Abstract
We motivate inflationary scenarios with many scalar fields, and give a complete formulation ofadiabatic and entropy perturbations. We find that if the potential is very flat, or if the theory hasa SO(N) symmetry, the calculation of the fluctuation spectrum can be carried out in terms of merelytwo variables without any further assumption. We do not have to assume slow roll orSO(N) invariance for the background fields. We give some examples to show that, even if the slowroll assumption holds, the spectrum of fluctuations can be quite different from the casewhen there is a single inflaton.
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