This study investigates ray trajectories and wave propagation in a static, <math altimg='si1.svg'><mo stretchy='false'>(</mo><mn>2</mn><mo linebreak='badbreak' linebreakstyle='after'>+</mo><mn>1</mn><mo stretchy='false'>)</mo></math>-dimensional, radially symmetric traversable wormhole (TWH) spacetime with a constant redshift function and a radial shape function proportional to <math altimg='si2.svg'><mn>1</mn><mo stretchy='false'>/</mo><mi>&#961;</mi></math>. The spatial geometry forms a minimal surface (a catenoid bridge), enabling a geometric-optical interpretation. An analysis of the ray trajectories reveals how the curvature-induced structure of the wormhole (WH) governs the ray paths, depending on the relative sizes of the radial coordinate <italic>&#961;</italic> and the throat radius <math altimg='si26.svg'><msub><mrow><mi>&#8467;</mi></mrow><mrow><mo>&#8728;</mo></mrow></msub></math>. Extending the study to wave dynamics, we derive a refractive index <math altimg='si4.svg'><mi>n</mi><mo stretchy='false'>(</mo><mi>&#961;</mi><mo>,</mo><mi>&#969;</mi><mo stretchy='false'>)</mo></math> that explicitly depends on both <italic>&#961;</italic> and the wave frequency <italic>&#969;</italic>, identifying a critical frequency that marks the transition between propagation and attenuation. These results demonstrate how the WH's topology distinctly influences wave propagation and may inform future developments in analogue gravity models and advanced optical media.

Türkiye

Semra Gurtas Dogan

Abdullah Guvendi

Omar Mustafa

Ray trajectories and wave optics in a traversable wormhole: Optics of a minimal surface

We investigate the effect of rainbow gravity on Klein-Gordon (KG) bosons in a quantized nonuniform magnetic field in the background of Bonnor-Melvin (BM) spacetime with a cosmological constant. In the process, we show that the BM spacetime introduces domain walls (i.e., infinitely impenetrable hard walls) at <math altimg='si1.svg'><mi>r</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>0</mn></math> and <math altimg='si2.svg'><mi>r</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mi>&#960;</mi><mo stretchy='false'>/</mo><msqrt><mrow><mn>2</mn><mi mathvariant='normal'>&#923;</mi></mrow></msqrt></math>, as a consequence of the effective gravitational potential field generated by such a magnetized BM spacetime. As a result, the motion of KG particles/antiparticles is restricted indefinitely within the range <math altimg='si3.svg'><mi>r</mi><mo>&#8712;</mo><mo stretchy='false'>[</mo><mn>0</mn><mo>,</mo><mi>&#960;</mi><mo stretchy='false'>/</mo><msqrt><mrow><mn>2</mn><mi mathvariant='normal'>&#923;</mi></mrow></msqrt><mo stretchy='false'>]</mo></math>, and the particles and antiparticles cannot be found elsewhere. Next, we provide a conditionally exact solution in the form of the general Heun function <math altimg='si118.svg'><msub><mrow><mi>H</mi></mrow><mrow><mi>G</mi></mrow></msub><mo stretchy='false'>(</mo><mi>a</mi><mo>,</mo><mi>q</mi><mo>,</mo><mi>&#945;</mi><mo>,</mo><mi>&#946;</mi><mo>,</mo><mi>&#947;</mi><mo>,</mo><mi>&#948;</mi><mo>,</mo><mi>z</mi><mo stretchy='false'>)</mo></math>. Within the BM domain walls and under the condition of exact solvability, we study the effects of rainbow gravity on KG bosonic fields in a quantized nonuniform external magnetic field in the BM spacetime background. We use three pairs of rainbow functions: <math altimg='si5.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>u</mi><mo stretchy='false'>)</mo><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><msup><mrow><mo stretchy='false'>(</mo><mn>1</mn><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo><mover accent='true'><mrow><mi>&#946;</mi></mrow><mrow><mo stretchy='false'>&#732;</mo></mrow></mover><mo stretchy='false'>|</mo><mi>E</mi><mo stretchy='false'>|</mo><mo stretchy='false'>)</mo></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo><mn>1</mn></mrow></msup><mo>,</mo><mspace width='0.2em' /><mi>h</mi><mo stretchy='false'>(</mo><mi>u</mi><mo stretchy='false'>)</mo><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>1</mn></math>; and <math altimg='si6.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>u</mi><mo stretchy='false'>)</mo><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>1</mn><mo>,</mo><mspace width='0.2em' /><mi>h</mi><mo stretchy='false'>(</mo><mi>u</mi><mo stretchy='false'>)</mo><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><msqrt><mrow><mn>1</mn><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo><mover accent='true'><mrow><mi>&#946;</mi></mrow><mrow><mo stretchy='false'>&#732;</mo></mrow></mover><mo stretchy='false'>|</mo><mi>E</mi><msup><mrow><mo stretchy='false'>|</mo></mrow><mrow><mi>&#965;</mi></mrow></msup></mrow></msqrt></math>, with <math altimg='si145.svg'><mi>&#965;</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></math>, where <math altimg='si23.svg'><mi>u</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mo stretchy='false'>|</mo><mi>E</mi><mo stretchy='false'>|</mo><mo stretchy='false'>/</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>p</mi></mrow></msub></math>, <math altimg='si123.svg'><mover accent='true'><mrow><mi>&#946;</mi></mrow><mrow><mo stretchy='false'>&#732;</mo></mrow></mover><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mi>&#946;</mi><mo stretchy='false'>/</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>p</mi></mrow></msub></math>, and <italic>&#946;</italic> is the rainbow parameter. We find that such pairs of rainbow functions, <math altimg='si10.svg'><mo stretchy='false'>(</mo><mi>f</mi><mo stretchy='false'>(</mo><mi>u</mi><mo stretchy='false'>)</mo><mo>,</mo><mi>h</mi><mo stretchy='false'>(</mo><mi>u</mi><mo stretchy='false'>)</mo><mo stretchy='false'>)</mo></math>, fully comply with the theory of rainbow gravity, ensuring that <math altimg='si11.svg'><msub><mrow><mi>E</mi></mrow><mrow><mi>p</mi></mrow></msub></math> is the maximum possible energy for particles and antiparticles alike. Moreover, we show that the corresponding bosonic states form magnetized, rotating vortices, as intriguing consequences of such a magnetized BM spacetime background.

Klein-Gordon particles in a nonuniform external magnetic field in Bonnor-Melvin rainbow gravity background

In this study, we explore the realization of spherically symmetric solutions in the context of modified teleparallel gravity, particularly in <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi mathvariant='script'>T</mi><mo stretchy='false'>)</mo></math> theory, where <math altimg='si2.svg'><mi mathvariant='script'>T</mi></math> denotes the torsion scalar. Traditional mimetic gravity and its extension using two scalar fields fail to reproduce general spherically symmetric spacetimes within <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi mathvariant='script'>T</mi><mo stretchy='false'>)</mo></math> gravity due to the requirement of a constant torsion scalar or a linear form of <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi mathvariant='script'>T</mi><mo stretchy='false'>)</mo></math>, which restricts the theory to the teleparallel equivalent of general relativity (TEGR). To address this limitation, we propose a four-scalar field model that extends the two-scalar framework, allowing the construction of arbitrary spherically symmetric spacetimes. We show that this model eliminates ghost degrees of freedom through suitable constraints enforced by Lagrange multipliers. As a test of our procedure, we consider a specific form of a spherically symmetric spacetime and derive the associated four scalars, analyzing their behavior. Within the framework of a quadratic correction term, <math altimg='si3.svg'><mi mathvariant='script'>T</mi><mo linebreak='goodbreak' linebreakstyle='after'>+</mo><mfrac><mrow><mi>&#945;</mi></mrow><mrow><mn>2</mn></mrow></mfrac><msup><mrow><mi mathvariant='script'>T</mi></mrow><mrow><mn>2</mn></mrow></msup></math>, our method demonstrates the ability to reconstruct physically relevant solutions with non-ghost scalar fields. These results underscore the broader applicability of scalar field models in constructing viable geometries within modified gravity theories, extending beyond the scope of standard formulations.

Egypt

South Africa

G.G.L. Nashed

Saudi Arabia

A. Eid

Four-scalar model and spherically symmetric solution in <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi mathvariant='script'>T</mi><mo stretchy='false'>)</mo></math> theory

The transition from the end of inflation to a hot, thermal Universe, commonly referred to as (re)heating, is a critical yet often misunderstood phase in early Universe cosmology. This short review aims to provide a comprehensive, conceptually clear, and accessible introduction to the physics of (re)heating, tailored to the particle physics community. We critically examine the standard Boltzmann approach, emphasizing its limitations in capturing the intrinsically non-perturbative and non-linear dynamics that dominate the early stages of energy transfer. These include explosive particle production, inflaton fragmentation, turbulence, and thermalization; phenomena often overlooked in perturbative treatments. We survey a wide range of theoretical tools, from Boltzmann equations to lattice simulations, clarifying when each is applicable and highlighting scenarios where analytic control is still feasible. Special attention is given to model-dependent features such as (pre)heating, the role of fermions, gravitational couplings, and the impact of multifield dynamics. We also discuss exceptional cases, including Starobinsky-like models and instant (pre)heating, where (re)heating proceeds through analytically tractable channels without requiring full non-linear simulations. Ultimately, this review serves both as a practical guide and a cautionary tale, advocating for a more nuanced and physically accurate understanding of this pivotal epoch within the particle physics community.

India

Basabendu Barman

United Arab Emirates

Nicolás Bernal

Spain

Javier Rubio

Two or three things particle physicists (mis)understand about (pre)heating

Fuzzy dark matter wormhole solutions coupled with anisotropic matter distribution are explored in higher-order curvature gravity. We derive the shape function for fuzzy wormholes and explore their possible stability. We study the embedding diagrams of the active gravitational mass associated with fuzzy dark matter wormholes by taking a certain shape function. Aiming to highlight the role of higher-order curvature gravity in the modeling of less complex fuzzy wormhole structures, we evaluate the complexity factor, the conservation equation, and null energy conditions. Our study reinforces more importance of uniformly distributed pressure effects throughout the less complex region than the emergence of energy density homogeneity in the stability of fuzzy wormholes. It is shown that the active gravitational mass of the fuzzy wormhole structures varies inversely with the radial distance, thereby suggesting the breaching of energy conditions at some arena of the Einasto index. Furthermore, it is revealed that stable fuzzy dark matter wormhole structures exist in nature in the surroundings of cold dark matter halos and galactic bulges. The important physics understood from our analysis is that in higher-order curvature gravity, feasible geometries of fuzzy dark matter wormholes exist naturally in the environments of different galactic haloes.

Pakistan

Z. Yousaf

Japan

Kazuharu Bamba

B. Almutairi

M.Z. Bhatti

M. Rizwan

Fuzzy dark matter less-complex wormhole structures in higher-order curvature gravity

We develop a formalism for computing the scattering amplitudes in maximally symmetric de Sitter spacetime with compact spatial dimensions. We describe quantum states by using the representation theory of de Sitter symmetry group and link the Hilbert space to “inertial” geodesic observers. The positive and negative “energy” wavefunctions are uniquely determined by the requirement that in observer's neighborhood, short wavelengths propagate as plane waves with positive and negative frequencies, respectively; they define a unique “Euclidean” (a.k.a. Bunch-Davies) de Sitter invariant vacuum, common to all inertial observers. By following the same steps as in Minkowski spacetime, we show that the scattering amplitudes are given by a generalized Dyson's formula. Compared to the flat case, they describe the scattering of wavepackets with the frequency spectrum determined by geometry. The frequency spread shrinks as the masses and/or momenta become larger than the curvature scale. Asymptotically, de Sitter amplitudes agree with the amplitudes evaluated in Minkowski spacetime.

United States

Poland

Tomasz R. Taylor

United Kingdom

Bin Zhu

Scattering of quantum particles in global de Sitter spacetime I: The formalism

We discuss and derive the off-shell nilpotent of order two and absolutely anti-commuting Becchi-Rouet-Stora-Tyutin (BRST), anti-BRST, co-BRST and anti-co-BRST symmetry transformations for the non-interacting Friedberg-Lee-Pang-Ren (FLPR) model in one (0 + 1)-dimension (1D) of spacetime by exploiting the standard techniques of the (anti-)chiral supervariable approach (ACSA) onto (1, 1)-dimensional super sub-manifold of the general (1, 2)-dimensional supermanifold, where the (anti-)BRST and (anti-)co-BRST invariant restrictions play a crucial role. We provide clear proof of nilpotency and absolute anti-commutativity properties of the (anti-)BRST as well as (anti-)co-BRST Noether's conserved charges within the framework of ACSA to BRST formalism, where we take only one Grassmannian variable in place of two usual Grassmannian variables (i.e., fermionic variables). Furthermore, we also demonstrate that the Lagrangian of this non-interacting FLPR model is (anti-)BRST as well as (anti-)co-BRST symmetries invariance within the ambit of the ACSA to BRST approach in (1, 1)-dimensional super sub-manifold.

Bhupendra Chauhan

Tapobroto Bhanja

FLPR model: (Anti-)chiral supervariable approach to quantum symmetries

This study explores the role of Finsler geometry in cosmology incorporating weak-field anisotropy through the Finsler-Kropina framework and the osculating Riemannian metric approach. The model naturally modifies the spacetime structure introducing anisotropic effects that influence cosmic expansion and energy conservation. By deriving the modified Friedmann equations we test their observational viability using observational datasets including cosmic chronometers, baryon acoustic oscillations and the Pantheon+ supernovae dataset. The results from MCMC analysis show deviations from the ΛCDM model particularly in the evolution of the Hubble parameter, matter density, and dark energy density. Compared to ΛCDM, the anisotropic model predicts a lower matter density parameter <math altimg='si1.svg'><msub><mrow><mi mathvariant='normal'>&#937;</mi></mrow><mrow><mi>m</mi><mn>0</mn></mrow></msub></math> a reduced dark energy density <math altimg='si102.svg'><msub><mrow><mi mathvariant='normal'>&#937;</mi></mrow><mrow><mi mathvariant='normal'>&#923;</mi></mrow></msub></math>, and a nonzero spatial curvature <math altimg='si223.svg'><msub><mrow><mi mathvariant='normal'>&#937;</mi></mrow><mrow><mi>K</mi></mrow></msub></math> indicating fundamental geometric differences. The deceleration parameter <math altimg='si4.svg'><mi>q</mi><mo stretchy='false'>(</mo><mn>0</mn><mo stretchy='false'>)</mo><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo><mn>0.57</mn><mo>&#177;</mo><mn>0.001</mn></math> confirms an accelerated expansion with a transition redshift <math altimg='si5.svg'><msub><mrow><mi>z</mi></mrow><mrow><mi>t</mi><mi>r</mi></mrow></msub><mo>&#8776;</mo><mn>0.77</mn></math>, aligning with observational estimates. The state-finder diagnostics reveal a transition from a Chaplygin gas-like phase to a quintessence regime before asymptotically approaching &#923;CDM demonstrating a dynamic evolution influenced by anisotropic corrections. The <math altimg='si6.svg'><mi>O</mi><mi>m</mi><mo stretchy='false'>(</mo><mi>z</mi><mo stretchy='false'>)</mo></math> diagnostic suggests phantom-like behavior at higher redshifts gradually stabilizing towards &#923;CDM at late times. We show that the geometry-induced effective dark energy term <math altimg='si109.svg'><msub><mrow><mi mathvariant='normal'>&#937;</mi></mrow><mrow><mi>&#958;</mi></mrow></msub></math> can be interpreted as a geometric component of dark energy, effectively driving late-time acceleration without invoking additional exotic matter fields. These findings highlight the significance of Finsler geometry in extending standard cosmology and suggest that anisotropic effects provide a geometric interpretation of dark energy while maintaining consistency with observational constraints.

J. Praveen

S.K. Narasimhamurthy

Cosmological model in Finsler-Kropina geometrical framework with weak-field anisotropy and observational data

Our paper examines effect of the recently developed <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mtext mathvariant='italic'>Q</mtext><mo>,</mo><mi mathvariant='normal'>T</mi><mo stretchy='false'>)</mo></math> theory on a structure of dense objects containing dense matter distribution. For this purpose, we consider viable solutions to study the interior region of considered compact stars. With the Darmois constraints we evaluate unidentified constants of metric coefficients. Additionally, assume a precise <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mtext mathvariant='italic'>Q</mtext><mo>,</mo><mi mathvariant='normal'>T</mi><mo stretchy='false'>)</mo></math> theory model to reduce complication of the system and obtain explicit equation of matter contents that further used to investigate various physical parameters in the interior of considered compact objects. The equilibrium state for dense compact stars is determined by the TOV equations. The stability state for the compact stars is determined by the causality method. We finalize that the anisotropic spheres in <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mtext mathvariant='italic'>Q</mtext><mo>,</mo><mi mathvariant='normal'>T</mi><mo stretchy='false'>)</mo></math> theory background are feasibly stable.

Azerbaijan

China

M. Zeeshan Gul

M. Sharif

Adeeba Arooj

Faisal Javed

Analysis of physical aspects in the interior of static spherical spacetime admitting Durgapal-IV spacetime in <italic>f</italic>( <italic>Q</italic>,T) theory

The Nambu–Jona-Lasinio (NJL) model involves a pointlike 4-fermion interaction. While it gives a useful description of chiral dynamics (mainly in QCD), it nonetheless omits the crucially important internal wave-function of a two-body bound state, <math altimg='si1.svg'><mi>&#981;</mi><mo stretchy='false'>(</mo><mi>r</mi><mo stretchy='false'>)</mo></math>. This becomes significant near critical coupling where <math altimg='si1.svg'><mi>&#981;</mi><mo stretchy='false'>(</mo><mi>r</mi><mo stretchy='false'>)</mo></math> extends to large distance, leading to dilution and suppression of induced couplings <math altimg='si2.svg'><mo>&#8733;</mo><mi>&#981;</mi><mo stretchy='false'>(</mo><mn>0</mn><mo stretchy='false'>)</mo></math>, such as the Yukawa and quartic couplings, as well as reduced fine-tuning of a hierarchy. In top quark condensation, where the Brout-Englert-Higgs (BEH) boson is a <math altimg='si3.svg'><mover accent='true'><mrow><mi>t</mi></mrow><mo>&#8254;</mo></mover><mi>t</mi></math> bound state and we have a UV completion such as topcolor, we must go beyond the NJL model and include effects of <math altimg='si1.svg'><mi>&#981;</mi><mo stretchy='false'>(</mo><mi>r</mi><mo stretchy='false'>)</mo></math>. We provide a formulation of this for the BEH boson, and find that it leads to an extended <math altimg='si1.svg'><mi>&#981;</mi><mo stretchy='false'>(</mo><mi>r</mi><mo stretchy='false'>)</mo></math>, a significantly reduced and natural composite scale of <math altimg='si4.svg'><msub><mrow><mi>M</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&#8764;</mo><mn>6</mn></math> TeV, a successful prediction for the quartic coupling, <italic>&#955;</italic>, and fine&#8211;tuning that is reduced to a few percent, providing a compelling candidate solution to the naturalness problem of the BEH boson. The theory is testable and the associated new physics may soon emerge at LHC energy scales.

Christopher T. Hill

Natural top quark condensation (a redux)