Positivity from Cosmological Correlators

TL;DR

This paper explores positivity bounds in cosmological correlators, showing they impose constraints on massive fields, anomalous dimensions, and observable signals in upcoming galaxy surveys, extending concepts from flat space quantum field theories.

Contribution

It demonstrates that positivity bounds apply to cosmological correlators, constraining anomalous dimensions and oscillatory signals, and connects these bounds to observable galaxy statistics.

Findings

Real anomalous dimensions for principal series fields in de Sitter are positive.

Limits are derived on the amplitude of inflationary oscillatory signals.

Constraints are shown to impact two-point statistics in upcoming galaxy surveys.

Abstract

Effective field theories in flat space and in anti-de Sitter space are constrained by causality and unitarity, often in the form of positivity bounds. Similar bounds have been harder to demonstrate in cosmological backgrounds, where the roles of unitarity and causality are more obscure. Fortunately, the expansion of the universe ensures that late-time cosmological correlators are effectively classical and the role of unitarity is played by classical statistical inequalities. For multi-field inflation, the resulting positivity constraints have long been known in terms of the Suyama-Yamaguchi inequality. In this paper, we demonstrate that similar statistical bounds imply nontrivial constraints for massive fields in the early universe. We show that any real anomalous dimensions for principal series fields in de Sitter space must be positive. We also derive a limit on the amplitude of oscillatory signals from inflation, including those arising in cosmological collider physics. Finally, we demonstrate that these constraints manifest themselves directly in the two-point statistics of matter and galaxies that will be measured in upcoming surveys.