</mo><mspace width='0.25em' /><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant='script'>G</mi></mrow></msub></math> and <math altimg='si4.svg'><msub><mrow><mi>B</mi></mrow><mrow><mi mathvariant='script'>G</mi></mrow></msub></math> correspond to the torsion, boundary term, teleparallel Gauss-Bonnet term, and Gauss-Bonnet boundary term, respectively. To explore the deviation from the teleparallel equivalent of general relativity, we apply the transformation <math altimg='si2.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>T</mi><mo>,</mo><mspace width='0.25em' /><mi>B</mi><mo>,</mo><mspace width='0.25em' /><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant='script'>G</mi></mrow></msub><mo>,</mo><mspace width='0.25em' /><msub><mrow><mi>B</mi></mrow><mrow><mi mathvariant='script'>G</mi></mrow></msub><mo stretchy='false'>)</mo></math> = <math altimg='si5.svg'><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo><mi>T</mi><mo linebreak='goodbreak' linebreakstyle='after'>+</mo><mi mathvariant='script'>F</mi><mo stretchy='false'>(</mo><mi>T</mi><mo>,</mo><mspace width='0.25em' /><mi>B</mi><mo>,</mo><mspace width='0.25em' /><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant='script'>G</mi></mrow></msub><mo>,</mo><mspace width='0.25em' /><msub><mrow><mi>B</mi></mrow><mrow><mi mathvariant='script'>G</mi></mrow></msub><mo stretchy='false'>)</mo></math>. For an in-depth analysis of the Big Bang nucleosynthesis, we choose five distinct models from gravity and compared the results with the observational limits on <math altimg='si6.svg'><mo stretchy='true'>|</mo><mfrac><mrow><mi mathvariant='normal'>&#916;</mi><msub><mrow><mi mathvariant='script'>T</mi></mrow><mrow><mi>f</mi></mrow></msub></mrow><mrow><msub><mrow><mi mathvariant='script'>T</mi></mrow><mrow><mi>f</mi></mrow></msub></mrow></mfrac><mo stretchy='true'>|</mo></math> to examine restrictions on the free parameters associated with these models. Our outcomes indicate that <math altimg='si2.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>T</mi><mo>,</mo><mspace width='0.25em' /><mi>B</mi><mo>,</mo><mspace width='0.25em' /><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant='script'>G</mi></mrow></msub><mo>,</mo><mspace width='0.25em' /><msub><mrow><mi>B</mi></mrow><mrow><mi mathvariant='script'>G</mi></mrow></msub><mo stretchy='false'>)</mo></math> gravity can agree with the constraint of big bang nucleosynthesis, and hence build a valid view of the universe. Moreover, we take the limiting cases of the assumed theory, that is, <math altimg='si7.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>T</mi><mo>,</mo><mi>B</mi><mo stretchy='false'>)</mo></math> and <math altimg='si8.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>T</mi><mo stretchy='false'>)</mo></math> theories, which also ensure consistency with BBN data.

Pakistan

Abdul Malik Sultan

Manahil Ali

China

Shamaila Rani

Azerbaijan

Nadeem Azhar

Kazakhstan

N. Myrzakulov

Uzbekistan

Sanjar Shaymatov

Constraining Big Bang nucleosynthesis in <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>T</mi><mo>,</mo><mi>B</mi><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant='script'>G</mi></mrow></msub><mo>,</mo><msub><mrow><mi>B</mi></mrow><mrow><mi mathvariant='script'>G</mi></mrow></msub><mo stretchy='false'>)</mo></math> gravity

We present a unified treatment of cosmic inflation within the framework of Myrzakulov Gravity, exploring its realization in three different formalisms: metric (curvature-based), teleparallel (torsion-based), and symmetric teleparallel (non-metricity-based). For each case, we derive the corresponding field equations in a flat FLRW background, study inflationary solutions driven by a scalar field, and compute observable quantities such as the scalar spectral index <math altimg='si1.svg'><msub><mrow><mi>n</mi></mrow><mrow><mi>s</mi></mrow></msub></math> and the tensor-to-scalar ratio <italic>r</italic>.

South Africa

United States

Davood Momeni

Ratbay Myrzakulov

Inflation in Myrzakulov <italic>F</italic>( <italic>R</italic>, <italic>T</italic>) gravity: A comparative study in metric, symmetric teleparallel, and Weitzenb&#246;ck formalisms

This article explores how modifications to gravity influence the structure of the brane, with the goal of identifying the gravitational model that most closely reflects the one governing our physical universe. To achieve this, we consider a generalization of standard General Relativity. The stability of the model is evaluated through probabilistic measurements, revealing minimum points that represent the most probable and stable configurations of the brane for different values of the gravitational terms. Furthermore, the location of fermions on the brane is affected by gravitational variations, with the presence of resonance modes and the possibility of leakage of massive fermions into the bulk. Numerical analyses are presented, showing that the increase in the influence of gravitational terms increases the certainty of the location of massless fermions on the brane. All these results provide important insights for understanding the dynamics of the braneworld universe.

Brazil

A.R.P. Moreira

Mexico

Shi-Hai Dong

Braneworld- <italic>f</italic>( <italic>R</italic>, <italic>T</italic>, <italic>G</italic>)

In this paper, we investigate pure geometric <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>R</mi><mo stretchy='false'>)</mo></math> cosmology branes embedded in five-dimensional spacetime. The form of <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>R</mi><mo stretchy='false'>)</mo></math> is chosen as a polynomial. The Five-dimensional scalar curvature <italic>R</italic> is assumed to be constant. Based on the value of the four-dimensional cosmological constant <math altimg='si2.svg'><msub><mrow><mi>&#955;</mi></mrow><mrow><mn>4</mn></mrow></msub></math>, the branes can be classified into Minkowski, de Sitter, and de anti-de Sitter cases. Solutions for each case can be calculated. These solutions are stable against linear tensor perturbations in all cases. In the Minkowski brane case, the zero mode of gravity can be localized on the brane. In the de Sitter brane case, the zero mode and one massive Kaluza-Klein mode can be localized on the brane. In the anti-de Sitter brane case, all massive Kaluza-Klein modes can be localized on the brane. The results of the analysis of tensor fluctuations are the same in both the Einstein frame and the Jordan frame.

Heng Guo

Cai-Ling Wang

Yong-Tao Lu

Yue Sun

Lang-Lang Wang

Pure geometric <italic>f</italic>( <italic>R</italic>) branes

<p>We investigate fermionic quantum field theories using functional renormalization. In the limit of many fermion flavors <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math>, we demonstrate that theories have exact solutions for their quantum effective actions given by quasilocal interaction functionals of fermion bilinears. The structure implies that local potential approximations are exact and exactly solvable and that field anomalous dimensions vanish. Theories with nontrivial anomalous dimensions may also arise under conditions that are identified. We further demonstrate that higher-derivative interactions are inevitably induced by pointlike ones, including at large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math>. The local potential flows for fermionic theories with the most general <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></math> symmetric interactions are provided. For sample theories with scalar, pseudoscalar, vector, or axial-vector interactions, we identify conformal fixed points, scaling dimensions, conformal manifolds, and quantum-induced shifts in scaling dimensions of higher-derivative interactions. We also study fermion mass generation and subleading modifications due to finite <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> corrections. Implications for conformal field theories and applications in condensed matter and particle physics are indicated.</p>

United Kingdom

Charlie Cresswell-Hogg

CERN

Daniel F. Litim

Fermions and the renormalization group at large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>f</mi></msub></math>

We investigate the impact of bulk viscosity on the accelerating expansion and large-scale structure formation of a Universe in which the underlying gravitational interaction is described by $\textit{f}$($\textit{Q}$) gravity. Various paradigmatic choices of the $\textit{f}$($\textit{Q}$) gravity theory, including power-law, exponential, and logarithmic models, are considered. To test the cosmological viability of these $\textit{f}$($\textit{Q}$) gravity models, we use the Baryon Acoustic Oscillations ($\textit{BAO}$) measurements from the Dark Energy Spectroscopic Instrument (DESI) Survey, cosmic chronometers ($\textit{CC}$) from Hubble measurements, the SNIa distance moduli measurements from the $\textit{PantheonP + SH0ES}$, growth rate ($\textit{f}$-data), and redshift-space distortions $$(f\sigma _8)$$ datasets, the latter two once the linear cosmological perturbations, growth rate $\textit{f}$($\textit{z}$), and redshift-space distortion $$f\sigma _8(z)$$ are studied. Thus, we perform the combined analyses for: $\textit{PantheonP + SH0ES}$, $\textit{PantheonP + SH0ES}$ + $\textit{f}$, and $\textit{PantheonP + SH0ES}$ + $$f\sigma _8$$ . We compute the best-fit values $$\varOmega _m,$$ $$H_0\,\mathrm {(km/s/Mpc)},$$ $$r_d,$$ $$M_{abs},$$ $$\gamma ,$$ $$\sigma _8,$$ $\textit{n}$, $\textit{p}$ and $$\varGamma $$ including the bulk viscosity coefficient $$\zeta .$$ Through a detailed statistical analysis, based on the Akaike Information Criterion (AIC) and Bayesian/Schwartz Information Criterion (BIC), a statistical comparison of the $\textit{f}$($\textit{Q}$) gravity models with $$\varLambda $$ CDM is made. Among the three $\textit{f}$($\textit{Q}$) models, only the non-viscous $\textit{f}$($\textit{Q}$) power-law model yields robust parameter estimates and substantial observational support without any outright rejections. In contrast, both exponential and logarithmic $\textit{f}$($\textit{Q}$) models (with or without bulk viscosity) are rejected by multiple model selection criteria. Moreover, adding bulk viscosity consistently increases $$\varDelta $$ AIC and $$\varDelta $$ BIC values, indicating that its inclusion is not statistically justified.

Ethiopia

Shambel Sahlu

Renier Hough

Amare Abebe

Spain

Álvaro Cruz-Dombriz

Constraining viscous-fluid models in $\textit{f}$($\textit{Q}$) gravity with data

This study explores wormhole solutions within two distinct modified gravity theories, namely <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo stretchy='false'>)</mo></math> gravity and <math altimg='si2.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>Q</mi><mo>,</mo><mi>T</mi><mo stretchy='false'>)</mo></math> gravity, incorporating Bose-Einstein condensate (BEC) dark matter to analyze their geometric properties. The primary objective is to comprehensively compare wormhole characteristics in these frameworks under the influence of BEC matter. The derived shape functions satisfy all fundamental traversability conditions. Furthermore, we examine the energy conditions, revealing that the NEC holds in <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo stretchy='false'>)</mo></math> gravity but is violated in <math altimg='si2.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>Q</mi><mo>,</mo><mi>T</mi><mo stretchy='false'>)</mo></math> gravity, highlighting the contrasting nature of wormhole solutions in these theories. Additionally, we investigate the effects of anisotropy, active gravitational mass, and surface diagram of wormhole geometries. Our findings confirm the existence of physically viable and stable wormhole models within these modified gravity theories.

India

Chaitra Chooda Chalavadi

H. Aruna Kumara

V. Venkatesha

Probing the geometries of wormholes: A comparative study of <italic>f</italic>( <italic>R</italic>, <italic>T</italic>) and <italic>f</italic>( <italic>Q</italic>, <italic>T</italic>) theories in the presence of BEC matter

This study investigates the evolution of Friedmann-Robertson-Walker (FRW) cosmological models within the <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>Q</mi><mo stretchy='false'>)</mo></math> gravity framework, utilizing a specific <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>Q</mi><mo stretchy='false'>)</mo></math> formulation and a novel Hubble parameter <math altimg='si2.svg'><mi>H</mi><mo stretchy='false'>(</mo><mi>z</mi><mo stretchy='false'>)</mo></math> parameterization to probe the universe's accelerating expansion. A central aspect is the application of advanced machine learning techniques for cosmological parameter estimation, alongside comparisons with traditional Bayesian (MCMC) methods. We employ a hybrid Mixed Neural Network (MNN), which synergistically combines Artificial Neural Networks (ANNs) and Mixture Density Networks (MDNs), to enhance the accuracy and robustness of parameter constraints. This MNN architecture is integrated into the CoLFI (Cosmological Likelihood-Free Inference) framework. CoLFI facilitates likelihood-free inference, a significant methodological advancement that provides an efficient and robust alternative, particularly for complex models with computationally expensive or intractable likelihood functions. Training efficiency for the neural networks is optimized by generating data via hyperellipsoid sampling. The <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>Q</mi><mo stretchy='false'>)</mo></math> model, constrained using these diverse approaches, successfully describes a universe transitioning from an early decelerating phase to the current accelerated expansion, with a computed transition redshift of <math altimg='si3.svg'><msub><mrow><mi>z</mi></mrow><mrow><mi>t</mi></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>0.60</mn></math>. The physical and kinematic properties of the model are discussed, underscoring the efficacy of the MNN-CoLFI methodology and its consistency with MCMC results, while highlighting its advantages for obtaining observational constraints in <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>Q</mi><mo stretchy='false'>)</mo></math> gravity.

Lokesh Kumar Sharma

Suresh Parekh

Anil Kumar Yadav

Observational constraints using Bayesian statistics and deep learning in <italic>f</italic>( <italic>Q</italic>) gravity

The M-theoretic emergence proposal claims that in an isotropic decompactification limit to M-theory the full effective action is generated via quantum effects by integrating out only the light towers of states of the theory. In the BPS particle sector, these include transversally wrapped $\textit{M}$2- and $\textit{M}$5-branes possibly carrying Kaluza–Klein momentum. This implies that a longitudinally wrapped $\textit{M}$5-brane, i.e. a wrapped $\textit{D}$4-brane, is not to be included in emergence computations. In this work we collect explicit evidence supporting this point by examining an $$F^4$$ gauge coupling in six dimensions, making use of the duality between heterotic string theory on $$T^4$$ and strongly coupled type IIA on K3. In this instance, the M-theoretic emergence proposal can be viewed as a tool for making predictions for the microscopic behavior of string theoretic amplitudes.

Germany

Manuel Artime

Ralph Blumenhagen

Antonia Paraskevopoulou

Emergence of $$F^4$$ -couplings in heterotic/type IIA dual string theories

The current paper reports an investigation of a warm inflationary scenario in the context of $\textit{f}$($\textit{T}$) gravity for a spatially flat FLRW universe. In our model, inflation is driven purely by the torsional sector of $\textit{f}$($\textit{T}$) gravity, without introducing any additional scalar fields. We focus on the high dissipative regime ( $$R \gg 1$$ ), reconstruct the Hubble parameter as a function of the e-folding number $\textit{N}$, and derive the slow-roll parameters $$\varepsilon _1(N)$$ and $$\varepsilon _2(N)$$ . The study has encapsulated the dynamics of inflation and its duration under strong dissipation. The dissipative coefficient $$\Gamma $$ is modeled with a temperature-dependent power-law form, linking the inflationary dynamics to thermal corrections and the particle content of the early universe. The analysis has affirmed that the torsion-induced energy density $$\rho _T$$ successfully transitions to radiation energy density $$\rho _{rad}$$ , facilitating a graceful exit from inflation. Finally, we have validated our model by comparing the scalar spectral index and tensor-to-scalar ratio with Planck 2018 results, demonstrating consistency within observational bounds. Additionally, it is verified that the thermal domination condition $$T_{*}/H > 1$$ and the torsion dominance condition $$\rho _T/\rho _{rad} > 1$$ are satisfied.

Moli Ghosh

Türkiye

Can Aktaş

Surajit Chattopadhyay

Reconstructing $\textit{f}$($\textit{T}$) gravity and exploring the torsion driven warm inflationary cosmology