Reconstructing the inflationary power spectrum from cosmic microwave background radiation data

The cosmic microwave background radiation (CMBR) holds information about almost all the fundamental cosmological parameters, and by performing a likelihood analysis of high precision CMBR fluctuation data, these parameters can be inferred. However, this analysis relies on assumptions about the initial power spectrum, which is usually taken to be a featureless power law, P(k)∝k^nₛ-1. Many inflationary models predict power spectra with non-power-law features. We discuss the possibility for detecting such features by describing the power spectrum as bins in k space. This method for power spectrum reconstruction is demonstrated in practice by performing likelihood optimization on synthetic spectra, and the difficulties arising from reconstructing smooth features using discontinuous bins are discussed in detail.