The Cosmological Bootstrap: Weight-Shifting Operators and Scalar Seeds

TL;DR

This paper develops a systematic method using conformal field theory tools to derive weight-raising and spin-raising operators, simplifying the calculation of cosmological correlators in the bootstrap approach.

Contribution

It introduces a streamlined, systematic derivation of operators for computing cosmological correlators, enhancing the theoretical framework of the bootstrap program.

Findings

Simplified derivation of weight-raising and spin-raising operators.

Unified framework for scalar and spinning particle correlators.

Enhanced computational efficiency for cosmological bootstrap calculations.

Abstract

A key insight of the bootstrap approach to cosmological correlations is the fact that all correlators of slow-roll inflation can be reduced to a unique building block---the four-point function of conformally coupled scalars, arising from the exchange of a massive scalar. Correlators corresponding to the exchange of particles with spin are then obtained by applying a spin-raising operator to the scalar-exchange solution. Similarly, the correlators of massless external fields can be derived by acting with a suitable weight-raising operator. In this paper, we present a systematic and highly streamlined derivation of these operators (and their generalizations) using tools of conformal field theory. Our results greatly simplify the theoretical foundations of the cosmological bootstrap program.