  In a large region of parameter space, the tree-level hybrid inflation model
is likely to be be invalidated by loop corrections. In particular, this is
likely to be the case if both quartic couplings are of order unity, as is often
supposed. It is likely also to be the case if there is an ultra-violet cutoff
far below the Planck scale, ($\luv\lsim 10^9\GeV(V_0^{1/4}/1\MeV)^{2/5}$, where
$V_0$ is the height of the potential) unless one allows field values bigger
than the cutoff.
