Who You Gonna Call? Runaway Ghosts, Higher Derivatives and Time-Dependence in EFTs

TL;DR

The paper addresses how EFTs behave in time-dependent settings and what constrains their validity. It presents a general argument via generating functionals showing that EFT backgrounds extremize the full action and thus inherit full-theory solutions order-by-order in the heavy-mass expansion, complemented by a concrete toy model in which integrating out a heavy field yields higher-derivative EFT terms. It then explains why apparent runaway solutions do not reflect UV physics within the EFT's regime, using a simple higher-derivative toy Lagrangian to illustrate non-adiabatic modes that lie beyond the EFT's applicability. The work underscores adiabatic time dependence as the mechanism enabling EFTs to describe fluctuations around time-dependent backgrounds and discusses special cases such as DBI/Horndeski/Lovelock-like structures as potential, but non-generic, exceptions. This clarifies the reliability and limits of time-dependent EFTs in cosmology and driven systems, guiding when higher-derivative terms can be trusted and how to interpret them.

Abstract

We briefly review the formulation of effective field theories (EFTs) in time-dependent situations, with particular attention paid to their domain of validity. Our main interest is the extent to which solutions of the EFT capture the dynamics of the full theory. For a simple model we show by explicit calculation that the low-energy action obtained from a sensible UV completion need not take the restrictive form required to obtain only second-order field equations, and we clarify why runaway solutions are nevertheless typically not a problem for the EFT. Although our results will not be surprising to many, to our knowledge they are only mentioned tangentially in the EFT literature, which (with a few exceptions) largely addresses time-independent situations.