Inflationary Correlation Functions without Infrared Divergences

          @misc{ pirsa_PIRSA:10100064,
            doi = {10.48660/10100064},
            url = {https://pirsa.org/10100064},
            author = {Hebecker, Arthur},
            keywords = {Cosmology},
            language = {en},
            title = {Inflationary Correlation Functions without Infrared Divergences},
            publisher = {Perimeter Institute},
            year = {2010},
            month = {oct},
            note = {PIRSA:10100064 see, \url{https://pirsa.org}}
          }
          

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.