skip to main content


Title: Extreme data compression for the CMB

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 Cl. 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 Cl 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
 [1] ;  [2]
  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:
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; FG02-95ER40896
Accepted Manuscript
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 93; Journal Issue: 8; Journal ID: ISSN 2470-0010
American Physical Society (APS)
Research Org:
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Sponsoring Org:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
Country of Publication:
United States
OSTI Identifier:
Alternate Identifier(s):
OSTI ID: 1249799