28 research outputs found
Unveiling acoustic physics of the CMB using nonparametric estimation of the temperature angular power spectrum for Planck
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 CDM
model with Planck 2013 data, we use the nuisance parameters associated with the
best-fit CDM angular power spectrum to remove foreground contributions
from the data at multipoles . 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 in the temperature
angular power spectrum. We present uncertainties in the peak/dip locations and
heights at the 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 CDM model
to be at confidence distance from the center of the nonparametric
confidence set -- this is considerably larger than the confidence distance
() 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 CDM cosmology.Comment: 15 pages, 8 figures, 2 table
Superconducting Gap Nodal Surface and Fermi Surface: their partial overlap in cuprates
Electron correlation in cuprates leads to a global constraint on the gap function resulting in a gap
nodal surface. We give physical arguments supported by numerical results and
discuss some experimental results to argue that correlations also lead to a
local constraint on charge fluctuations in -space close to the Fermi
surface, which may result in a substantial overlap of the Fermi surface with
the gap nodal surface.Comment: RevTeX 3.0, 4 Pages, 6 PostScript Figures
Evolution of the Cosmic Microwave Background power spectrum across Wilkinson Microwave Anisotropy Probe data releases: A nonparametric analysis
Using a nonparametric function estimation methodology, we present a comparative analysis of the Wilkinson Microwave Anisotropy Probe (WMAP) 1-, 3-, 5-, and 7-year data releases for the cosmic microwave background (CMB) angular power spectrum with respect to the following key questions. (1) How well is the power spectrum determined by the data alone? (2) How well is the ΛCDM model supported by a model-independent, data-driven analysis? (3) What are the realistic uncertainties on peak/dip locations and heights? Our results show that the height of the power spectrum is well determined by data alone for multipole l approximately less than 546 (1-year), 667 (3-year), 804 (5-year), and 842 (7-year data). We show that parametric fits based on the ΛCDM model are remarkably close to our nonparametric fits in l-regions where data are sufficiently precise. In contrast, the power spectrum for an HΛCDM model is progressively pushed away from our nonparametric fit as data quality improves with successive data realizations, suggesting 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% (2σ) level of confidence and show how these uncertainties translate into hyperbolic "bands" on the acoustic scale (lA ) and peak shift (Φ
m ) parameters. Based on the confidence set for the 7-year data, we argue that the low-l upturn in the CMB power spectrum cannot be ruled out at any confidence level in excess of about 10% (≈0.12σ). Additional outcomes of this work are a numerical formulation for minimization of a noise-weighted risk function subject to monotonicity constraints, a prescription for obtaining nonparametric fits that are closer to cosmological expectations on smoothness, and a method for sampling cosmologically meaningful power spectrum variations from the confidence set of a nonparametric fit