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Title: Smoothing spline primordial power spectrum reconstruction

Abstract

We reconstruct the shape of the primordial power spectrum (PPS) using a smoothing spline. Our adapted smoothing spline technique provides a complementary method to existing efforts to search for smooth features in the PPS, such as a running spectral index. With this technique we find no significant indication with Wilkinson Microwave Anisotropy Probe first-year data that the PPS deviates from a Harrison-Zeldovich spectrum and no evidence for loss of power on large scales. We also examine the effect on the cosmological parameters of the additional PPS freedom. Smooth variations in the PPS are not significantly degenerate with other cosmological parameters, but the spline reconstruction greatly increases the errors on the optical depth and baryon fraction.

Authors:
; ;  [1]
  1. Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104 (United States)
Publication Date:
OSTI Identifier:
20711547
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 72; Journal Issue: 10; Other Information: DOI: 10.1103/PhysRevD.72.103520; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANISOTROPY; BARYONS; COSMIC RADIATION; COSMOLOGY; ENERGY SPECTRA; RADIOWAVE RADIATION; RELICT RADIATION

Citation Formats

Sealfon, Carolyn, Verde, Licia, and Jimenez, Raul. Smoothing spline primordial power spectrum reconstruction. United States: N. p., 2005. Web. doi:10.1103/PhysRevD.72.103520.
Sealfon, Carolyn, Verde, Licia, & Jimenez, Raul. Smoothing spline primordial power spectrum reconstruction. United States. doi:10.1103/PhysRevD.72.103520.
Sealfon, Carolyn, Verde, Licia, and Jimenez, Raul. Tue . "Smoothing spline primordial power spectrum reconstruction". United States. doi:10.1103/PhysRevD.72.103520.
@article{osti_20711547,
title = {Smoothing spline primordial power spectrum reconstruction},
author = {Sealfon, Carolyn and Verde, Licia and Jimenez, Raul},
abstractNote = {We reconstruct the shape of the primordial power spectrum (PPS) using a smoothing spline. Our adapted smoothing spline technique provides a complementary method to existing efforts to search for smooth features in the PPS, such as a running spectral index. With this technique we find no significant indication with Wilkinson Microwave Anisotropy Probe first-year data that the PPS deviates from a Harrison-Zeldovich spectrum and no evidence for loss of power on large scales. We also examine the effect on the cosmological parameters of the additional PPS freedom. Smooth variations in the PPS are not significantly degenerate with other cosmological parameters, but the spline reconstruction greatly increases the errors on the optical depth and baryon fraction.},
doi = {10.1103/PhysRevD.72.103520},
journal = {Physical Review. D, Particles Fields},
number = 10,
volume = 72,
place = {United States},
year = {Tue Nov 15 00:00:00 EST 2005},
month = {Tue Nov 15 00:00:00 EST 2005}
}
  • The primordial curvature fluctuation spectrum is reconstructed by the maximum likelihood reconstruction method using the five-year Wilkinson Microwave Anisotropy Probe data of the cosmic microwave background temperature anisotropy. We apply the covariance matrix analysis and decompose the reconstructed spectrum into statistically independent band powers. The prominent peak off a simple power-law spectrum found in our previous analysis turn out to be a 3.3{sigma} deviation. From the statistics of primordial spectra reconstructed from mock observations, the probability that a primordial spectrum including such excess is realized in a power-law model is estimated to be about 2%.
  • The primordial curvature fluctuation spectrum is reconstructed by the cosmic inversion method using the five-year Wilkinson Microwave Anisotropy Probe data of the cosmic microwave background temperature anisotropy. We apply the covariance matrix analysis and decompose the reconstructed spectrum into statistically independent band-powers. The statistically significant deviation from a simple power-law spectrum suggested by the analysis of the first-year data is not found in the five-year data except possibly at one point near the border of the wave number domain where accurate reconstruction is possible.
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  • We introduce a new method for reconstructing the primordial power spectrum, P(k), directly from observations of the Cosmic Microwave Background (CMB). We employ Singular Value Decomposition (SVD) to invert the radiation perturbation transfer function. The degeneracy of the multipole l to wavenumber k linear mapping is thus reduced. This enables the inversion to be carried out at each point along a Monte Carlo Markov Chain (MCMC) exploration of the combined P(k) and cosmological parameter space. We present best-fit P(k) obtained with this method along with other cosmological parameters.
  • We develop a method to reconstruct the primordial power spectrum, P(k), using both temperature and polarisation data from the joint analysis of a number of Cosmic Microwave Background (CMB) observations. The method is an extension of the Richardson-Lucy algorithm, first applied in this context by Shafieloo and Souradeep [1]. We show how the inclusion of polarisation measurements can decrease the uncertainty in the reconstructed power spectrum. In particular, the polarisation data can constrain oscillations in the spectrum more effectively than total intensity only measurements. We apply the estimator to a compilation of current CMB results. The reconstructed spectrum is consistentmore » with the best-fit power spectrum although we find evidence for a 'dip' in the power on scales k ≈ 0.002 Mpc{sup −1}. This feature appears to be associated with the WMAP power in the region 18 ≤ l ≤ 26 which is consistently below best-fit models. We also forecast the reconstruction for a simulated, Planck-like [2] survey including sample variance limited polarisation data.« less