Inflationary Correlation Functions without Infrared Divergences

TL;DR

This paper introduces infrared-safe inflationary correlation functions that eliminate sensitivity to large-scale observational regions, allowing for clear, resummed calculations of quantum corrections including non-Gaussianity.

Contribution

It defines IR-safe correlation functions in inflationary cosmology, enabling explicit, all-orders resummation of infrared corrections and clarifying their impact on observables.

Findings

Infrared-safe correlators remove dependence on measurement region size.

Explicit all-orders expressions for scalar IR corrections are derived.

Corrections to non-Gaussianity parameter f_NL from tensor modes are calculated.

Abstract

Inflationary correlation functions are potentially affected by infrared divergences. For example, the two-point correlator of curvature perturbation at momentum k receives corrections ~ln(kL), where L is the size of the region in which the measurement is performed. We define infrared-safe correlation functions which have no sensitivity to the size L of the box used for the observation. The conventional correlators with their familiar log-enhanced corrections (both from scalar and tensor long-wavelength modes) are easily recovered from our IR-safe correlation functions. Among other examples, we illustrate this by calculating the corrections to the non-Gaussianity parameter f_NL coming from long-wavelength tensor modes. In our approach, the IR corrections automatically emerge in a resummed, all-orders form. For the scalar corrections, the resulting all-orders expression can be evaluated explicitly.