TY - JOUR

T1 - Reconstruction of the primordial power spectrum of curvature perturbations using multiple data sets

AU - Hunt, Paul

AU - Sarkar, Subir

PY - 2014/1/15

Y1 - 2014/1/15

N2 - Detailed knowledge of the primordial power spectrum of curvature perturbations is essential both in order to elucidate the physical mechanism (`inflation') which generated it, and for estimating the cosmological parameters from observations of the cosmic microwave background and large-scale structure. Hence it ought to be extracted from such data in a model-independent manner, however this is difficult because relevant cosmological observables are given by a convolution of the primordial perturbations with some smoothing kernel which depends on both the assumed world model and the matter content of the universe. Moreover the deconvolution problem is ill-conditioned so a regularisation scheme must be employed to control error propagation. We demonstrate that `Tikhonov regularisation' can robustly reconstruct the primordial spectrum from multiple cosmological data sets, a significant advantage being that both its uncertainty and resolution are then quantified. Using Monte Carlo simulations we investigate several regularisation parameter selection methods and find that generalised cross-validation and Mallow's Cp method give optimal results. We apply our inversion procedure to data from the Wilkinson Microwave Anisotropy Probe, other ground-based small angular scale CMB experiments, and the Sloan Digital Sky Survey. The reconstructed spectrum (assuming the standard ΛCDM cosmology) is not scale-free but has an infrared cutoff at k \lesssim 5 × 10−4 Mpc^−1 (due to the anomalously low CMB quadrupole) and several features with ~ 2σ significance at k/Mpc^−1 ~ 0.0013–0.0025, 0.0362–0.0402 and 0.051–0.056, reflecting the `WMAP glitches'. To test whether these are indeed real will require more accurate data, such as from the Planck satellite and new ground-based experiments.

AB - Detailed knowledge of the primordial power spectrum of curvature perturbations is essential both in order to elucidate the physical mechanism (`inflation') which generated it, and for estimating the cosmological parameters from observations of the cosmic microwave background and large-scale structure. Hence it ought to be extracted from such data in a model-independent manner, however this is difficult because relevant cosmological observables are given by a convolution of the primordial perturbations with some smoothing kernel which depends on both the assumed world model and the matter content of the universe. Moreover the deconvolution problem is ill-conditioned so a regularisation scheme must be employed to control error propagation. We demonstrate that `Tikhonov regularisation' can robustly reconstruct the primordial spectrum from multiple cosmological data sets, a significant advantage being that both its uncertainty and resolution are then quantified. Using Monte Carlo simulations we investigate several regularisation parameter selection methods and find that generalised cross-validation and Mallow's Cp method give optimal results. We apply our inversion procedure to data from the Wilkinson Microwave Anisotropy Probe, other ground-based small angular scale CMB experiments, and the Sloan Digital Sky Survey. The reconstructed spectrum (assuming the standard ΛCDM cosmology) is not scale-free but has an infrared cutoff at k \lesssim 5 × 10−4 Mpc^−1 (due to the anomalously low CMB quadrupole) and several features with ~ 2σ significance at k/Mpc^−1 ~ 0.0013–0.0025, 0.0362–0.0402 and 0.051–0.056, reflecting the `WMAP glitches'. To test whether these are indeed real will require more accurate data, such as from the Planck satellite and new ground-based experiments.

KW - Faculty of Science

KW - CMBR theory cosmological parameters from LSS inflation cosmological parameters from CMBR

U2 - 10.1088/1475-7516/2014/01/025

DO - 10.1088/1475-7516/2014/01/025

M3 - Journal article

VL - 2014

JO - Journal of Cosmology and Astroparticle Physics

JF - Journal of Cosmology and Astroparticle Physics

SN - 1475-7516

IS - 01

M1 - 025

ER -