  In the present work, the observational consequences of a subclass of of the
Horndeski theory have been investigated. In this theory a scalar field (tachyon
field) non-minimally coupled to the Gauss-Bonnet invariant through an arbitrary
function of the scalar field. By considering a spatially flat FRW universe, the
free parameters of the model have been constrained using a joint analysis from
observational data of the Type Ia supernovae and Baryon Acoustic Oscillations
measurements. The best fit values obtained from these datasets are then used to
reconstruct the equation of state parameter of the scalar field. The results
show the phantom, quintessence and phantom divide line crossing behavior of the
equation of state and also cosmological viability of the model.
