Limits on non-Gaussianities from WMAP data

Abstract

We develop a method for constraining the level of non-Gaussianity of density perturbationswhen the three-point function is of the ‘equilateral’ type. Departures from Gaussianity ofthis form are produced by single field models such as ghost or Dirac–Born–Infeld inflationand in general by the presence of higher order derivative operators in the effectiveLagrangian of the inflaton. We show that the induced shape of the three-pointfunction can be very well approximated by a factorizable form, making the analysispractical. We also show that, unless one has a full sky map with uniform noise, inorder to saturate the Cramer–Rao bound for the error on the amplitude of thethree-point function, the estimator must contain a piece that is linear in the data. Weapply our technique to the WMAP data obtaining a constraint on the amplitudefNLequil of ‘equilateral’non-Gaussianity: −366 < fNLequil < 238 at 95% C.L. We also apply our technique to constrain the so-called ‘local’ shape, which is predicted forexample by the curvaton and variable decay width models. We show that the inclusion of thelinear piece in the estimator improves the constraint over those obtained by the WMAP team, to−27 < fNLlocal < 121 at 95% C.L.