Inflationary Correlation Functions without Infrared Divergences

Abstract

The definition of correlation functions relies on measuring distances on some late surface of equal energy density. If invariant distances are used, the curvature correlation functions of single-field inflation are free of any IR sensitivity. By contrast, conventional correlation functions, defined using the coordinate distance between pairs of points, receive large IR corrections if measured in a "large box" and if inflation lastet for a sufficiently long period. The underlying large logarithms are associated with long-wavelength fluctuations of both the scalar and the graviton background. This effect is partially captured by the familiar delta-N-formalism. Conventional, IR-sensitive correlation functions are related to their IR-safe counterparts by simple and very general formulae. In particular, the coefficient of the leading logarithmic correction to any n-point function is controlled by the first and second logarithmic derivatives of this function with respect to the overall momentum scale. This allows for a simple evaluation of corrections to leading and higher-order non-Gaussianity parameters.