Vacuum fluctuations in the inflaton field driving chaotic inflation with a quadratic potential give a red spectrum of primordial density perturbations , n = 0.97 .
However angular fluctuations in an O ( N ) -symmetric quadratic potential have a very nearly scale-invariant spectrum , n = 0.9998 .
We investigate the possibility that these isocurvature field perturbations could give the dominant contribution to the primordial density perturbation after inflation .