Growth of inflaton perturbations and the post-inflation era in supersymmetric hybrid inflation models

Abstract

It has been shown that hybrid inflation may end with the formation of non-topological solitons of the inflaton field. As a first step towards a fully realistic picture of the post-inflation era and reheating in supersymmetric hybrid inflation models, we study the classical scalar field equations of a supersymmetric hybrid inflation model using a semianalytical ansatz for the spatial dependence of the fields. Using the minimal D-term inflation model as an example, the inflaton field is evolved using the full 1-loop effective potential from the slow-rolling era to the ${U(1)}_{\mathrm{FI}}$ symmetry-breaking phase transition. Spatial perturbations of the inflaton corresponding to quantum fluctuations are introduced for the case where there is spatially coherent ${U(1)}_{\mathrm{FI}}$ symmetry breaking. The maximal growth of the dominant perturbation is found to depend only on the ratio of superpotential coupling $\ensuremath{\lambda}$ to the gauge coupling g. The inflaton condensate fragments to non-topological solitons for $\ensuremath{\lambda}/g\ensuremath{\gtrsim}0.09.$ The possible consequences of nontopological soliton formation in fully realistic supersymmetric hybrid inflation models are discussed.