Universal Bound on $N$-Point Correlations from Inflation

Universal Bound on $N$ -Point Correlations from Inflation

Kendrick M. Smith, Marilena LoVerde, and Matias Zaldarriaga

Phys. Rev. Lett. 107, 191301 – Published 4 November 2011

Abstract

Models of inflation in which non-Gaussianity is generated outside the horizon, such as curvaton models, generate distinctive higher-order correlation functions in the cosmic microwave background and other cosmological observables. Testing for violation of the Suyama-Yamaguchi inequality $τ_{N L} \geq (\frac{6}{5} f_{N L})^{2}$ , where $f_{N L}$ and $τ_{N L}$ denote the amplitude of the three-point and four-point functions in certain limits, has been proposed as a way to distinguish qualitative classes of models. This inequality has been proved for a wide range of models, but only weaker versions have been proved in general. In this Letter, we give a proof that the Suyama-Yamaguchi inequality is always satisfied. We discuss scenarios in which the inequality may appear to be violated in an experiment such as Planck and how this apparent violation should be interpreted.

Received 13 August 2011

DOI:https://doi.org/10.1103/PhysRevLett.107.191301

Authors & Affiliations

Kendrick M. Smith¹, Marilena LoVerde², and Matias Zaldarriaga²

¹Princeton University Observatory, Peyton Hall, Ivy Lane, Princeton, New Jersey 08544, USA
²Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540, USA