Seeding of Primordial Perturbations During a Decelerated Expansion

A scalar field with a modified dispersion relation may seed, under certain conditions, the primordial perturbations during a decelerated expansion. In this note we examine whether and how these perturbations can be responsible for the structure formation of observable universe. We discuss relevant difficulties and possible solutions.
Comment: 5 pages, 3 figures, more details and clarifications added, refs. added, new version with 6 pages has been splitted into various sections, to be published in PRD, v3, matched to published version