CMB from CFT

TL;DR

This paper demonstrates that conformal symmetry in de Sitter space uniquely constrains the three-point correlation function involving two scalar and one tensor mode during inflation, providing a test for conformal invariance in the inflaton sector.

Contribution

It shows that conformal symmetry determines the scalar-scalar-tensor three-point function in single field inflation, highlighting the role of special conformal transformations.

Findings

The three-point function is uniquely fixed by conformal symmetry.

Special conformal transformations are crucial in the analysis.

The result offers a way to test conformal invariance during inflation.

Abstract

During inflation, spacetime is approximately described by de Sitter space which is conformally invariant with the symmetry group SO(1,4). This symmetry can significantly constrain the quantum perturbations which arise in the inflationary epoch. We consider a general situation of single field inflation and show that the three point function involving two scalar modes and one tensor mode is uniquely determined, up to small corrections, by the conformal symmetries. Special conformal transformations play an important role in our analysis. Our result applies only to models where the inflaton sector also approximately preserves the full conformal group and shows that this three point function is a good way to test if special conformal invariance was preserved during inflation.