On local inflation and cosmolagical perturbations

Abstract

It is known that a scale free spectrum of the density perturbations gives appropriate initial conditions for the structure formation in the universe. In this thesis, we determine the power spectrum of the density perturbations entering into a local patch of inflating region embedded in a radiation dominated Robertson-Walker universe. Generally, the physical wavelengths of these perturbations exceed the Hubble radius upon entrance, therefore, their amplitudes freeze out immediately. The corresponding power spectrum turns out to be scale dependent which may point out a conflict with the observations in scenarios using local inflation.