A metric-affine version of the Horndeski theory

Understand

We study the metric-affine versions of scalar-tensor theories whose connection enters the action only algebraically.

• We show that the connection can be integrated out in this case, resulting in an equivalent metric theory.
• Specifically, we consider the metric-affine generalisations of the subset of the Horndeski theory whose action is linear in second derivatives of the scalar field.
• We determine the connection and find that it can describe a scalar-tensor Weyl geometry without a Riemannian frame.