Unveiling acoustic physics of the CMB using nonparametric estimation of the temperature angular power spectrum for Planck

TL;DR

This paper introduces a model-independent, nonparametric method to estimate the CMB temperature power spectrum from Planck data, resolving acoustic peaks and testing the ΛCDM model's consistency.

Contribution

It presents a novel nonparametric estimation approach for the CMB power spectrum that does not rely on specific models and assesses the ΛCDM model's fit to Planck data.

Findings

Resolved six peaks and five dips in the spectrum.

Found the ΛCDM model at 36% confidence distance from the nonparametric estimate.

Planck data show no low-multipole upturn, contrary to ΛCDM expectations.

Abstract

Estimation of the angular power spectrum is one of the important steps in Cosmic Microwave Background (CMB) data analysis. Here, we present a nonparametric estimate of the temperature angular power spectrum for the Planck 2013 CMB data. The method implemented in this work is model-independent, and allows the data, rather than the model, to dictate the fit. Since one of the main targets of our analysis is to test the consistency of the $\Lambda$CDM model with Planck 2013 data, we use the nuisance parameters associated with the best-fit $\Lambda$CDM angular power spectrum to remove foreground contributions from the data at multipoles $\ell \geq50$. We thus obtain a combined angular power spectrum data set together with the full covariance matrix, appropriately weighted over frequency channels. Our subsequent nonparametric analysis resolves six peaks (and five dips) up to $\ell \sim1850$ in the temperature angular power spectrum. We present uncertainties in the peak/dip locations and heights at the $95\%$ confidence level. We further show how these reflect the harmonicity of acoustic peaks, and can be used for acoustic scale estimation. Based on this nonparametric formalism, we found the best-fit $\Lambda$CDM model to be at $36\%$ confidence distance from the center of the nonparametric confidence set -- this is considerably larger than the confidence distance ($9\%$) derived earlier from a similar analysis of the WMAP 7-year data. Another interesting result of our analysis is that at low multipoles, the Planck data do not suggest any upturn, contrary to the expectation based on the integrated Sachs-Wolfe contribution in the best-fit $\Lambda$CDM cosmology.