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Technical Report CMS-TR-20110704


Title Evolution of the CMB power spectrum across WMAP data releases: A nonparametric analysis
Author/s Amir Aghamousa
Centre for Modeling and Simulation, Savitribai Phule Pune University, Pune 411 007 India


Mihir Arjunwadkar
Centre for Modeling and Simulation, Savitribai Phule Pune University, Pune 411 007 India
and
National Centre for Radio Astrophysics, Savitribai Phule Pune University Campus, Pune 411 007, India


Tarun Souradeep
Inter-University Centre for Astronomy and Astrophysics, Savitribai Phule Pune University Campus, India
Abstract We present a comparative analysis of the WMAP 1-, 3-, 5-, and 7-year data releases for the CMB angular power spectrum, with respect to the following three key questions: (a) How well is the angular power spectrum determined by the data alone? (b) How well is the Lambda-CDM model supported by a model-independent, data-driven analysis? (c) What are the realistic uncertainties on peak/dip locations and heights? Our analysis is based on a nonparametric function estimation methodology [1,2]. Our results show that the height of the power spectrum is well determined by data alone for multipole index l approximately less than 600 (1-year), 800 (3-year), and 900 (5- and 7-year data realizations). We also show that parametric fits based on the Lambda-CDM model are remarkably close to our nonparametric fit in l-regions where the data are sufficiently precise. A contrasting example is provided by an H-Lambda-CDM model: As the data become precise with successive data realizations, the H-Lambda-CDM angular power spectrum gets progressively pushed away from our nonparametric fit, indicating the incompatibility of this particular cosmological model with respect to the WMAP data sets. We present uncertainties on peak/dip locations and heights at the 95% level of confidence, and show how these uncertainties translate into hyperbolic "bands" on the acoustic scale (l_A) and the peak shift (phi_m) parameters. Based on the confidence set for the fit to the 7-year data, we also argue that the low-l up-turn in the CMB angular power spectrum cannot be ruled out at any confidence level in excess of about 10%. Additional outcomes of this work are a numerical formulation for risk minimization subject to monotonicity constraints for a noise-weighted risk function, and a prescription for obtaining nonparametric fits that are closer to cosmological expectations on smoothness. (abridged).
Keywords cosmic background radiation; cosmological parameters; methods: data analysis; methods: statistical
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Citing This Document Amir Aghamousa, Mihir Arjunwadkar, and Tarun Souradeep , Evolution of the CMB power spectrum across WMAP data releases: A nonparametric analysis . Technical Report CMS-TR-20110704 of the Centre for Modeling and Simulation, Savitribai Phule Pune University, Pune 411007, India (2011); available at http://cms.unipune.ac.in/reports/.
Notes, Published Reference, Etc. Published as Astrophysical Journal 745, 114 (2012).
Contact amir AT cms.unipune.ac.in
mihir AT cms.unipune.ac.in
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