On the Asymptotic Nature of Cosmological Effective Theories

TL;DR

This work reveals that cosmological effective field theories (EFTs) on expanding backgrounds exhibit factorial growth in the contributions of high-dimension operators, rendering the EFT expansion typically asymptotic rather than convergent. By examining toy models in de Sitter space, the authors show that meaningful predictions can be extracted through resummation techniques such as Mittag-Leffler and Mellin-space methods, with strict matching to the UV theory in the non-dynamical heavy-field case. In the zero sound speed scenario, EFT resummation captures only local dynamics and omits nonlocal UV terms unless boundary data from the UV completion are included; Mellin-space resummation offers an alternative, convergent path but introduces contour ambiguities tied to boundary conditions of the heavy field. The results provide quantitative expectations for general cosmological EFTs and highlight the need for cosmology-native power counting and boundary-aware matching to account for nonlocal UV physics in time-dependent backgrounds.

Abstract

Much of our intuition about Effective Field Theories (EFTs) stems from their formulation in flat spacetime, yet EFTs have become indispensable tools in cosmology, where time-dependent backgrounds are the norm. In this work, we demonstrate that in spacetimes undergoing significant expansion-such as accelerated FLRW and de Sitter backgrounds-the contributions of operators with mass dimension $Δ$ to physical observables grow factorially with $Δ$ at fixed couplings. This behavior stands in stark contrast to static flat spacetime. As a result, the cosmological EFT expansion is generally asymptotic rather than convergent, even at tree level. To illustrate this phenomenon, we analyze simple toy models involving a massless or conformally coupled scalar field interacting with a heavy scalar with zero or infinite sound speed. We demonstrate that meaningful EFT predictions can still be extracted via appropriate resummation techniques, performed in both Fourier and Mellin-momentum space. In the infinite sound speed limit, where the heavy field is effectively non-dynamical, the resummed EFT reproduces the exact result of the full theory. In other cases, the EFT captures only the local part of the dynamics, omitting nonlocal terms, which are exponentially suppressed in the large-mass limit for the Bunch-Davies state. Our results provide detailed and quantitative expectations for more general cosmological EFTs.

Figures (1)

• Figure 1: (Left) For any term in the series \ref{['eq:Mellin formal sum']} of integrals, any complex linear combination of the contours in the figure gives the same value to the integral, as long as the coefficients sum to $1$. The region of convergence of the series of Mellin integrands is illustrated by the dashed circle. (Right) New poles are produced by summing the series of Mellin integrands. Depending on the coefficients of the contours on the left, the red poles' residues can be added to the value of the resummed integral.