Non-Gaussianities in single field inflation and their optimal limits from the WMAP 5-year data

Abstract

Using the recently developed effective field theory of inflation, we argue that the size and the shape of the non-Gaussianities generated by single-field inflation are generically well described by two parameters: f NL equil , which characterizes the size of the signal that is peaked on equilateral configurations, and f NL orthog , which instead characterizes the size of the signal which is peaked both on equilateral configurations and flat-triangle configurations (with opposite signs). The shape of non-Gaussianities associated with f NL orthog is orthogonal to the one associated to f NL equil , and former analysis have been mostly blind to it. We perform the optimal analysis of the WMAP 5-year data for both of these parameters. We find no evidence of non-Gaussianity, and we have the following constraints: −125 ⩽ f NL equil ⩽ 435, −369 ⩽ f NL orthog ⩽ 71 at 95% CL. We show that both of these constraints can be translated into limits on parameters of the Lagrangian of single-field inflation. For one of them, the speed of sound of the inflaton fluctuations, we find that it is either bounded to be c s ⩾ 0.011 at 95% CL. or alternatively to be so small that the higher-derivative kinetic term dominate at horizon crossing. We are able to put similar constraints on the other operators of the inflaton Lagrangian.