Density perturbation for multi-component scalar field in general slow-roll approximation

Abstract

The early universe had to undergo inflation era. Inflation offers an elegant solution to several problems of the Standard Big Bang model. And the density perturbation generated during inflation made the structure formation of the present universe. Recent combined results from the Wilkinson Microwave Anisotropy Probe(WMAP) and Sloan Digital Sky Survey(SDSS) provides a remarkable set of data which requires more accurate and general investigation. So we need to derive formulae for the power spectrum P(k) of the density perturbations produced during inflation in general slow-roll approximation. These formulae can give accurate results in observationally viable cases where the standard formulae would be qualitatively incorrect. The δN formula that relates the final curvature perturbation on comoving slices to the inflaton perturbation on flat slices after horizon crossing is a powerful and intuitive tool to compute the curvature perturbation spectrum from inflation. However, is is customarily assumed further that the conventional slow-roll condition is satisfied during horizon crossing. So we develop a new δN-formalism for multi-component inflation that can be applicable to most general situations and, in particular, that is useful for the situation of general slow-roll inflation. Then we compute the power spectrum of the curvature perturbation in multi-component general slow-roll inflation.