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.

Iran

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 $\textit{M}$ /$\textit{F}$ .

Sweden

Johan Bijnens

Norway

Daniil Krichevskiy

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

A central difficulty in the physics of traversable wormholes is the requirement of exotic matter, which arises from the violation of the null energy condition within classical general relativity. This motivates the study of modified gravitational frameworks and quantum-gravitational corrections that collectively reshape the effective stress-energy sector. In this work, we develop a unified construction combining three physically well-motivated ingredients: noncommutative geometry (NCG), the generalized uncertainty principle (GUP), and <italic>f</italic>( <italic>R, T</italic>) modified gravity with <math altimg='si15.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo>)</mo><mo>=</mo><mi>R</mi><mo linebreak='goodbreak'>+</mo><mn>2</mn><mi>&#955;</mi><mi>T</mi></mrow></math>. We adopt the matter Lagrangian <math altimg='si16.svg'><mrow><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo linebreak='goodbreak'>=</mo><mo>&#8722;</mo><mi>&#961;</mi></mrow></math> and derive the corresponding modified field equations carefully, specifying the explicit form of the effective stress-energy tensor. The NCG Gaussian matter distribution regularises the source profile over a minimal length scale <math altimg='si17.svg'><msqrt><mi>&#952;</mi></msqrt></math> and may reduce the amount of exotic matter required near the throat, while the GUP introduces quantum-gravitational corrections to the energy density and pressure at sub-Planckian scales. We perform a complete derivation of the wormhole shape function, writing it as <math altimg='si18.svg'><mrow><mi>b</mi><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>=</mo><msub><mi>b</mi><mrow><mrow><mi mathvariant='normal'>N</mi></mrow><mi>C</mi><mi>G</mi></mrow></msub><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow><mo linebreak='goodbreak'>+</mo><msub><mi>b</mi><mrow><mrow><mi mathvariant='normal'>G</mi></mrow><mi>U</mi><mi>P</mi></mrow></msub><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow></mrow></math>, where each contribution is obtained through an explicit integration of the corresponding source term. The throat conditions, flare-out criterion, and asymptotic flatness are verified analytically, and the key limiting cases <italic>&#946;</italic>&#8239;&#8594;&#8239;0, <italic>&#955;</italic>&#8239;&#8594;&#8239;0, and <italic>&#952;</italic>&#8239;&#8594;&#8239;0 are checked for consistency. An analysis of the null energy condition shows that the NEC violation is spatially localised near the throat owing to the Gaussian suppression provided by the NCG matter distribution, and the volume integral quantifier is evaluated with the <italic>f</italic>( <italic>R, T</italic>) coupling included explicitly. The effective potential for axial perturbations is derived and used to compute the gravitational wave echo time delay, which provides potential phenomenological signatures relevant for future gravitational-wave echo searches.

Azerbaijan

Pakistan

Allah Ditta

Noncommutative wormholes with generalized uncertainty principle in <italic>f</italic>( <italic>R, T</italic>) gravity: Energy conditions and gravitational wave echo time delay

We study the forward-backward asymmetry in the three-body decay process <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>H</mi><mo stretchy="false">→</mo><mi>Z</mi><mi>γ</mi><mo stretchy="false">→</mo><mover accent="true"><mi>f</mi><mo stretchy="false">¯</mo></mover><mi>f</mi><mi>γ</mi></math>, induced by complex form factors in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>H</mi><mi>Z</mi><mi>γ</mi></math> vertex. To estimate its magnitude, we derive constraints on the real and imaginary parts of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-violating form factor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>h</mi><mn>3</mn><mrow><mi>Z</mi><mi>γ</mi></mrow></msubsup></math> using current LHC measurements, obtaining upper limits of about 0.9 GeV. These bounds are of the same order of magnitude as those derived from electric dipole moments. We find that the asymmetry can reach values of order <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> and may be accessible at the HL-LHC.

Mexico

A.I. Hernández-Juárez

D. Watko

A. Fernández-Téllez

G. Tavares-Velasco

Forward-backward asymmetry in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>H</mi><mo stretchy="false">→</mo><mi>Z</mi><mi>γ</mi><mo stretchy="false">→</mo><mover accent="true"><mi>f</mi><mo stretchy="false">¯</mo></mover><mi>f</mi><mi>γ</mi></math> decay

The $$ f(T, T_G) $$ gravity theory is an extension of general relativity that incorporates the torsion scalar $$ T $$ as well as the teleparallel equivalent to the Gauss-Bonnet term $$ T_G $$ , to explore early and late time universe cosmology beyond the standard model. In this work, we obtain exact solutions of the field equations in the framework of $$ f(T, T_G) $$ gravity in the context of cosmological bouncing scenarios. For this, we explore the non-singular evolution of the universe by considering various bouncing cosmological models characterized by different scale factors such as the symmetric bounce, oscillatory bounce, superbounce, matter bounce, and singular bounce scenarios. For each scale factor model, we obtained the functional form of $$ f(T, T_G) $$ defining different ansatz like $$g(T)+h(T_G),~T_G~g(T)$$ and $$T+T_G ~g(T)$$ that satisfy the modified field equations and yields viable cosmological solutions. The analytical behaviors of the scale factor, Hubble parameter, energy density and pressure are examined to discuss the nature of the bounce and the avoidance of initial singularities. Our results demonstrate that the $$ f(T, T_G) $$ framework provides consistent and physically acceptable bouncing cosmologies capable of describing a smooth transition from contraction to expansion, thereby offering a viable alternative to inflationary models for the early universe.

Abdul Sultan

Ali Sabir

Malta

Jackson Said

Exact cosmological bouncing solutions in $$f(T,T_G)$$ gravity

Under the hypothesis that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>1370</mn><mo stretchy="false">)</mo></math> is a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>κ</mi><mover accent="true"><mi>κ</mi><mo stretchy="false">¯</mo></mover></math> molecular state, we calculate the partial widths of its various decay channels, including the two-body decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi><mi>η</mi></math> and the four-body decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi><mi>ρ</mi><mo>/</mo><mi>σ</mi><mi>σ</mi><mo stretchy="false">→</mo><mn>4</mn><mi>π</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mi>π</mi><mi>π</mi></math>. Treating the coupling <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mrow><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>1370</mn><mo stretchy="false">)</mo><mi>κ</mi><mover accent="true"><mi>κ</mi><mo stretchy="false">¯</mo></mover></mrow></msub></math> as a free parameter, we find that a value of 25–40 GeV brings the total width of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>1370</mn><mo stretchy="false">)</mo></math> in line with the measured value 200–500 MeV. At the center-of-mass energy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>1.37</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, the channels that mainly contribute to the total width are <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>4</mn><mi>π</mi></math> ranked as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Γ</mi><mo stretchy="false">(</mo><mi>K</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mo stretchy="false">)</mo><mo>&gt;</mo><mi mathvariant="normal">Γ</mi><mo stretchy="false">(</mo><mn>4</mn><mi>π</mi><mo stretchy="false">)</mo><mo>&gt;</mo><mi mathvariant="normal">Γ</mi><mo stretchy="false">(</mo><mi>π</mi><mi>π</mi><mo stretchy="false">)</mo></math> with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mrow><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>1370</mn><mo stretchy="false">)</mo><mi>κ</mi><mover accent="true"><mi>κ</mi><mo stretchy="false">¯</mo></mover></mrow></msub><mo>=</mo><mn>35</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. Around 1.37 GeV, the decay widths of the two-body channels <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi><mi>η</mi></math> remain stable with variation in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt></math>, whereas the decay widths of the four-body channels <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>4</mn><mi>π</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover><mi>π</mi><mi>π</mi></math> increase continuously with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt></math>. Most current data are model dependent and conflicting, particularly regarding the conclusion of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>4</mn><mi>π</mi></math> dominance and the ratio of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi></math> decay widths. The current data cannot rule out the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>κ</mi><mover accent="true"><mi>κ</mi><mo stretchy="false">¯</mo></mover></math> assignment for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>1370</mn><mo stretchy="false">)</mo></math>. Further reliable theoretical and experimental analyses of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>1370</mn><mo stretchy="false">)</mo></math> are required to reveal its nature.

China

Yin Cheng

Bing-Song Zou

Study of the decay pattern of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>1370</mn><mo stretchy="false">)</mo></math> as a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>κ</mi><mover accent="true"><mi>κ</mi><mo stretchy="false">¯</mo></mover></math> molecular state

We analyze <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>F</mi></mrow></math>-term hybrid inflation (FHI) within various grand unified theories in the presence of a Kähler potential for the inflaton field which parametrizes the Kähler manifolds <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo stretchy="false">)</mo><mo>/</mo><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mn>2</mn><mo stretchy="false">)</mo><mo>/</mo><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math>. We take into account supergravity, radiative, and soft supersymmetry-breaking corrections to the tree-level potential and find that viable FHI can be realized without extrema along the inflationary trajectory for a broad region of the parameter space. For selected superpotential parameters, the models’ predictions are largely influenced by the curvature of the internal space and the magnitude of the tadpole parameter which are constrained so as to achieve compatibility with the current Atacama Cosmology Telescope and the South Pole Telescope data. We also discuss the formation of cosmic strings and their associated gravitational wave signals, potentially detectable by current and upcoming experiments.

Waqas Ahmed

Greece

Constantinos Pallis

Saudi Arabia

Mansoor Ur Rehman

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>F</mi></mrow></math>-term hybrid inflation with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>T</mi></math>-model Kähler geometry and beyond

In this paper we analyze the optical appearance of black holes embedded in a cosmological background in some popular <italic>f</italic>( <italic>R</italic>) models which are often considered as viable alternatives to the &#923;CDM model in General Relativity. After obtaining analytical approximations for the Hubble rate <italic>H</italic>( <italic>z</italic>) and angular diameter distance <italic>d<inf>A</inf></italic>( <italic>z</italic>), we compute the approximate shadow size for a spherically symmetric black hole embedded in these <italic>f</italic>( <italic>R</italic>) models as viewed by a comoving observer located very far from the black hole. This is then compared with the shadow size of a black hole embedded in the &#923;CDM model as obtained recently in Bisnovatyi-Kogan &amp; Tsupko (PRD <bold>98</bold>, 084,020 (2018)). Differences in the shadow size for cosmological black holes between <italic>f</italic>( <italic>R</italic>) gravity and General Relativity are discussed in light of the recent observations by the EHT collaboration.

Joseph Sultana

Optical appearance of cosmological black holes in <italic>f</italic>( <italic>R</italic>) gravity

The persistent 4–6 <italic>&#963;</italic> Hubble tension between Planck and SH0ES measurements challenges the standard &#923;CDM framework. We propose a solution combining generalized inhomogeneous spacetime geometry with Hu-Sawicki <italic>F</italic>( <italic>R</italic>) gravity. Using a spherically symmetric metric with independent functions <italic>A</italic>( <italic>t, r</italic>) and <italic>B</italic>( <italic>t, r</italic>), we show that local underdensities with modified gravity produce a &#8220;Hubble bubble&#8221; effect while maintaining global CMB consistency. Bayesian analysis incorporating SH0ES, Pantheon+, BAO, and cosmic chronometers yields <math altimg='si1.svg'><mrow><msubsup><mi>H</mi><mn>0</mn><mtext>local</mtext></msubsup><mo linebreak='goodbreak'>=</mo><mn>72.76</mn><mo>&#177;</mo><mn>1.18</mn></mrow></math> km/s/Mpc and <math altimg='si2.svg'><mrow><msubsup><mi>H</mi><mn>0</mn><mtext>global</mtext></msubsup><mo linebreak='goodbreak'>=</mo><mn>68.18</mn><mo>&#177;</mo><mn>0.76</mn></mrow></math> km/s/Mpc, reconciling the tension. The model achieves this through enhanced gravitational forces in underdense regions, chameleon screening preserving Solar System tests, and consistent structure formation. With <math altimg='si25.svg'><mrow><mi>ln</mi><mi>B</mi><mo linebreak='goodbreak'>=</mo><mn>2.28</mn><mo>&#177;</mo><mn>0.39</mn></mrow></math> favoring our model over &#923;CDM, we present compelling evidence for the interplay between local inhomogeneities and modified gravity as the origin of the Hubble tension.

 Mehnaz

Jordan

Adnan Malik

Jamshed Khan

Ahdab K. Althukair

Resolving the hubble tension: A unified approach using inhomogeneous Hu-Sawicki <italic>F</italic>( <italic>R</italic>) gravity

We study the local horizon residue and minimally coupled massless-scalar quasinormal modes of the logarithmic connection-hair background obtained perturbatively in the quadratic model $$f(Q)=Q+\alpha Q^2$$ . After mass renormalization the displayed order- $$\alpha ^2$$ blackening function is $$F(r)=1-[2M+\eta \ln (r/r_\star )]/r$$ , with $$\eta =\alpha ^2\mu $$ . Euclidean regularity and the simple pole of 1/$\textit{F}$ give the same Hawking temperature, while the same residue multiplies the near-horizon logarithm of the scalar tortoise coordinate. We derive the massless-scalar master equation, its effective potential, the photon-sphere equation, and the controlled first-order shifts of the eikonal scalar frequency and damping rate. We do not identify the integration parameter $\textit{M}$ with a Hamiltonian or Noether mass: the logarithmic tail leaves the perturbative regime at large radius and does not satisfy the standard falloff required for a finite ADM charge. Consequently no physical entropy, heat capacity, Ruppeiner metric, or gravitational quasinormal-mode spectrum is claimed. For comparison only, we retain an explicitly labelled auxiliary Hessian construction and an algebraic evaluation of the resummed truncated metric at $$r_h=2\eta $$ . That point has $$|\eta |/r_h=1/2$$ and is therefore outside perturbative control; its finite scalar null-orbit and WKB frequencies are properties of the truncated function, not predictions of quadratic $\textit{f}$($\textit{Q}$) gravity. The controlled result is the local temperature–scalar-monodromy residue identity and the distinct small-hair shifts sampled at the horizon and photon sphere.

Wen-Xiang Chen

Horizon residues and test-scalar quasinormal modes of a perturbative Schwarzschild-type black hole in quadratic $\textit{f}$($\textit{Q}$) gravity