Galileon and generalized Galileon with projective invariance in a metric-affine formalism

Understand

We study scalar-tensor theories respecting the projective invariance in the metric-affine formalism.

• The metric-affine formalism is a formulation of gravitational theories such that the metric and the connection are independent variables in the first place.
• In this formalism, the Einstein-Hilbert action has an additional invariance, called the projective invariance, under a shift of the connection.
• Respecting this invariance for the construction of the scalar-tensor theories, we find that the Galileon terms in curved spacetime are uniquely specified at least up to quartic order which does not coincide with either the covariant Galileon or the covariantized Galileon.