Title: Extreme data compression for the CMB

Abstract

We apply the Karhunen-Loéve methods to cosmic microwave background (CMB) data sets, and show that we can recover the input cosmology and obtain the marginalized likelihoods in Λ cold dark matter cosmologies in under a minute, much faster than Markov chain Monte Carlo methods. This is achieved by forming a linear combination of the power spectra at each multipole l, and solving a system of simultaneous equations such that the Fisher matrix is locally unchanged. Instead of carrying out a full likelihood evaluation over the whole parameter space, we need evaluate the likelihood only for the parameter of interest, with the data compression effectively marginalizing over all other parameters. The weighting vectors contain insight about the physical effects of the parameters on the CMB anisotropy power spectrum C_l. The shape and amplitude of these vectors give an intuitive feel for the physics of the CMB, the sensitivity of the observed spectrum to cosmological parameters, and the relative sensitivity of different experiments to cosmological parameters. We test this method on exact theory C_l as well as on a Wilkinson Microwave Anisotropy Probe (WMAP)-like CMB data set generated from a random realization of a fiducial cosmology, comparing the compression results to those frommore » a full likelihood analysis using CosmoMC. Furthermore, after showing that the method works, we apply it to the temperature power spectrum from the WMAP seven-year data release, and discuss the successes and limitations of our method as applied to a real data set.« less

Authors:

Zablocki, Alan ^[1]; Dodelson, Scott ^[2]

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+ Show Author Affiliations

1. Univ. of Chicago, Chicago, IL (United States)
2. Univ. of Chicago, Chicago, IL (United States); Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)

Publication Date:

Thu Apr 28 00:00:00 EDT 2016

Research Org.:

Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)

Sponsoring Org.:

USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:

1253181

Alternate Identifier(s):

OSTI ID: 1249799

Report Number(s):

FERMILAB-PUB-15-542-A; arXiv:1512.00072
Journal ID: ISSN 2470-0010; PRVDAQ; 1407435

Grant/Contract Number:  

AC02-07CH11359; FG02-13ER41958; SC0009924

Resource Type:

Accepted Manuscript

Journal Name:

Physical Review D

Additional Journal Information:

Journal Volume: 93; Journal Issue: 8; Journal ID: ISSN 2470-0010

Publisher:

American Physical Society (APS)

Country of Publication:

United States

Language:

English

Subject:

79 ASTRONOMY AND ASTROPHYSICS