Non-Gaussianities in Single Field Inflation and their Optimal Limits
  from the WMAP 5-year Data
  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.
