Inflation in Flatland
arXiv:1609.09497 · doi:10.1088/1475-7516/2017/01/044
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 , these relations constrain the traceless part of the tensorial coefficient at each order in in terms of a lower-point function. As a check, we verify that the identity is satisfied by inflationary correlation functions in the limit of small sound speed.
27 pages. v2: Minor corrections, version to appear in JCAP
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