Quantum corrected correlation functions and power spectra of spectator scalar and inflaton fields during inflation

Abstract

The inflationary cosmology not only explains apparently mysterious features of the universe like the flatness, horizon, and relic particle abundance problems, but also provides a natural mechanism to produce primordial density fluctuations that eventually lead to the cosmic structure formation. The primordial density perturbations are generated spontaneously from the quantum fluctuations of a scalar field, called inflaton, that drives the inflation. The physical origin of quantum fluctuations is the uncertainty principle that manifests itself as the virtual particle pair production out of vacuum. The observed anisotropies in the cosmic microwave background (CMB) are believed to be the amplified imprints of the fluctuations of an inflaton which later grow, due to gravitational instability, to become galaxies and clusters of galaxies. Variation of the amplitudes of fields with length scales is measured by the spectral index. Predictions of the inflation models for the spectral index and its variation with scale, quantified the by running of the spectral index, can be compared with observations to discriminate between the alternative inflation models. It is, therefore, important to study the correlation function and power spectrum of the quantum fluctuations to understand the distribution and the origin of large scale structure in the universe.