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arXiv · 2512.13453

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

Eugeny Babichev·Sukŗti Bansal·Maria Mylova·Antonio Padilla
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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.

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Eugeny Babichev, Sukŗti Bansal, Maria Mylova, Antonio Padilla. 2025-12-15. Extending Weinberg's EFT: effective scalar-tensor theories up to sixth order. https://doi.org/10.1007/jhep08(2026)002

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