Scale-invariant perturbations from chaotic inflation

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 $\mathrm{O}(\mathrm{N})$-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.