  We examine the class of initial conditions which give rise to inflation. Our
analysis is carried out for several popular models including: Higgs inflation,
Starobinsky inflation, chaotic inflation, axion monodromy inflation and
non-canonical inflation. In each case we determine the set of initial
conditions which give rise to sufficient inflation, with at least $60$
e-foldings. A phase-space analysis has been performed for each of these models
and the effect of the initial inflationary energy scale on inflation has been
studied numerically. This paper discusses two scenarios of Higgs inflation: (i)
the Higgs is coupled to the scalar curvature, (ii) the Higgs Lagrangian
contains a non-canonical kinetic term. In both cases we find Higgs inflation to
be very robust since it can arise for a large class of initial conditions. One
of the central results of our analysis is that, for plateau-like potentials
associated with the Higgs and Starobinsky models, inflation can be realised
even for initial scalar field values which lie close to the minimum of the
potential. This dispels a misconception relating to plateau potentials
prevailing in the literature. We also find that inflation in all models is more
robust for larger values of the initial energy scale.
