<p>We consider diffeomorphism invariant theories of gravity with arbitrary higher derivative corrections to the two derivative Einstein’s theory in the presence of Proca fields—vector fields without <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> gauge invariance. We prove that, in such theories, the surface gravity remains constant across the Killing horizon of stationary black hole solutions, without requiring the existence of a bifurcation surface. Our analysis is carried out within an effective field theory framework, where higher derivative contributions are treated perturbatively around the two derivative theory. The proof relies on specific components of the coupled gravity—Proca field equations together with constraints implied by the near horizon boost symmetry of stationary black hole geometries, analyzed using boost-weight arguments. Implementing these arguments in the presence of Proca fields introduces new subtleties beyond those encountered in the pure gravity case. We provide a systematic resolution of these subtleties and demonstrate that the surface gravity remains constant to all orders in the perturbative expansion, thereby establishing the zeroth law. Finally, we outline how this framework can be generalized to broader classes of vector theories with four propagating degrees of freedom, which exhibit qualitative differences from both the Proca and gauge invariant vector theories.</p>

India

Parthajit Biswas

Alokananda Kar

Anowar Shaikh

Zeroth law of black hole thermodynamics for higher derivative Proca theories

We investigate Power-Law Plateau (PLP) inflation in standard gravity and its consistency with ACT DR6 data. While many inflationary models, including the Starobinsky inflation, are disfavored by ACT observations, the PLP potential remains viable across a broad range of its parameters. Then, the dynamics of the reheating phase are investigated, with a primary focus on the reheating temperature and its relationship with the inflationary phase and primordial gravitational waves. Incorporating the overproduction of the primordial gravitational waves can affect the effective number of relativistic species during reheating. The constraint on Δ <italic>N</italic> <inf>eff</inf> can impose a lower bound on the reheating temperature. This constraint will be more efficient for a stiff equation of state. It is determined that for <italic>w<inf>re</inf></italic>&#8239;&#8819;&#8239;0.58, this constraint would be efficient. Combining the result of the reheating temperature and the inflationary phase, it is concluded that to have both a viable result standing in 1 <italic>&#963;</italic> of ACT DR6 and also to satisfy the reheating lower bound, the number of remaining e-folds of inflation after the pivot scale exits the horizon should be <italic>N<inf>k</inf></italic>&#8239;&#8818;&#8239;62. Higher e-folds of expansion result in a reheating temperature below the bound, which is disfavored. Finally, for the constraint values of the reheating temperature, the energy spectrum of the primordial gravitational waves (PGWs) has been explored. The results indicate that there is a higher chance of detection of PGWs for lower reheating temperatures and higher reheating equation of state. We also address the condensate fragmentation during reheating for stiff <italic>w<inf>re</inf></italic>&#8239;&#8805;&#8239;0.58. It is discussed that for our model, the stiff phase could last for some e-folds before <italic>w<inf>re</inf></italic>&#8239;&#8594;&#8239;1/3. This leads to a larger reheating temperature <italic>T<inf>re</inf></italic>, however, the resulting PGWs energy spectrum is suppressed and it is below the detectable level.

China

Abolhassan Mohammadi

 Yogesh

United States

Anzhong Wang

Power law plateau inflation and primordial gravitational waves in the light of ACT

In this manuscript, we examine geometrical and physical properties of wormhole ( $$\mathcal{W}\mathcal{H}$$ ) solutions with monopole charge by considering three distinct shape function models in power-law gravity, i.e., Starobinsky $\textit{f}$($\textit{R}$) gravity, where $\textit{R}$ is Ricci scalr. The modified gravitational field equations are solved under the assumption of anisotropic energy–momentum tensor ( $$\mathcal {EMT}$$ ), with particular attention given to the role of exotic matter ( $$\mathcal{E}\mathcal{M}$$ ) in sustaining these solutions. The impact of the global monopole charge ( $$\mathcal {GMC}$$ ) is examined in detail, revealing that higher monopole charges enlarge the throat radius and produce flatter embedding surfaces through two and three dimensional embedding diagrams, thereby affecting both traversability and structural stability. A comprehensive investigation of physical quantities, energy conditions and stability analysis is carried out using several physical and geometrical criteria, including the adiabatic index approach, Herrera’s cracking criterion, and causality conditions approach, along with anisotropic effects. Moreover, the total amount of $$\mathcal{E}\mathcal{M}$$ is quantified through the volume integral quantifier method. These findings highlight supportive directions for future explorations of exotic spacetime structures in both theoretical and astrophysical contexts.

Azerbaijan

Pakistan

M. Yousaf

H. Asad

Kashif Yasir

Oman

S. Maurya

Saudi Arabia

Akram Ali

Uzbekistan

Farruh Atamurotov

Global monopole induced wormholes in power-law gravity: stability and physical viability

<list id='lst0002'><list-item id='lstitem0001'><label>&#8226;</label><para id='p0001'>Wormhole solutions are constructed in power-law f(R) = <italic>&#945;R<sup>n</sup></italic> gravity by incorporating the Kiselev anisotropic energy density.</para></list-item><list-item id='lstitem0002'><label>&#8226;</label><para id='p0002'>An exact shape function is derived and shown to satisfy traversability conditions, including the flare-out criterion and asymptotic flatness.</para></list-item><list-item id='lstitem0003'><label>&#8226;</label><para id='p0003'>All classical energy conditions (NEC, WEC, SEC, DEC) are evaluated using closed-form expressions, with violations quantified through &#916;NEC plots in the (r,<italic>&#969;</italic>) domain.</para></list-item><list-item id='lstitem0004'><label>&#8226;</label><para id='p0004'>The Volume Integral Quantifier (VIQ) and Tolman&#8211;Oppenheimer&#8211;Volkoff (TOV) analysis reveal that configu rations with n &gt; 0 require less exotic matter and exhibit mechanical stability.</para></list-item><list-item id='lstitem0005'><label>&#8226;</label><para id='p0005'>The anisotropy parameter <math altimg='si28.svg'><mrow><mstyle mathvariant='normal'><mi>&#916;</mi></mstyle><mo linebreak='goodbreak'>=</mo><mi>p</mi><mi>t</mi><mo linebreak='goodbreak'>&#8722;</mo><mi>p</mi><mi>r</mi></mrow></math> confirms the presence of repulsive pressure near the throat, essential for sustaining the wormhole geometry in the modified gravity setup</para></list-item></list>

J. Praveen

S.K. Narasimhamurthy

Construction and analysis of Kiselev Wormholes in power-Law <italic>f</italic>( <italic>r</italic>) gravity framework

In this paper, combining the thermodynamical arguments of the horizon with the quadratic generalised uncertainty principle (GUP), we heuristically obtain the modified equipartition law of energy. Employing this modified equipartition law of energy, we derive the Friedmann equations in Verlinde’s entropic gravity. We find a maximum energy density at the beginning of the Universe. Remarkably, this feature emerges not only for positive GUP parameter but also for negative GUP parameter. From the initial acceleration, we deduce that the negative GUP parameter is more preferable. We also obtain maximum Hubble parameter from the first Friedmann equation, indicating a universe without initial singularity. Moreover, we compute the Kretschmann curvature scalar, again indicating a non-singular universe. Interestingly, we find that GUP-modified Friedmann equations share some similarities with braneworld cosmolgy where the quadratic term in energy density appears. We also compute the deceleration parameter. Finally, we revisit the gravitational baryogenesis and show that the GUP-modified equipartition law of energy provides a mechanism for generating baryon asymmetry. Moreover, we constrain the GUP parameter from observations.

Türkiye

Özgür Ökcü

Friedmann equations from GUP-modified equipartition law

In this work, we study the Barrow Holographic Dark Energy (BHDE) model (Phys Rev D 102:123525, 2020), which is based on Barrow’s modification of entropy. We show that this model is a special case of the more general Nojiri–Odintsov HDE (NO-HDE) framework (Eur Phys J C 77:528, 2017). In the same way, the Granda–Oliveros (GO) cutoff also appears as a particular case of the NO cutoff. After this, we reconstruct the dynamics of BHDE using a k-essence scalar field, which provides a field theory picture of its evolution. The results show how the Barrow deformation parameter and the infrared cutoff affect the kinetic term and the behaviour of the scalar field. Further, we test the thermodynamic consistency of the model by checking the generalized second law on cosmological horizons. Overall, the study confirms that both BHDE and the GO cutoff can be understood as limits of the NO-HDE framework, and that they are consistent with scalar field theory and the principles of thermodynamics. Also we confront the reconstructed BHDE–k-essence model with late-time cosmological data from cosmic chronometers and baryon acoustic oscillations. The features derived in the study the models under as viable models to explain the late-time cosmic acceleration.

Kazakhstan

Guldana Bekova

Aziza Altaibayeva

Ulbossyn Ualikhanova

Surajit Chattopadhyay

Cosmology of barrow holographic dark energy with generalized infrared cutoffs and validity of the generalized second law of thermodynamics

This work considers the dynamics of the gauge vector and inflaton (dilaton) fields inspired by Kaluza–Klein theory in an inflationary universe with Bianchi type-I spacetime. The inverse power-law potential of the inflaton field is used to study dynamical system analysis. As a result, all fixed points in the autonomous system are non-hyperbolic fixed points, and one cannot determine their stability. Therefore, a center manifold theory is required to analyze the stability of the dynamical system properly. Interestingly, we found an isotropic attractor point which means that the universe undergoes accelerated expansion (inflation) from an anisotropic phase to an isotropic phase of the universe. According to the dynamical system analysis of the anisotropic Bianchi type-I universe with the inspired Kaluza–Klein model, our results supported the isotropization of the observed universe.

Thailand

Jaturaporn Watanakampolkij

Patinya Ma-ardlerd

Natthason Autthisin

Pornpatara Chuvala

Nutthaphat Lunrasri

Chakrit Pongkitivanichkul

Daris Samart

Kaluza–Klein inspired a model of the inflation with the inverse power law potential in Bianchi type-I universe

We consider the inhomogeneous Morris–Thorne wormhole metric with matter tensors characterised by a novel linear equation of state in $\textit{f}$($\textit{R}$) gravity. Using the Einstein’s field equations in metric $\textit{f}$($\textit{R}$) gravity we model solutions for both wormhole as well as $\textit{f}$($\textit{R}$) gravity. We obtain four different wormhole models, two wormholes are characterised by solid angle deficit, three are not asymptotically extendible, while one is asymptotically flat with zero tidal force. These are supported by four different power law $\textit{f}$($\textit{R}$) models. The parameter space of the models can support both null energy conditions (NEC) satisfying as well as violating wormhole. In case of NEC satisfying matter, the associated $\textit{f}$($\textit{R}$) is ghost. The $\textit{f}$($\textit{R}$) models obtained have been independently substantiated for cosmological feasibility and valid parameter space was obtained corresponding to cosmologically viable $\textit{f}$($\textit{R}$). Suitable scalar-tensor representation of the corresponding $\textit{f}$($\textit{R}$) models have been presented using the correspondence of $\textit{f}$($\textit{R}$) gravity with Brans–Dicke (BD) theory of gravity. The robustness of the wormhole solutions were further analysed with the BD scalar fields in the hybrid metric-Palatini gravity, which showed excellent results. Lastly as an independent astrophysical probe for the wormhole we have obtained the location of their photon spheres and have connected them with the Herrera Complexity factor in $\textit{f}$($\textit{R}$). Our results show that the relation between the complexity factor and existence of photon spheres remains fundamentally unaltered in $\textit{f}$($\textit{R}$) as compared to Einstein’s gravity.

Subhasis Nalui

Subhra Bhattacharya

Designing wormholes in novel power-law $\textit{f}$($\textit{R}$): a mathematical approach with a linear equation of state

In this work we elaborate on solving the trans-Planckian censorship problem of standard slow-roll inflation by using a power-law inflationary tail generated by a scalar field with an exponential potential. We use a quantitative approach by studying in detail the phase space of a combined <math altimg='si30.svg'><mrow><mi>F</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>&#981;</mi><mo>)</mo></mrow></math> cosmological system, focusing on the de Sitter and power-law subspaces of the total phase space. As we show, the de Sitter subspace of the <math altimg='si30.svg'><mrow><mi>F</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>&#981;</mi><mo>)</mo></mrow></math> system shares the same fixed points as the vacuum <math altimg='si29.svg'><mrow><mi>F</mi><mo>(</mo><mi>R</mi><mo>)</mo></mrow></math> gravity system and the trajectories in the phase space tend to these fixed points. However, the power-law subspace is not stable and cannot be realized by the combined <math altimg='si30.svg'><mrow><mi>F</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>&#981;</mi><mo>)</mo></mrow></math> system. To this end, we propose a well-motivated phenomenological <math altimg='si29.svg'><mrow><mi>F</mi><mo>(</mo><mi>R</mi><mo>)</mo></mrow></math> gravity model for which the <math altimg='si1.svg'><msup><mi>R</mi><mn>2</mn></msup></math> term is switched off below a critical curvature near the end of the <math altimg='si1.svg'><msup><mi>R</mi><mn>2</mn></msup></math> slow-roll inflationary era, and below that critical curvature, only the Einstein-Hilbert gravity term and the scalar field remain in the effective inflationary Lagrangian. The remaining system can successfully realize a power-law tail of the <math altimg='si1.svg'><msup><mi>R</mi><mn>2</mn></msup></math> slow-roll era.

Spain

S.D. Odintsov

Greece

V.K. Oikonomou

Eleni I. Manouri

Asterios T. Papadopoulos

Solving the trans-Planckian censorship problem with a power-law tail in <math altimg='si1.svg'><msup><mi>R</mi><mn>2</mn></msup></math> inflation: A dynamical system approach

We evaluate the validity of the generalized second law for Kerr black holes perturbed by fermionic and bosonic fields. We derive that the critical frequency for a test field below which the area of a Kerr black hole would decrease, coincides with the superradiance limit which pertains to bosonic fields. The fact that the absorption of fermionic fields with arbitrarily low frequencies is allowed, leads to a generic violation of the generalized second law as both the black hole and the environment lose entropy. The result does not contradict the proof of the area theorem which pre-assumes the validity of the null energy condition. We also construct a thought experiment involving bosonic fields to check whether the minimum increase in the area can compensate for the decrease in the entropy of the environment. We minimize the entropy increase by considering a black hole at the extremal limit, perturbed by a bosonic field at the superradiance limit. We show that the generalized second law remains valid for bosonic fields that satisfy the null energy condition. The result does not require the employment of entropy bounds when one assigns von Neumann entropy to test fields.

Koray Düztaş

The generalized second law for fermionic and bosonic fields