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 $H_0=67.7043_{-1.4102}^{+1.4354}$ km/s/Mpc, ${\mathrm{\Omega }}_{m0}=0.2668_{-0.0217}^{+0.0212}$, ${\omega }_0=-0.8827_{-0.0967}^{+0.1076}$ and ${\omega }_a=0.0011_{-0.0622}^{+0.0660}$. Model comparison using information criteria yields $\mathrm{\Delta }AIC=1.46$ and $\mathrm{\Delta }BIC=11.5$ indicating that the Galileon model is a strong contender to the $\mathrm{\Lambda }$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 $\mathrm{\Lambda }$CDM in describing late-time cosmic acceleration.