A Simultaneous Constraint on the Amplitude and Gaussianity of Mass Fluctuations in the Universe

We consider constraints on the amplitude of mass fluctuations in the universe, sigma_8, derived from two simple observations: the present number density of clusters and the amplitude of their correlation function. Allowing for the possibility that the primordial fluctuations are non-gaussian introduces a degeneracy in the value of sigma_8 preferred by each of these constraints. However, when the constraints are taken together this degeneracy is broken, yielding a precise determination of sigma_8 and the degree of non-gaussianity for a given background cosmology. For a flat, Omega_m=1 universe with a power spectrum parameterized by a CDM shape parameter Gamma=0.2, we find that the perturbations are consistent with a gaussian distribution with sigma_8=0.49(+0.08-0.07) (95% limits). For some popular choices of background model, including the favored low matter density models, the hypothesis that the primordial fluctuations are gaussian is ruled out with a high degree of confidence.