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

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.