In this paper, a wormhole solution incorporating various dark energy parameterizations has been presented. Three chosen dark energy parameterizations, namely CPL, JBP, and BA, are employed at first to derive the Hubble parameter in terms of redshift through Friedmann’s equations for general relativity. After employing the Metropolis-Hastings Markov Chain Monte Carlo to sample the parameters of each dark energy parametrization, it is found that dark energy is characterized by <math altimg='si103.svg'><mrow><msub><mi>&#969;</mi><mn>0</mn></msub><mo linebreak='goodbreak'>&gt;</mo><mo>&#8722;</mo><mn>1</mn></mrow></math>, <italic>&#969;<inf>a</inf></italic>&#8239;&lt;&#8239;0, and <math altimg='si104.svg'><mrow><msub><mi>&#969;</mi><mn>0</mn></msub><mo linebreak='goodbreak'>+</mo><msub><mi>&#969;</mi><mi>a</mi></msub><mo linebreak='goodbreak'>&lt;</mo><mo>&#8722;</mo><mn>1</mn></mrow></math>, consistent with Quintom-B type behavior rather than a cosmological constant. A comparative statistical analysis relative to the baseline &#923;CDM model using <math altimg='si105.svg'><mrow><mrow><mo>|</mo><mstyle mathvariant='normal'><mi>&#916;</mi></mstyle><mi>ln</mi></mrow><msub><mi mathvariant='script'>Z</mi><mrow><mstyle mathvariant='normal'><mi>&#923;</mi></mstyle><mtext>CDM</mtext><mo>,</mo><mtext>Model</mtext></mrow></msub><mrow><mo>|</mo></mrow></mrow></math> shows that, while CPL, JBP, and BA provide weak or inconclusive evidence with CC + DESI DR2 and Pantheon <math altimg='si106.svg'><msup><mrow /><mo>+</mo></msup></math> datasets, they achieve moderate support when DES-SN5Y and Union3 are included, with JBP and CPL being particularly favored. With the best-fit values so obtained, the shape function <italic>b</italic>( <italic>r</italic>) is calculated for all three dark energy models while the redshift function is chosen as <math altimg='si107.svg'><mrow><mstyle mathvariant='normal'><mi>&#934;</mi></mstyle><mo>(</mo><mi>r</mi><mo>)</mo><mo>=</mo><mo>&#8722;</mo><mn>2</mn><mi>&#951;</mi><mo linebreak='goodbreak'>/</mo><mi>r</mi></mrow></math>, <italic>&#951;</italic> being a dimensionless constant. Traversability conditions associated with the wormhole shape function are then studied through graphs, and also the validity of the four types of energy conditions, namely null, weak, dominant, and strong, is investigated for the derived wormhole solutions. Lastly, stability analysis of the wormhole solutions are performed via the TOV equation and speed of sound.

India

Soubhik Paramanik

Azerbaijan

Romania

Himanshu Chaudhary

Ujjal Debnath

Uzbekistan

Farruh Atamurotov

Dark energy parameterization in wormhole

This study investigates the construction and stability of thin-shell wormholes derived from the modified Bardeen anti-de Sitter (AdS) black hole. The thin-shell wormhole is constructed using Visser’s cut-and-paste method, which involves matching two identical black hole spacetimes at a hypersurface to form a throat that connects the geometries. Wormhole’s stability is examined through the Israel formalism, which provides the surface stress-energy tensor at the throat. The violation of energy conditions, a hallmark of exotic matter, is explored in detail. Linearised stability analysis is performed by perturbing the wormhole throat and analysing the resulting equations of motion. Various equations of state (EoS), including barotropic, generalised phantom-like, and generalised Chaplygin gas models, are considered to study the behaviour of the system under radial perturbations. Our findings demonstrate that a thin-shell wormhole’s stability strongly depends on the throat radius, charge parameters, and cosmological constant. Furthermore, the influence of EoS parameters is crucial in determining the stable and unstable configurations of the wormhole. This study highlights the critical role of modified black hole geometries in constructing physically viable and stable wormhole solutions in the context of AdS spacetimes.

Biswajit Sarkar

Anirudh Pradhan

Thin-shell wormhole from modified Bardeen AdS black hole

In this work, we derive a new class of analytic black hole solutions within the framework of <math altimg='si8.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math> gravity, where the black hole is surrounded by an anisotropic fluid acting as the matter source. We consider both linear and nonlinear forms of the function <math altimg='si8.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math>, enabling a detailed exploration of how anisotropic pressures and different <math altimg='si8.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math> influence the spacetime structure. Furthermore, we derive the conditions on the coupling parameters ( <italic>&#946;</italic> <inf>1</inf>, <italic>&#946;</italic> <inf>2</inf>, <italic>&#946;</italic> <inf>3</inf>) under which the energy condition is satisfied. Utilising these constraints, we then investigate the thermodynamic behaviour of the resulting black hole solutions in the presence of various matter fields. An important outcome of this study is that the results obtained deviate from those predicted by standard General Relativity. It is also observed that these deviations depend explicitly on the interaction between the matter Lagrangian <math altimg='si9.svg'><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub></math> and the trace <italic>T</italic> of the energy-momentum tensor.

Aniruddha Ghosh

The new black hole solution with anisotropic fluid in <math altimg='si8.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math> gravity: Thermodynamics

The <italic>D</italic>(&#8239;&gt;&#8239;4) dimensional Einstein-Gauss-Bonnet(EGB) gravity is widely researched gravity that originates from the correction of quadratic curvature terms in Einstein-Hilbert action. Recently several methods have been suggested to obtain regularized EGB gravity in <italic>D</italic>&#8239;&#8594;&#8239;4 limit. The 4 <italic>D</italic> EGB gravity has drawn interests of researchers as it avoids Ostrogradsky&#8217;s instability and forecasts several cosmological phenomenon and black hole mechanics. In this paper we extensively study the effect of Gauss-Bonnet parameter and quintessence state parameter on black hole thermodynamics in EGB gravity by considering &#923; as thermodynamic pressure in AdS space. We examine critical behavior near critical, Gibbs free energy, local stability through heat capacity, Joule-Thomson expansion. We also obtained the efficiency of the newly proposed rectangular heat engine and found that it is always less than the Carnot efficiency, which is in agreement with the second law of black hole mechanics.

Debojyoti Mondal

Charged AdS black hole thermodynamics in Einstein-Gauss-Bonnet gravity under quintessence field: heat engine

Cosmic evolution is the most sensational topic among researchers of modern cosmology. This article explores cosmic evolution in 4D Einstein Gauss Bonnet gravity, focusing on mass accretion of compact objects (black holes and wormholes) by dark energy. Three DE models CPL, JBP, and BA parameterizations are studied within 4D EGB gravity, with their Hubble parameters derived and compared against observational data (Cosmic Chronometers, Type Ia Supernovae, and Baryon Acoustic Oscillations). Bayesian analysis favors the CPL and BA models, with CPL providing the best fit. For black holes, mass accretion of CPL and JBP DE shows transitions between quintessence and phantom eras, while BA and ΛCDM strictly exhibit quintessence-like behavior, driving cosmic acceleration. In contrast, wormholes exhibit the opposite trend, favoring a phantom-dominated era for the BA and ΛCDM models. The study highlights the dynamic nature of DE in 4D EGB gravity and its role in cosmic expansion.

Puja Mukherjee

China

G. Mustafa

Compact objects in 4D Einstein Gauss Bonnet gravity: A data based perspective

In this work, we explore the Barrow Agegraphic Dark Energy (BADE) and New Barrow Agegraphic Dark Energy (NBADE) models within the framework of a fractal universe, incorporating Barrow entropy and the holographic principle with a time scale as the infrared (IR) cut-off. By analyzing both conformal time and the universe's age as IR cutoffs, we investigate the cosmological implications of these dark energy models and examine the evolution of a universe filled with the proposed dark energy components alongside pressureless matter. Using BAO and <math altimg='si1.svg'><mi>P</mi><mi>a</mi><mi>n</mi><mi>t</mi><mi>h</mi><mi>e</mi><mi>o</mi><msup><mrow><mi>n</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow></msup></math> datasets, we constrain the model parameters and plot the Hubble parameter and distance modulus for both datasets. The results align well with current observations and demonstrate excellent agreement with the &#923;CDM model. Additionally, we extract various cosmological parameters and assess the stability of the BADE and NBADE models through squared sound speed analysis. We study the <math altimg='si2.svg'><msub><mrow><mi>&#969;</mi></mrow><mrow><mi>d</mi></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>&#8722;</mo><msubsup><mrow><mi>&#969;</mi></mrow><mrow><mi>d</mi></mrow><mrow><mo>&#8242;</mo></mrow></msubsup></math> analysis of the BADE and NBADE models and the statefinder diagnostic for both models in the <math altimg='si3.svg'><mi>q</mi><mo linebreak='goodbreak' linebreakstyle='after'>&#8722;</mo><mtext mathvariant='bold'>S</mtext></math> and <math altimg='si4.svg'><mi>q</mi><mo linebreak='goodbreak' linebreakstyle='after'>&#8722;</mo><mi>r</mi></math> planes. Also, we studied the energy conditions, evaluated our models through the framework of thermodynamics, and analyzed their thermal stability. Furthermore, in a dedicated section, we investigate the impact of introducing an interaction term between dark energy and dark matter on the classical and thermal stability of the models, as well as its role in alleviating the Hubble tension. Then, we correspond each model with quintessence, tachyon, DBI-essence, and k-essence scalar field models of DE in FRW space-time to reconstruct potentials and the dynamics for these scalar fields. Finally, we test the swampland conjecture for each reconstructed model, providing insights into their theoretical consistency within string theory. We also examine the inflationary behavior of the models by analyzing the evolution of the slow-roll parameters <italic>&#1013;</italic> and <italic>&#951;</italic>.

Anamika Kotal

Alok Sardar

Arijit Malakar

Parameter estimation of Barrow Agegraphic and New Barrow Agegraphic Dark Energy models in fractal universe: Correspondence with scalar field models

In this study, we investigate the gravitational lensing effects of deformed Horava-Lifshitz black holes, considering both strong and weak-field limit approximations and incorporating the impact of rainbow functions. Initially, we numerically compute the coefficients of the deflection angle, <math altimg='si1.svg'><mover accent='true'><mrow><mi>a</mi></mrow><mrow><mo stretchy='false'>&#175;</mo></mrow></mover></math>, <math altimg='si2.svg'><mover accent='true'><mrow><mi>b</mi></mrow><mrow><mo stretchy='false'>&#175;</mo></mrow></mover></math>, and <math altimg='si3.svg'><msub><mrow><mi>u</mi></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msub><mo stretchy='false'>/</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>s</mi></mrow></msub></math>, and plot the deflection angle <math altimg='si132.svg'><msub><mrow><mi>&#945;</mi></mrow><mrow><mi>d</mi></mrow></msub></math> as a function of the impact parameter <italic>u</italic>. We then proceed to calculate observable quantities, including the angular deflection <math altimg='si5.svg'><msub><mrow><mi>&#952;</mi></mrow><mrow><mo>&#8734;</mo></mrow></msub></math>, the total deflection area <italic>S</italic>, and the radius of the multiple gravitational arcs, <math altimg='si6.svg'><msub><mrow><mi>r</mi></mrow><mrow><mi>m</mi><mi>g</mi><mi>a</mi></mrow></msub></math>, for supermassive black holes such as <math altimg='si7.svg'><mi>M</mi><msup><mrow><mn>87</mn></mrow><mrow><mo>&#8270;</mo></mrow></msup></math>, <math altimg='si8.svg'><mi>S</mi><mi>g</mi><mi>r</mi><msup><mrow><mi>A</mi></mrow><mrow><mo>&#8270;</mo></mrow></msup></math>, and <math altimg='si9.svg'><mi>N</mi><mi>G</mi><mi>C</mi><mn>4649</mn></math>. Additionally, we examine the Einstein ring, <math altimg='si10.svg'><msubsup><mrow><mi>&#952;</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>E</mi></mrow></msubsup></math>, for a range of supermassive black holes. Using the Gauss-Bonnet theorem, we derive the deflection angle in the weak-field limit for deformed Horava-Lifshitz black holes while considering rainbow functions. The results are compared with those for a Schwarzschild black hole, where <math altimg='si11.svg'><mi>&#945;</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>0</mn></math> and <math altimg='si12.svg'><mi>g</mi><mo>,</mo><mi>h</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>1</mn></math>.

Gravitational lensing by deformed Horava-Lifshitz black hole in rainbow gravity

In this work, we have studied the mass accretion mechanism of a 4-dimensional black hole in the Bumblebee gravity framework. We work with three well-known red-shift parameterizations of dark energy EoS, namely, Linear, Chevallier–Polarski–Lindler (CPL), and Jassal–Bagla–Padmanabhan (JBP) parameterization. First, we discussed the fundamentals of Bumblebee gravity theory, specifically the basic field equations, and then went on to discuss the three dark energy models and their respective equations of state, energy density equations, and associated Hubble parameter equations. Next, the free parameters for the Bumblebee theory of gravity are constrained using the MCMC analysis. After determining the necessary parameters, we initiated the mass accretion procedure. We derived the mass equation for the models using the redshift function and then graphically depicted how the black hole’s mass changed with redshift. The accretion of all the dark energy candidates discussed above led us to the final conclusion that the mass of a 4-dimensional Bumblebee Black Hole will progressively rise in accordance with the universe’s evolution.

Anuka Basak

Accretion of dark energy onto black hole in Bumblebee field

We present a comprehensive investigation exploring the theoretical framework of Einstein–Aether gravity theory when combined with two modified cosmological paradigms: the Barrow Agegraphic Dark Energy (BADE) and its newer variant, the New Barrow Agegraphic Dark Energy (NBADE). Our study focuses on reconstructing the functional form of the Einstein–Aether Lagrangian component $\textit{F}$($\textit{K}$) from these phenomenological dark energy models. Model parameters are constrained using a Markov Chain Monte Carlo (MCMC) approach based on multiple datasets, including cosmic chronometers (CC), Baryon Acoustic Oscillations (BAO), and the Pantheon+SH0ES compilation. Using best-fit parameters, we analyze various cosmological diagnostics: Hubble and deceleration parameter evolution, dark energy equation of state ( $$\omega _{DE}$$ ), density parameter trajectories, $$\omega _{DE}'$$ – $$\omega _{DE}$$ phase space behavior, statefinder diagnostics $$(r,s^*)$$ and ($\textit{r}$, $\textit{q}$), and Om(z) trajectories. Both models exhibit late-time acceleration, with the dark energy sector showing a quintessence-like nature in the current epoch and evolving toward a phantom regime in the future. Stability analysis based on the squared sound speed ( $$v_s^2$$ ) highlights partial epoch-dependent stability. While our results demonstrate reasonable agreement with observational data and reveal physically plausible dynamics, the models do not yet offer a fundamentally superior alternative to other dark energy reconstructions. Nonetheless, their behavior under modified entropy assumptions and their flexibility in dynamical diagnostics provide a useful framework for probing non-standard extensions of Einstein–Aether gravity and dark energy phenomenology.

Banadipa Chakraborty

Tamal Mukhopadhyay

Reconstructions of Einstein–Aether gravity from Barrow agegraphic and new Barrow agegraphic dark energy models: examinations and observational limits

This research focuses on examining a non-flat Friedmann–Robertson–Walker (FRW) cosmological model of the universe incorporating both dark matter and dark energy. Two intriguing dark energy models, Barrow agegraphic dark energy (BADE) and new Barrow agegraphic dark energy (NBADE), which were introduced in accordance with the holographic principle incorporating Barrow entropy, have been selected to play the role of dark energy. Using datasets from cosmic chronometers and baryon acoustic oscillations, we utilized the Markov Chain Monte Carlo (MCMC) technique to constrain the parameters of our model. This enables us to make several possible comparisons between these novel models of dark energy and the $$\Lambda $$ CDM models. Here, we explore cosmological parameters, including the equation of state(EoS) parameter, jerk parameter, deceleration parameter, and cosmological planes such as the $$q-r$$ plane, $$\omega _d - \omega '_d$$ for different values of the model parameters by considering both the presence and absence of mutual interactions of the dark sector of the universe. In addition, we examined the thermal stability and the Swampland criteria of our constructed models. Additionally, we analyze the energy conditions and find that NEC and DEC are fulfilled, but SEC is broken, indicating model stability and supporting the current acceleration of the universe. In order to give a more precise explanation of the origin of cosmic structures, we lastly conduct a linear perturbation analysis to examine the growth in matter density perturbations.