Probing the origin of large inhomogeneities in inflation using a toy quantum mechanical model

Abstract

We study the quantum evolution of the homogeneous mode of a scalar field with simple potentials in Robertson-Walker spacetime. The simplicity of the model allows one to work out the exact quantum evolution of a wave packet. The model mimics the inflationary scenario quite well and is used to study the nature and origin of various constraints. We conclude that any model in which (i) the potential has only a single energy scale (10¹⁴ –10¹⁵ GeV) and dimensionless parameters of order unity and (ii) the inflationary phase is endowed with a minimum temperature of (H/2π) will produce density inhomogeneity which is too large.