Reconstructing features of the inflationary scattering potential from primordial power spectra

Abstract

It is widely believed that the large scale structures in our present Universe have originated from quantum mechanical fluctuations of a scalar field dur- ing an inflationary epoch in the early Universe. According to the inflationary scenario, the phenomenon of super-adiabatic amplification is responsible for generating these large scale structures. This phenomenon can be viewed as a quantum mechanical scattering by a potential barrier in the early Universe, which we call the inflationary scattering potential. There has been a lot of work on reconstructing the scalar inflaton potential using the observed spectrum of initial perturbations. However, this is the first attempt at recovering the related initial scattering potential which is model independent characterization of the inflationary scenario in terms of super- adiabatic amplification phenomenon. We are not presently in a position where there is a well established fundamental inflationary theory. In the absence of a single distinguished inflationary model it may be wiser to characterize and constrain inflation in terms of the model independent scattering potential. We begin with a quick review of the standard cosmology and motivations of inflation. We analyze various problems the standard model is facing with and explain how the inflationary scenario resolves the problems of the Hot Big Bang Universe. Then we study in more details the dynamics of the inflaton field, which fills the Universe in the inflationary epoch. This will lead us to study of the relicsfrom inflation and evolution of scales. We also will derive the results giving the form of perturbations produced by inflation. Then we discuss briefly the density power spectrum of the cosmic mi- crowave background (CMB) and the shapes of the spectrum one can observe from the CMB. We explain in detail the Starobinsky’s method for generating steps in the power spectrum by considering a singular inflaton potential. This method can be considered as the framework of this project. We present a method for recovering features of the scattering potential from broken scale-invariant power spectrum. We show the recovery of the effective mass features for toy power spectra. In the future, we plan to recon- struct the inflationary scattering potential features for the real power spectrum determined from WMAP.