Determining cosmic microwave background structure from its peak distribution

Abstract

We present a new method for time-efficient and accurate extraction of the power spectrum from future cosmic microwave background (CMB) maps based on properties of peaks and troughs of the Gaussian CMB sky. We construct a statistic describing their angular clustering - analogously to galaxies, the 2-point angular correlation function, ${\xi }_{\nu }(\theta )$. We show that for increasing peak threshold, $\nu$, the ${\xi }_{\nu }(\theta )$ is strongly amplified and becomes measurable for $\nu \ge$1 on angular scales $\le 10^{\circ }$. Its amplitude at every scale depends uniquely on the CMB temperature correlation function, $C(\theta )$, and thus the measured ${\xi }_{\nu }$ can be uniquely inverted to obtain $C(\theta )$ and its Legendre transform, the power spectrum of the CMB field. Because in this method the CMB power spectrum is deduced from high peaks/troughs of the CMB field, the procedure takes only $[f(\nu ){]}^2{N}^2$ operations where $f(\nu )$ is the fraction of pixels with $|\delta T|\ge \nu$ standard deviations in the map of $N$ pixels and is e.g. 0.045 and 0.01 for $\nu$=2 and 2.5 respectively. We develop theoretical formalism for the method and show with detailed simulations, using MAP mission parameters, that this method allows to determine very accurately the CMB power spectrum from the upcoming CMB maps in only $\sim (10^{-4}-10^{-3})\times N^2$ operations.

To be published in Ap.J. Letters. Minor changes to match the journal version

Cited by in corpus (8)

• Evidence of a truncated spectrum in the angular correlation function of the cosmic microwave background
• The effect of photometric redshift uncertainties on galaxy clustering and baryonic acoustic oscillations
• Clustering of Local Extrema in Planck CMB maps
• Correlation Statistics of Quantized Noiselike Signals
• Peaks in the CMBR power spectrum. I. Mathematical analysis of the associated real space features
• Using peak distribution of the cosmic microwave background for MAP and Planck data analysis: formalism and simulations
• Statistics of the excursion sets in models with local primordial non-Gaussianity
• A Modified chi^2-Test for CMB Analyses