Propagator positivity bounds for cosmological correlators

TL;DR

The paper develops a de Sitter EFT framework for heavy fields driving cosmological correlators and derives an infinite tower of two-sided positivity bounds on EFT coefficients from unitarity and causality in the in-in formalism. It casts the de Sitter self-energy in a spectral representation, yielding constraints on combinations g_n of the spectral density and linking them to the EFT parameters c_n and gamma_n, with careful treatment of the mass-gap absence. The authors test these bounds against explicit UV completions (tree-level mixing, one-loop bubble, two-loop sunset) and discuss convergence, bounded regions in parameter space, and implications for cosmological collider signals and primordial non-Gaussianity. The work also highlights a positive-geometry perspective akin to the EFThedron, suggesting a principled, geometry-driven characterization of allowed EFTs in cosmology and outlining future directions for tightening bounds and extending to more general cosmological settings.

Abstract

Using unitarity and causality, we derive an infinite tower of two-sided positivity bounds on the effective field theory coefficients which describe the propagation of heavy fields on de Sitter spacetime. We design this EFT to describe propagators with the in-in boundary conditions that are relevant for cosmological correlators. Our positivity bounds therefore identify EFT correlators that can never emerge from a consistent underlying model of inflation. This implies non-trivial constraints on primordial non-Gaussianity; for instance the cosmological collider oscillations in the squeezed bispectrum from the exchange of a heavy scalar are tied to the shape of its EFT background.

Figures (3)

• Figure 1: Our positivity bounds \ref{['eqn:pos']} forbid EFT coefficients in the grey region, for which there is no unitary/causal UV completion. We verify that a number of explicit UV completions---the interactions $\phi \chi$, $\phi \chi^2$ and $\phi \chi^3$ with a heavy field $\chi$ in different spatial dimensions $d$---produce EFTs that lie in the allowed region. The largest region from the $\phi \chi^2$ interaction occurs in $d=1$, and we show with a dashed red line the $d=3$ region for comparison.
• Figure 2: The region of EFT parameter space traced out by the one-loop bubble in $d=3$ dimensions as the cut-off $\Lambda$ and mass $\mu$ are varied. Different values of $\Lambda/\mu$ are coloured so that all $\Lambda > \mu$ are displayed as red. Black lines show contours of $\mu = 1, 2$ and $4$. The boundary ABCD is described analytically in the text.
• Figure 3: The relative size of the first 25 terms appearing in the EFT expansion $\rho = \sum_n \pi \gamma_n' \nu^{2n+1}$ of the one-loop bubble in $d=2$, with $\mu=5$ and $\nu = 1, 4, 7, 10, 13$. For $\nu \leq 1$, the terms strictly decrease and the EFT can be truncated at any order. For $1 \leq \nu < 2 \mu =10$, the largest contribution comes from a finite $n$ and thus the EFT series only provides a reliable approximation if sufficiently many terms are included. For $\nu \geq \sqrt{ 4\mu^2 + 1 } \approx 10.05$, the terms become increasingly negative at large $n$ and the series does not converge.