Extending Weinberg's EFT: effective scalar-tensor theories up to sixth order

TL;DR

This paper systematically constructs the most general six-derivative scalar-tensor theories extending Weinberg's four-derivative framework, providing a comprehensive basis for exploring advanced gravitational phenomena and corrections.

Contribution

It introduces a complete classification of six-derivative scalar-tensor interactions, extending the effective field theory framework to higher derivatives with confirmed operator counting.

Findings

Identifies five parity-even and three parity-odd independent six-derivative interactions.

Provides a basis for next-to-leading-order scalar-tensor gravity theories.

Enables exploration of quantum, stringy, and strong-curvature effects in cosmology and black hole physics.

Abstract

We present a systematic construction of the six-derivative effective scalar-tensor theories, extending the four-derivative framework previously developed by Steven Weinberg. The on-shell effective field theory comprises five parity-even and three parity-odd independent six-derivative scalar-tensor interactions, representing all inequivalent deformations consistent with general covariance. We further confirm this operator counting through an independent analysis using the scattering amplitude formalism in four-dimensional flat spacetime. The six-derivative Lagrangian constructed here provides the next-to-leading-order extension of scalar-tensor gravity, furnishing a robust framework for exploring quantum or stringy corrections, parity-violating interactions, and strong-curvature effects in cosmology, black hole physics and gravitational wave observations.