Evidences for evolving dark energy are shown using baryon acoustic oscillation measurements from the recent Dark Energy Spectroscopic Instrument Data Release 2, combined with different Type Ia supernova datasets (Pantheon $$^+$$ , DES-Dovekie, and Union3) and the CMB compressed likelihood. We examine several dark energy parameterizations, including the Logarithmic, Exponential, CPL, BA, JBP, Thawing, Mirage, and GEDE models. Analyzing the DESI DR2 measurements alone, we find that evidence for evolving dark energy is primarily driven by the LRG1-2 tracers, as their inclusion yields a preferred value of $$w_0 > -1$$ . However, as each tracer provides only limited observables, this preference can result in an underconstrained and potentially unstable inference. Further, we find that each dark energy model predicts values in the $$w_0 > -1$$ , $$w_a < 0$$ quadrant, a region characterized by the Quintom-B type dark energy scenario. The logarithmic bayes factor shows that, among all models, the Mirage model shows the inconclusive-to-moderate evidence across all dataset combinations. Consistently, the statistical significance remains modest, with $$N\sigma \sim 1.1$$ -2.3, and no model showing a robust preference for dynamical dark energy using late-time datasets alone. The evolution of $\textit{w}$($\textit{z}$) shows a phantom crossing around $$z \sim 0.5$$ in most dynamical dark energy models, and the evolution of $$f_{\textrm{DE}}(z)$$ converges to $$f_{\textrm{DE}}(0) = 1$$ in all dark energy models.

Romania

Azerbaijan

Himanshu Chaudhary

Italy

Salvatore Capozziello

India

Vipin Sharma

Switzerland

Isidro Gómez-Vargas

Thailand

China

G. Mustafa

Evidence for evolving dark energy from DESI DR2 BAO and Pantheon $$^+$$ , DES-Dovekie, and Union3

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.

Soubhik Paramanik

Ujjal Debnath

Uzbekistan

Farruh Atamurotov

Dark energy parameterization in wormhole

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

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

We propose a novel dynamical dark energy model within the frameworks of Einstein gravity and Horava–Lifshitz gravity, utilizing the DCMPM parametrization of the dark energy equation of state to derive the Hubble parameter. We keep $$ r_d $$ as a free parameter, and use different cosmological datasets such as cosmic chronometer measurements, Type Ia Supernovae observations, and Baryon Acoustic Oscillation data from DESI Y1 and SDSS-IV to extract the posterior distributions of each model parameters. Furthermore, we investigate the evolution of the Universe using various cosmographic parameters and conduct diagnostic analyses, including the statefinder and $$ O_m $$ diagnostics. Using various statistical metrics, we compare both models against the standard $$\Lambda $$ CDM model and find that all are well-supported by current data. Notably, the DCMPM parameterization within Einstein gravity emerges as a promising extension to the standard $$\Lambda $$ CDM framework.

Niyaz Molla

S. Pacif

Estimation of $$ H_0 $$ and $$ r_d $$ in the $$\omega (z)$$ parameterization within Einstein and Horava–Lifshitz gravity using DESI-Y1 and SDSS-IV

We study the orbital and oscillatory motion of test particles around a charged, non-commutative black hole surrounded by perfect fluid dark matter. We derive analytical expressions for the radial profiles of specific energy and angular momentum of stable equatorial circular orbits and discuss their stability using the effective potential approach. We also analyze the innermost stable circular orbits, the effective force acting on particles, and the frequencies of radial and latitudinal harmonic oscillations. The paper explores the quasi-periodic oscillations of particles near stable orbits and addresses periastron precession. We find that the model parameters strongly influence the motion of particles around black holes. Using observational data from multiple X-ray binary structures, we apply Monte Carlo Markov Chain (MCMC) analyses to restrain certain parameters such as <italic>&#945;</italic>, <italic>&#946;</italic>, and <italic>Q</italic> corresponding to the considered black hole.

Asifa Ashraf

Pakistan

Tayyab Naseer

Algeria

Abdelmalek Bouzenada

Türkiye

Batuhan Çil

Ertan Güdekli

Observational constraints on QPOs with orbital motion around charged non-commutative Schwarzschild black hole surrounded by perfect fluid dark matter

This study deals with the new class of embedded wormhole solutions in the background of general relativity. Two newly calculated wormhole solutions satisfy all the required properties. The embedded diagrams for both calculated wormhole solutions are provided. All the energy conditions are discussed through their validity regions for the different ranges of involved parameters. In maximum regions, all energy conditions are violated. We investigate the shadow and strong gravitational lensing by the wormhole throat for the two new wormhole models, namely Model-I and Model-II. The present paper considers the wormhole throat to act as a photon sphere. We first derive null geodesics using the Hamilton-Jacobi separation method to investigate the shadow and strong gravitational lensing caused by the wormhole throat. We then numerically obtain the radius of wormhole shadow, strong deflection angle, and various lensing observables by taking the example of supermassive black M87* and Sgr A* in the context of both Model-I and Model-II. Keeping all other parameters fixed, it is observed that the parameters $$\zeta _1$$ and $$\zeta _2$$ for Model-I; and $$\chi _1$$ and $$\chi _2$$ for Model-II have significant effects on the wormhole shadow and strong gravitational lensing phenomena. Our conclusion is that it is possible to detect relativistic images, such as Einstein rings, produced by wormholes with throat radii of $$r_{th}=3M$$ . The stability analysis via Tolman–Oppenheimer–Volkov equation is included for both wormhole solutions. Additionally, current technology enables us to test hypotheses related to astrophysical wormholes.

Oman

S. Maurya

Shadow and strong gravitational lensing of new wormhole solutions supported by embedding Class-I condition

We study the <math><mi>f</mi><mo>(</mo><mi>Q</mi><mo>,</mo><mi>T</mi><mo>)</mo></math> gravity in the framework of Weyl geometry (known as Weyl-type <math><mi>f</mi><mo>(</mo><mi>Q</mi><mo>,</mo><mi>T</mi><mo>)</mo></math> gravity), where Q denotes the non-metricity scalar, and T denotes the energy-momentum tensor trace. In this work, we consider the <math><mi>f</mi><mo>(</mo><mi>Q</mi><mo>,</mo><mi>T</mi><mo>)</mo></math> model, which is defined as <math><mi>f</mi><mo>(</mo><mi>Q</mi><mo>,</mo><mi>T</mi><mo>)</mo><mo>=</mo><mi>α</mi><msup><mrow><mi>Q</mi></mrow><mrow><mi>m</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mfrac><mrow><mi>β</mi></mrow><mrow><mn>6</mn><msup><mrow><mi>κ</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mi>T</mi></math> and investigating two scenarios: (I) <math><mi>m</mi><mo>=</mo><mn>0</mn></math> (linear model) and <math><mo>(</mo><mi>I</mi><mi>I</mi><mo>)</mo></math> <math><mi>m</mi><mo>≠</mo><mn>0</mn></math> (nonlinear model). For both scenarios, we find the explicit solution for the field equations by using the barotropic equation of state as <math><mi>p</mi><mo>=</mo><mi>w</mi><mi>ρ</mi></math>, where w is the equation-of-state (EoS) parameter. Further, we study the obtained solutions statistically using the <math><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>+</mo></mrow></msup></math> (Without SHOES Calibrated) dataset with 1701 data points. For both models, the best-fit values of model parameters for <math><mn>1</mn><mo>−</mo><mi>σ</mi></math> and <math><mn>2</mn><mo>−</mo><mi>σ</mi></math> confidence level. The higher Hubble constant values in both models emphasize the presence of Tension. We statistically compare our models to the ΛCDM model using <math><msubsup><mrow><mi>χ</mi></mrow><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msubsup></math>, <math><msubsup><mrow><mi>χ</mi></mrow><mrow><mi>r</mi><mi>e</mi><mi>d</mi></mrow><mrow><mn>2</mn></mrow></msubsup></math>, AIC, <math><mi>Δ</mi><mi>A</mi><mi>I</mi><mi>C</mi></math>, BIC and <math><mi>Δ</mi><mi>B</mi><mi>I</mi><mi>C</mi></math>. We also examine cosmological parameters such as deceleration and EoS parameters to determine the current acceleration expansion of the Universe. Furthermore, we test our model using Om diagnostic and compare it to the ΛCDM model to determine its dark energy profile. Finally, we draw the conclusion that statistically speaking, both linear and nonlinear models show good compatibility with the ΛCDM model.

Gaurav N. Gadbail

Morocco

Amine Bouali

P.K. Sahoo

Statistical and observation comparison of Weyl-type ( , ) models with the ΛCDM paradigm

In this paper, we investigate the phenomenon of the accelerated cosmic expansion in the late universe and the mass accretion process for a four-dimensional Einstein-Aether black hole. Starting with the basics of Einstein-Aether gravity theory, we first consider the field equations and two well-known models of Chaplygin gas, i.e., the generalized cosmic Chaplygin gas model and viscous modified Chaplygin gas model. We then obtain the energy density and Hubble parameter equations for these models in terms of various dimensionless density parameters and some unknown parameters. After finding the required parameters, we proceed with the mass accretion process. For both models, we obtain the equation of mass in terms of the redshift function and graphically represent the change in the mass of the black hole with a redshift. At the same time, we perform a graphical comparison between these models and the  $$\Lambda $$  <math> <mi>Λ</mi> </math>  CDM model of the universe. Finally, we conclude that the mass of a four-dimensional black hole will increase along the evolution of the universe within the framework of Einstein-Aether gravity.

Constraining the parameters of generalized and viscous modified Chaplygin gas and black hole accretion in Einstein-Aether gravity

The present study is based on  $$f(\mathscr {T})$$  <math> <mrow> <mi>f</mi> <mo>(</mo> <mi>T</mi> <mo>)</mo> </mrow> </math>   gravity, where we impose possible observational constraints on the model parameters to obtain physically plausible features of compact stars, specifically neutron stars. To do so, as a first step, we consider the field equations in the  $$f(\mathscr {T})$$  <math> <mrow> <mi>f</mi> <mo>(</mo> <mi>T</mi> <mo>)</mo> </mrow> </math>   gravity framework. We then solve the field equations to generate a set of new exact solutions in  $$f(\mathscr {T})$$  <math> <mrow> <mi>f</mi> <mo>(</mo> <mi>T</mi> <mo>)</mo> </mrow> </math>   gravity where model parameters are found by using boundary conditions. A few tests are performed to asses the stability of the model and compare the obtained results with observations of compact stars, in particular with the compact binary merger event GW190814. We observe the maximum mass of the star beyond the  $$3M_{\odot }$$  <math> <mrow> <mn>3</mn> <msub> <mi>M</mi> <mo>⊙</mo> </msub> </mrow> </math>   when the surface density is of the order  $$10^{14}$$  <math> <msup> <mn>10</mn> <mn>14</mn> </msup> </math>  gm/cm $$^3$$  <math> <msup> <mrow></mrow> <mn>3</mn> </msup> </math>   for the higher torsion parameter, which implies that an anisotropic solution in teleparallel gravity is more suitable for modeling of massive compact objects in lower  $$mass-gap$$  <math> <mrow> <mi>m</mi> <mi>a</mi> <mi>s</mi> <mi>s</mi> <mo>-</mo> <mi>g</mi> <mi>a</mi> <mi>p</mi> </mrow> </math>  , and thus the model presented herein provides a satisfactory physical scenario with respect to the observational signature.

Allah Ditta

Saibal Ray

Study of self-bound compact stars in  $$f(\mathscr {T})$$  <math> <mrow> <mi>f</mi> <mo>(</mo> <mi>T</mi> <mo>)</mo> </mrow> </math>   gravity and observational constraints on the model parameters

We investigate the strong gravitational lensing phenomena caused by a black hole with a dark matter halo in the presence of cloud string and quintessence. This study examines strong gravitational lensing with two significant dark matter models: the universal rotation curve model and the cold dark matter model. To do this, we first numerically estimate the strong lensing coefficients and strong deflection angles for both the universal rotation curve and cold dark matter models. It is observed that the deflection angle, denoted as  $$\alpha _D$$  <math> <msub> <mi>α</mi> <mi>D</mi> </msub> </math>  , increases with the parameter  $$\alpha $$  <math> <mi>α</mi> </math>   while holding the value of  $$2M \gamma $$  <math> <mrow> <mn>2</mn> <mi>M</mi> <mi>γ</mi> </mrow> </math>   constant. Additionally, it increases with the parameter  $$2M \gamma $$  <math> <mrow> <mn>2</mn> <mi>M</mi> <mi>γ</mi> </mrow> </math>   while keeping the value of  $$\alpha $$  <math> <mi>α</mi> </math>   constant. The strong deflection angle  $$\alpha _D$$  <math> <msub> <mi>α</mi> <mi>D</mi> </msub> </math>  , for the black hole with a dark matter halo, with parameters  $$\alpha $$  <math> <mi>α</mi> </math>   and  $$2\,M \gamma $$  <math> <mrow> <mn>2</mn> <mspace width="0.166667em"></mspace> <mi>M</mi> <mi>γ</mi> </mrow> </math>  , greatly enhances the gravitational bending effect and surpasses the corresponding case of the standard Schwarzschild black hole ( $$A=B=0=\alpha =2M\gamma $$  <math> <mrow> <mi>A</mi> <mo>=</mo> <mi>B</mi> <mo>=</mo> <mn>0</mn> <mo>=</mo> <mi>α</mi> <mo>=</mo> <mn>2</mn> <mi>M</mi> <mi>γ</mi> </mrow> </math>  ). Furthermore, we investigate the astrophysical consequences through strong gravitational lensing observations, using examples of two supermassive black holes, namely  $$M87^{*}$$  <math> <mrow> <mi>M</mi> <msup> <mn>87</mn> <mrow> <mrow></mrow> <mo>∗</mo> </mrow> </msup> </mrow> </math>   and  $$Sgr A^{*}$$  <math> <mrow> <mi>S</mi> <mi>g</mi> <mi>r</mi> <msup> <mi>A</mi> <mrow> <mrow></mrow> <mo>∗</mo> </mrow> </msup> </mrow> </math>  , located at the center of nearby galaxies. It is observed that black holes with dark matter halos in the presence of cloud string and quintessence can be quantitatively distinguished and characterized from the standard Schwarzschild black hole ( $$A=B=0=\alpha =2M\gamma $$  <math> <mrow> <mi>A</mi> <mo>=</mo> <mi>B</mi> <mo>=</mo> <mn>0</mn> <mo>=</mo> <mi>α</mi> <mo>=</mo> <mn>2</mn> <mi>M</mi> <mi>γ</mi> </mrow> </math>  ). The findings in our analysis suggest that observational tests for black holes influenced by dark matter halos, cloud string and quintessence are indeed feasible and viable.

Dhruv Arora

Strong gravitational lensing by  $$Sgr A^*$$  <math> <mrow> <mi>S</mi> <mi>g</mi> <mi>r</mi> <msup> <mi>A</mi> <mo>∗</mo> </msup> </mrow> </math>   and  $$M87^*$$  <math> <mrow> <mi>M</mi> <msup> <mn>87</mn> <mo>∗</mo> </msup> </mrow> </math>   black holes embedded in dark matter halo exhibiting string cloud and quintessential field