Healthy Horndeski cosmologies with torsion

We show that the full Horndeski theory with both curvature and torsion can support nonsingular, stable and subluminal cosmological solutions at all times. Thus, with torsion, the usual No-Go theorem that holds in a curved spacetime is avoided. In particular, it is essential to include the nonminimal derivative couplings of the $\mathcal{L}_{5}$ part of the Horndeski action ($G^{\mu\nu}\,\nabla_\mu \nabla_\nu \phi,$ and $(\nabla^2 \phi)^3$). Without the latter a No-Go already impedes the eternal subluminality of nonsingular, stable cosmologies.