Joint constraints on $R_h=ct$ cosmology from DESI DR2 BAO, CC, and SN\textit{Ia} Pantheon$^+$ sample
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 (CC), 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 $χ^2$ statistics, Akaike Information Criterion $(AIC)$, Bayesian Information Criterion $(BIC)$, 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, obtaining $t_0^{ΛCDM}= 13.676_{-0.81}^{+0.92}$Gyr and $t_0^{R_h=ct}= 16.035_{-0.98}^{+1.09}$Gyr. The posterior-derived age in the $Λ$CDM framework is broadly consistent with the Planck 2018 CMB result. This agreement is interpreted as a validation of the analysis pipeline and the reliability of the DESI DR2, CC, and supernova constraints, rather than as a new result for $Λ$CDM, and serves as a benchmark for assessing the viability of the $R_h=ct$ model. Recent JWST observations of unexpectedly mature high-redshift galaxies have renewed discussion regarding the timeline of early structure formation; although these results remain under active investigation, they underscore that fully resolving cosmic evolution may require refinements beyond the concordance paradigm.