Reviving Horndeski theory using teleparallel gravity after GW170817

Horndeski gravity was highly constrained from the recent gravitational wave observations by the LIGO Collaboration down to vertical bar c(g)/c - 1 vertical bar greater than or similar to 10(-15). In this paper, we study the propagation of gravitational waves in a recently proposed model of Horndeski gravity in which its teleparallel gravity analog is formulated. As usually done in these analyses, we consider a flat cosmological background in which curvature is replaced by torsion as the expression of gravitation. It is found that in this approach, one can construct a more general Horndeski theory satisfying c(T) = c(g)/c = 1 without eliminating the coupling functions G(5)(phi, X) and G(4)(phi, X) that were highly constrained in standard Horndeski theory. Hence, in the teleparallel approach one is able to restore these terms, creating an interesting way to revive Horndeski gravity. In this way, we retain the original spirit of Horndeski gravity (unlike beyond Horndeski theories) while only changing the form in which the geometry of gravitation is expressed.