Reconstructing the Expansion History of the Universe in Galileon Gravity

ABSTRACT The late‐time dynamics of the Universe are studied in Galileon gravity by employing a model‐independent deceleration parametrization of the form , which allows a versatile reconstruction of the expansion history without assuming any specific dark‐energy scenario. Using the derived analytic , we conduct a Bayesian MCMC study combining 31 cosmic‐chronometer measurements, DESI DR2 BAO distances and three principal Type Ia supernova compilations: Pantheon+ DES‐SN5Y, and Union 3. The results from the joint datasets produce consistent estimates: , , . The transition redshift falls within and all deceleration parameter reconstructions approach at late times, indicating a de Sitter–like expansion phase. Analysis of the Galileon dark‐energy component shows that remains positive, is negative and asymptotically approaches , with a current value of . Energy‐condition indicate that NEC and DEC hold, while SEC violation occurs, as expected in a cosmos undergoing acceleration. Statefinder diagnostics place the model in the quintessence regime. Predictions for the present‐day age of the Universe, Gyr, are consistent with the Planck measurements. Taken together, the strong concordance with high‐precision observational data indicates that the Galileon deceleration parametrization is a robust and observationally sound model for describing late‐time cosmic evolution.