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

We explore the shifted  $$f(R) (\propto R^{1+\delta })$$  <math> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>R</mi> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mo>∝</mo> <msup> <mi>R</mi> <mrow> <mn>1</mn> <mo>+</mo> <mi>δ</mi> </mrow> </msup> <mo>)</mo> </mrow> </mrow> </math>   model with  $${\delta }$$  <math> <mi>δ</mi> </math>   as a distinguishing physical parameter for the study of constraints at local scales. The corresponding dynamics confronted with different geodesics (null and non-null) along with their conformal analog are investigated. For null geodesics, we discuss the light deflection angle, whereas, for non-null geodesics under the weak field limit, we investigate the perihelion advance of the Mercury orbit in f(R) Schwarzschild background, respectively. The extent of an additional force, appearing for non-null geodesics, depends on  $$\delta $$  <math> <mi>δ</mi> </math>  . Such phenomenological investigations allow us to strictly constrain  $$\delta $$  <math> <mi>δ</mi> </math>   to be approximately  $${\mathcal {O}}(10^{-6})$$  <math> <mrow> <mi>O</mi> <mo>(</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>6</mn> </mrow> </msup> <mo>)</mo> </mrow> </math>   with a difference of unity in orders at galactic and planetary scales and seem to provide a unique f(R) at local scales. Our results suggest that the present form of the model is suitable for the alternative explanation of dark matter-like effects at local scales.

CERN

Murli Verma

Unified f(R) gravity at local scales

We explore a new realisation of the galactic scale dynamics via gravitational lensing phenomenon in power-law f(R) gravity theory of the type  $$f(R)\propto R^{1+\delta }$$  <math> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>R</mi> <mo>)</mo> </mrow> <mo>∝</mo> <msup> <mi>R</mi> <mrow> <mn>1</mn> <mo>+</mo> <mi>δ</mi> </mrow> </msup> </mrow> </math>   with  $$\delta&lt;&lt;1$$  <math> <mrow> <mi>δ</mi> <mo>&lt;</mo> <mo>&lt;</mo> <mn>1</mn> </mrow> </math>   for interpreting the clustered dark matter effects. We utilize the single effective point like potential (Newtonian potential + f(R) background potential) obtained under the weak field limit to study the combined observations of galaxy rotation curve beyond the optical disk size and their lensing profile in f(R) frame work. We calculate the magnitude of light deflection angle with the characteristic length scale (because of Noether symmetry in f(R) theories) appearing in the effective f(R) rotational velocity profile of a typical galaxy with the model parameter  $$\delta \approx O(10^{-6})$$  <math> <mrow> <mi>δ</mi> <mo>≈</mo> <mi>O</mi> <mo>(</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>6</mn> </mrow> </msup> <mo>)</mo> </mrow> </math>   constrained in previous work. For instance, we work with the two nearby controversial galaxies NGC 5533 and NGC 4138 and explore their galactic features by analysing the lensing angle profiles in f(R) background. We also contrast the magnitudes of f(R) lensing angle profiles and the relevant parameters of such galaxies with the generalised pseudo-isothermal galaxy halo model and find consistency.

Bal Yadav

Light deflection angle through velocity profile of galaxies in f(R) model

An attempt has been made to explore the geometric effects of f(R) action on the galactic dynamics under the weak field approximation. The rotational velocity is calculated beyond the Einstein’s geometric theory of gravity. It is inspired by the cosmological geometric relation obtained in the power-law f(R) gravity model in vacuum. We analyse the action with a small positive deviation from the Einstein–Hilbert gravity action (taking R as $$f(R)\propto R^{1+\delta }$$ <math><mrow><mi>f</mi><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow><mo>∝</mo><msup><mi>R</mi><mrow><mn>1</mn><mo>+</mo><mi>δ</mi></mrow></msup></mrow></math> ) at the galactic scales for the explanation of the flatness paradox associated with the clustered galactic dark matter. We obtain the contribution of a dynamical f(R) cosmological background geometry on accelerating the test mass. Furthermore, the integrated effective acceleration of the test mass due to a massive spherically symmetric source in f(R) background is calculated via the study of geodesics for the suitable spacetime metric and an equation for the effective rotational velocity has been developed. We test the viability of the proposed model by tracing the motion of a test mass far from the disk of galactic matter for smaller $$\delta $$ <math><mi>δ</mi></math> . The possible galactic rotational velocity curves in f(R) background are discussed for the formula obtained with $$\delta&lt;&lt; 1$$ <math><mrow><mi>δ</mi><mo>&lt;</mo><mo>&lt;</mo><mn>1</mn></mrow></math> . We also obtain constraints on $$\delta $$ <math><mi>δ</mi></math>  $$O(10^{-6})$$ <math><mrow><mi>O</mi><mo>(</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup><mo>)</mo></mrow></math>  confirmed by observations.

Extended galactic rotational velocity profiles in f(R) gravity background