Inflaton condensate fragmentation: Analytical conditions and application
  to $\alpha$-attractor models
  We study the stability of an inflaton condensate in the presence of
attractive inflaton self-interactions, in order to determine analytical
conditions on the self-interaction couplings under which the condensate
undergoes fragmentation. As an application of our results, we consider the
stability of the inflaton condensate in $\alpha$-attractor inflation. We show
that the stability of the condensate depends upon the value of $\alpha$. For
the T-model with $n = 1$, we find that it is unstable for $\alpha \lesssim
10^{-4}$. In this case it is expected that inflation will be followed by an
oscillon-dominated era.
