Reconstructing the primordial power spectrum from the CMB

TL;DR

This paper introduces a model-independent method to analyze the sensitivity of CMB experiments to features in the primordial power spectrum, providing a detailed understanding of what can be reconstructed from data.

Contribution

It develops a function space generalization of the Fisher matrix formalism to characterize the detectability of primordial spectrum features in CMB data.

Findings

Quantifies the statistical significance of reconstructing features in the primordial spectrum.

Analyzes the information content of CMB data regarding primordial spectrum irregularities.

Provides a framework for assessing the sensitivity of future experiments to primordial features.

Abstract

We propose a straightforward and model independent methodology for characterizing the sensitivity of CMB and other experiments to wiggles, irregularities, and features in the primordial power spectrum. Assuming that the primordial cosmological perturbations are adiabatic, we present a function space generalization of the usual Fisher matrix formalism, applied to a CMB experiment resembling Planck with and without ancillary data. This work is closely related to other work on recovering the inflationary potential and exploring specific models of non-minimal, or perhaps baroque, primordial power spectra. The approach adopted here, however, most directly expresses what the data is really telling us. We explore in detail the structure of the available information and quantify exactly what features can be reconstructed and at what statistical significance.