Degenerate higher-order scalar-tensor theories in metric-affine gravity

TL;DR

This paper develops a metric-affine version of quadratic DHOST scalar-tensor theories, analyzing their structure, degeneracy conditions, and implications for gravitational wave propagation.

Contribution

It constructs the metric-affine analogue of quadratic DHOST theories, derives a closed-form effective metric theory, and explores observational constraints from gravitational waves.

Findings

Identifies a Palatini Class Ia branch determined by two free functions.

Shows gravitational wave speed constraints restrict the theory to a one-function family.

Provides a detailed characterization of quadratic metric-affine Class Ia sector.

Abstract

We construct the metric-affine analogue of the quadratic degenerate higher-order scalar-tensor (DHOST) theories. We begin with the metric-affine completion of the quadratic DHOST scalar-tensor action, which is linear in curvature and contains all operators that are at most quadratic in the covariant second derivatives of the scalar field, ensuring that the connection enters only through curvature and these second derivatives. Solving the connection equation by performing a full decomposition of the distortion tensor gives a closed-form effective metric theory. Imposing the standard metric DHOST degeneracy conditions then selects a Palatini Class Ia branch that is fully determined by two free functions in the original action. Analyzing the tensor sector shows that requiring gravitational waves to propagate at the speed of light further restricts the theory to a one-function family. These results provide a detailed and self-contained characterization of the quadratic metric-affine Class Ia sector within this operator basis and identify the theoretical conditions implied by gravitational wave observations.