Combining power spectrum and bispectrum measurements to detect oscillatory features

TL;DR

This paper develops a combined analysis method for power spectrum and bispectrum data to improve the detection of oscillatory features in the primordial density perturbations, enhancing the ability to test early Universe models.

Contribution

It introduces an optimal amplitude estimator for combined spectrum and bispectrum searches and models the statistical significance of potential feature detections.

Findings

Estimates of feature amplitudes from power spectrum and bispectrum are largely independent under Gaussian assumptions.

The proposed combined estimator improves detection sensitivity for oscillatory features.

Analytic models for amplitude estimate distributions enable reliable significance assessments.

Abstract

The simplest inflationary models present us with few observable parameters to discriminate between them. A detection of features in the spectra of primordial density perturbations could provide valuable insights and lead to stringent tests of models of the early Universe. So far, searches for oscillatory features have not produced statistically significant results. In this work we consider a combined search for features in the power spectrum and bispectrum. We show that possible dependencies between the estimates of feature model amplitudes based on the two- and three-point correlators are largely statistically independent under the assumption of the null hypothesis of a nearly Gaussian featureless CMB. Building on this conclusion we propose an optimal amplitude estimator for a combined search and study the look-elsewhere effect in feature model surveys. In particular we construct analytic models for the distribution of amplitude estimates that allow for a reliable assessment of the significance of potential findings. We also propose a well-behaved integrated statistic that is designed to detect evidence for models exhibiting features at multiple frequencies.