Horndeski: beyond, or not beyond?

Understand

Determining the most general, consistent scalar tensor theory of gravity is important for building models of inflation and dark energy.

• In this work we investigate the number of degrees of freedom present in the theory of beyond Horndeski.
• We discuss how to construct the theory from the extrinsic curvature of the constant scalar field hypersurface, and find a simple expression for the action which guarantees the existence of the primary constraint necessary to avoid the Ostrogradsky instability.
• Our analysis is completely gauge-invariant.