Helical Inflation Correlators: Partial Mellin-Barnes and Bootstrap Equations

TL;DR

This paper derives analytical formulas for helical inflation correlators involving massive spinning particles, revealing how helicity-dependent chemical potentials can exponentially enhance oscillatory signals, with implications for cosmological collider physics.

Contribution

It provides complete analytical results for 4-point and 3-point inflation correlators with massive spinning particles, using partial Mellin-Barnes and bootstrap methods, extending the de Sitter bootstrap program.

Findings

Chemical potential exponentially enhances oscillatory signals.

Analytical formulas enable efficient phenomenological exploration.

Results verify the cosmological collider cutting rule.

Abstract

Massive spinning particles acquire helicity-dependent chemical potentials during the inflation from axion-type couplings. Such spinning fields can mediate sizable inflaton correlators which we call the helical inflation correlators. Helical inflaton correlators are approximately scale invariant, dS boost breaking, parity-violating, and are promising observables of cosmological collider physics. In this work, we present complete and analytical results for 4-point helical inflation correlators with tree-level exchanges of massive spinning particles, including both the smooth background and the oscillatory signals. We compute the bulk Schwinger-Keldysh integrals in two independent ways, including the partial Mellin-Barnes representation and solving bootstrap equations. We also present new closed-form analytical results for 3-point functions with massive scalar or helical spinning exchanges. The analytical results allow us to concretely and efficiently explore the phenomenological consequences of helicity-dependent chemical potentials. In particular, we show that the chemical potential can exponentially enhance oscillatory signals of both local and nonlocal types, but only affects the background in a rather mild way. Our results extend the de Sitter bootstrap program to include nonperturbative breaking of de Sitter boosts. Our results also explicitly verify the recently proposed cutting rule for cosmological collider signals.