Well-posed initial value formulation of general effective field theories of gravity

TL;DR

This paper proves that polynomial higher-derivative effective field theories of gravity can be reformulated into a well-posed initial value problem using regularising terms, ensuring consistent evolution without fine-tuning.

Contribution

It introduces a method to rewrite higher-derivative gravity theories as second-order nonlinear wave equations with regularising terms, ensuring well-posedness and covariance.

Findings

Applicable to quadratic, cubic, and quartic truncations of gravity EFTs

Regularising terms correspond to massive modes heavier than the cutoff

Formulation remains valid beyond weak coupling regimes

Abstract

We provide a proof that all polynomial higher-derivative effective field theories of vacuum gravity admit a well-posed initial value formulation when augmented by suitable regularising terms. These regularising terms can be obtained by field redefinitions and allow to rewrite the resulting equations of motion as a system of second-order nonlinear wave equations. For instance, our result applies to the quadratic, cubic, and quartic truncations of the effective field theory of gravity that have previously appeared in the literature. The regularising terms correspond to fiducial massive modes, however, their masses can be chosen to be non-tachyonic and heavier than the cutoff scale and hence these modes should not affect the dynamics in the regime of validity of effective field theory. Our well-posed formulation is not limited to the weakly coupled regime of these theories, is manifestly covariant and does neither require fine tuning of free parameters nor involves prescribing arbitrary equations.