Bayesian optimal reconstruction of the primordial power spectrum

TL;DR

This paper uses Bayesian model selection to reconstruct the primordial power spectrum from WMAP data, finding it prefers a simple spectrum with few features, indicating limited complexity in early universe perturbations.

Contribution

It introduces a Bayesian evidence-based method for optimally reconstructing the primordial power spectrum with minimal features, avoiding overfitting.

Findings

Reconstruction favors only three nodes in the spectrum.

Data suggests a scale-dependent tilt with a turn-over around k ~ 0.016 Mpc^{-1}.

More complex models are disfavored by Bayesian evidence.

Abstract

The form of the primordial power spectrum has the potential to differentiate strongly between competing models of perturbation generation in the early universe and so is of considerable importance. The recent release of five years of WMAP observations have confirmed the general picture of the primordial power spectrum as deviating slightly from scale invariance with a spectral tilt parameter of n_s ~ 0.96. Nonetheless, many attempts have been made to isolate further features such as breaks and cutoffs using a variety of methods, some employing more than ~ 10 varying parameters. In this paper we apply the robust technique of Bayesian model selection to reconstruct the optimal degree of structure in the spectrum. We model the spectrum simply and generically as piecewise linear in ln k between `nodes' in k-space whose amplitudes are allowed to vary. The number of nodes and their k-space positions are chosen by the Bayesian evidence so that we can identify both the complexity and location of any detected features. Our optimal reconstruction contains, perhaps, surprisingly few features, the data preferring just three nodes. This reconstruction allows for a degree of scale dependence of the tilt with the `turn-over' scale occuring around k ~ 0.016 Mpc^{-1}. More structure is penalised by the evidence as over-fitting the data, so there is currently little point in attempting reconstructions that are more complex.