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Nonparametric test of consistency between cosmological models and multiband CMB measurements

We present a novel approach to test the consistency of the cosmological models with multiband CMB data using a nonparametric approach. In our analysis we calibrate the REACT (Risk Estimation and Adaptation after Coordinate Transformation) confidence levels associated with distances in function space (\textit{confidence distances}) based on the Monte Carlo simulations in order to test the consistency of an assumed cosmological model with observation. To show the applicability of our algorithm, we confront Planck 2013 temperature data with concordance model of cosmology considering two different Planck spectra combination. In order to have an accurate quantitative statistical measure to compare between the data and the theoretical expectations, we calibrate REACT confidence distances and perform a bias control using many realizations of the data. Our results in this work using Planck 2013 temperature data put the best fit $Λ$CDM model at $95\% (\sim 2σ)$ confidence distance from the center of the nonparametric confidence set while repeating the analysis excluding the Planck $217 \times 217$ GHz spectrum data, the best fit $Λ$CDM model shifts to $70\% (\sim 1σ)$ confidence distance. The most prominent features in the data deviating from the best fit $Λ$CDM model seems to be at low multipoles $ 18 < \ell < 26$ at greater than $2σ$, $\ell \sim 750$ at $\sim1$ to $2 σ$ and $\ell \sim 1800$ at greater than $2σ$ level. Excluding the $217\times217$ GHz spectrum the feature at $\ell \sim 1800$ becomes substantially less significance at $\sim1$ to $2 σ$ confidence level. Results of our analysis based on the new approach we propose in this work are in agreement with other analysis done using alternative methods.