Testing $f(Q)$ Gravity with DESI DR2 and Strong-Lensing Time Delays

Abstract

Symmetric teleparallel gravity provides an alternative description of gravitation in which non-metricity replaces curvature and torsion. Its extension through $f(Q)$ gravity offers a different geometric description of the late-time expansion of the Universe and its accelerated phase. In this work, we investigate two $f(Q)$ models, a normalized power-law model and a square-root exponential model, and test their ability to describe the late-time expansion history. We constrain the model parameters through Markov chain Monte Carlo analyses using Cosmic Chronometer measurements, DESI DR2 baryon acoustic oscillations, strong-lensing time-delay observations, and three Type Ia supernova compilations, Pantheon$^+$, Union 3.0, and DES Y5. We compare both models with the flat $\Lambda$CDM model using the minimum $\chi^2$, Akaike information criterion, and Bayesian information criterion. The square-root exponential model provides a better statistical fit than $\Lambda$CDM for the combinations of Cosmic Chronometer, DESI DR2, and strong-lensing time-delay data with Pantheon$^+$ and Union 3.0, with improvements in both the goodness of fit and information criteria. The normalized power-law model remains statistically competitive with $\Lambda$CDM for the supernova-inclusive combinations, although the information criteria do not favor its additional parameter. We also determine the transition redshift from cosmic deceleration to acceleration for both models, obtaining consistent values across the different dataset combinations. The transition redshifts agree with observational estimates of the cosmic acceleration epoch. Overall, our results support $f(Q)$ gravity as a viable alternative to $\Lambda$CDM for explaining the late-time accelerated expansion of the Universe without requiring a cosmological constant.