Initial conditions for hybrid inflation
  In hybrid inflation models, typically only a tiny fraction of possible initial conditions give rise to successful inflation, even if one assumes spatial homogeneity. We analyze some possible solutions to this initial conditions problem, namely assisted hybrid inflation and hybrid inflation on the brane. While the former is successful in achieving the onset of inflation for a wide range of initial conditions, it lacks sound physical motivation at present. On the other hand, in the context of the presently much discussed brane cosmology, extra friction terms appear in the Friedmann equation which solve this initial conditions problem in a natural way. 
Luis E Mendes and Andrew R Liddle