DESI DR2 Constraints on the $R_h=ct$ Universe: Model Viability and Comparison with $Λ$CDM

Abstract: We carry out a comparative analysis of the standard $Λ$CDM cosmological model and the alternative $R_h=ct$ framework using recent observational data from cosmic chronometers, Type Ia supernova, and baryon acoustic oscillations. The study evaluates the ability of each model to reproduce the observed expansion history of the Universe through a joint statistical assessment based on the chi-squared statistics, Akaike Information Criterion (AIC), Bayesian Information Criteria (BIC), and Bayes factor. While both models yield acceptable fits, $Λ$CDM consistently attains lower information-criterion values and higher likelihood, indicating a superior overall performance. An examination of the redshift evolution of the Hubble parameter $H(z)$ and the deceleration parameter $q(z)$ shows that $Λ$CDM naturally captures the transition from early-time deceleration to late-time acceleration, where as $R_h=ct$ predicts a strictly linear expansion. We also estimate the age of the Universe within both models, finding that $Λ$CDM prediction agrees with the Planck 2018 result, while the linear expansion in $R_h=ct$ leads to an older cosmic age. Recent JWST observations of unexpectedly mature high-redshift galaxies have reopened the discussion regarding whether the Universe may be older than implied by the standard model; although these results remain under active investigation, they underscore that fully resolving cosmic evolution may require refinements beyond the concordance paradigm.