Cosmological Constraints on Minimal Cubic Galileon Models in Teleparallel Gravity
Cubic Galileon cosmological models provide a well-motivated framework for investigating late-time cosmic acceleration beyond the standard $Λ$CDM paradigm. In this work, we study observational constraints on cubic Galileon models within the teleparallel gravity framework, where deviations from the standard teleparallel equivalent of general relativity are encoded through the model parameter $b_1$. We consider two scalar-field potentials, namely quadratic and exponential potentials, and analyze four representative scenarios: quadratic and exponential potentials with $b_1$ treated as a free parameter, together with the corresponding cases in which $b_1=2$ is fixed. Using the $\text{Pantheon}^+$ Type Ia supernova sample, cosmic chronometer measurements, SH0ES information, and baryon acoustic oscillation data, we constrain the cosmological and model parameters and compare the observational viability of the different scenarios. We find that the considered teleparallel cubic Galileon models can accommodate the late-time expansion history, although the statistical preference depends on the choice of potential and on whether $b_1$ is fixed or varied. In particular, the fixed-$b_1$ model with a quadratic potential provides the most competitive fit among the Galileon scenarios when BAO data are included, showing a lower $χ^2_{\min}$ than $Λ$CDM and comparable support according to the AIC criterion. However, the BIC criterion continues to favor the minimal $Λ$CDM model because of the larger parameter space of the extended models. These results suggest that teleparallel cubic Galileon cosmologies remain phenomenologically viable, while a stronger claim regarding the Hubble tension requires further consistency tests.