Open AccessMeasuring the primordial power spectrum: principal component analysis of the cosmic microwave background
Author(s) -
Leach Samuel
Publication year - 2006
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1111/j.1365-2966.2006.10842.x
Subject(s) - physics , cmb cold spot , cosmic microwave background , spectral density , planck , cosmic background radiation , astrophysics , spectral index , scale invariance , principal component analysis , statistical physics , anisotropy , spectral line , quantum mechanics , statistics , mathematics
We implement and investigate a method for measuring departures from scale‐invariance, both scale‐dependent as well as scale‐free, in the primordial power spectrum of density perturbations using cosmic microwave background (CMB) C ℓ data and a principal component analysis (PCA) technique. The primordial power spectrum is decomposed into a dominant scale‐invariant Gaussian adiabatic component plus a series of orthonormal modes whose detailed form only depends the noise model for a particular CMB experiment. However, in general these modes are localized across wavenumbers with 0.01 < k < 0.2 Mpc −1 displaying rapid oscillations on scales corresponding the acoustic peaks where the sensitivity to primordial power spectrum is greatest. The performance of this method is assessed using simulated data for the Planck satellite, and the full cosmological plus power spectrum parameter space is integrated out using Markov Chain Monte Carlo. As a proof of concept we apply this data‐compression technique to the current CMB data from Wilkinson Microwave Anisotropy Probe ( WMAP ), ACBAR, CBI, VSA and Boomerang. We find no evidence for the breaking of scale‐invariance from measurements of four PCA mode amplitudes, which is translated to a constraint on the scalar spectral index n S ( k 0 = 0.04 Mpc −1 ) = 0.94 ± 0.04 in accordance with WMAP studies.