Inflation in Flatland

TL;DR

This paper explores the unique infinite-dimensional symmetry structure of 2+1 dimensional inflationary models, revealing new soft theorems and constraints on correlation functions linked to the conformal symmetries of de Sitter space slices.

Contribution

It demonstrates the correspondence between asymptotic symmetries and adiabatic modes in 2+1 dimensions, deriving new soft theorems specific to this setting.

Findings

Infinite-dimensional Virasoro symmetry algebra in 2+1D inflation.

New soft theorems constraining inflationary correlation functions.

Verification of soft theorem at order q^2 in small sound speed limit.

Abstract

We investigate the symmetry structure of inflation in 2+1 dimensions. In particular, we show that the asymptotic symmetries of three-dimensional de Sitter space are in one-to-one correspondence with cosmological adiabatic modes for the curvature perturbation. In 2+1 dimensions, the asymptotic symmetry algebra is infinite-dimensional, given by two copies of the Virasoro algebra, and can be traced to the conformal symmetries of the two-dimensional spatial slices of de Sitter. We study the consequences of this infinite-dimensional symmetry for inflationary correlation functions, finding new soft theorems that hold only in 2+1 dimensions. Expanding the correlation functions as a power series in the soft momentum $q$, these relations constrain the traceless part of the tensorial coefficient at each order in $q$ in terms of a lower-point function. As a check, we verify that the ${\cal O}(q^2)$ identity is satisfied by inflationary correlation functions in the limit of small sound speed.