CPL-parametrized cosmic expansion in Galileon gravity: Constraints from recent data

We explore the cosmic expansion history within the framework of Galileon gravity by employing a redshift-based expression for the Hubble rate, $H(z)$, derived from the CPL parametrization $\omega_{DE}(z)=\omega_{0}+\omega_{a}\frac{z}{1+z}$. This parametrization allows for a time-dependent expansion history consistent with the non-linear Galileon field equations. To constrain the model parameters, we perform a MCMC analysis using $46$ Hubble parameter measurements, DESI DR2 BAO data and $1701$ Pantheon+ datasets. The best fit values obtained are $H_0 = 67.7043^{+1.4354}_{-1.4102}$ km/s/Mpc, $\Omega_{m0} = 0.2668^{+0.0212}_{-0.0217}$, $\omega_0 = -0.8827^{+0.1076}_{-0.0967}$ and $\omega_a = 0.0011^{+0.0660}_{-0.0622}$. Model comparison using information criteria yields $\Delta AIC=1.46$ and $\Delta BIC = 11.5$ indicating that the Galileon model is a strong contender to the $\Lambda$CDM model. The deceleration parameter shows a transition at $z_{tr} = 0.7873$, with $q_0 = -0.598$. Energy density and pressure remain physically viable with $\rho_{de}(z)>0$ and $p_{de}(z)<0$ with the present day equation of state $\omega(z)$ value of $-0.2915$, which suggests mild dynamical dark energy. NEC and DECare satisfied, while SEC is violated. The model yields $r_{0}=0.657$, $s_{0}=0.1173$ and Om diagnostic shows a peak value of $-0.45$ at $z = 0.377$, converging to $-1$ at late times.These results demonstrate that Galileon gravity remains a viable and flexible alternative to $\Lambda$CDM in describing late-time cosmic acceleration.