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.
Highlights
It is remarkable how much physics can sometimes be derived from just a few basic principles
The cosmological bootstrap exploits the approximate de Sitter symmetries — which act as conformal transformations on the boundary [8,9,10,11,12] — along with consistency requirements on the singularity structure of correlation functions to reconstruct the output of bulk time evolution without ever talking about time
We show that the soft limit of these correlators with weakly perturbed scaling dimension leads to inflationary three-point functions
Summary
It is remarkable how much physics can sometimes be derived from just a few basic principles. We show that the lift to embedding space provides an elegant way to derive and generalize the cosmological weightshifting operators found in [1] This new viewpoint clarifies the fact that all inflationary correlators can be obtained from a unique seed function corresponding to the exchange of a scalar particle and streamlines its derivation from the boundary perspective. We present the de Sitter four-point function of conformally coupled scalars, arising from the tree-exchange of a generic scalar This solution is the essential building block from which all other correlators will be derived via the action of suitable differential operators.
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