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A combined analysis of 3D Weak Lensing, Lyman-alpha forest and WMAP year three data

J. Lesgourgues, M. Viel, M. G. Haehnelt, R. Massey

TL;DR

This paper tackles the problem of constraining the amplitude and shape of the matter power spectrum within the standard LambdaCDM framework by combining three cosmological probes: CMB temperature and polarization from WMAP3, three-dimensional weak lensing from the COSMOS survey, and LyAlpha forest flux power spectra from VHS and SDSS. The authors employ Markov Chain Monte Carlo with CAMB-based linear power spectra, non-linear Halofit corrections, and hydrodynamical simulations to perform a joint analysis, marginalizing over extensive nuisance parameters. They find that LyAlpha forest and weak lensing prefer a higher amplitude of structure on small and intermediate scales than the WMAP3 CMB data alone, with joint analyses yielding $sigma_8$ around 0.80–0.82, $n_s$ near 0.96–0.97, and $ _run$ consistent with zero. The study demonstrates that combining diverse data sets breaks parameter degeneracies and provides more precise constraints, reinforcing the LambdaCDM model and showcasing the value of multi-probe cosmology for probing small-scale structure and potential running of the spectral index.

Abstract

We present constraints on the amplitude and shape of the matter power spectrum and the density of dark matter within the framework of a standard LambdaCDM model. We use a Markov Chain Monte Carlo approach to combine independent measurements of the three dimensional weak gravitational lensing shear field by the COSMOS survey, of low and high resolution Ly-alpha forest flux power spectrum by SDSS and LUQAS, and of Cosmic Microwave Background temperature and polarization anisotropies by WMAP. We note good agreement between the amplitude of the matter power spectrum on intermediate and small scales as inferred from Ly-alpha forest and lensing data. The Ly-alpha forest data helps to break the sigma_8-Omega_m degeneracy characteristic of weak lensing results, yielding sigma_8 = 0.876 +- 0.048 for COSMOS plus Ly-alpha SDSS data. This is somewhat larger than the value preferred by the WMAP year three CMB data. Combining all three data sets significantly tightens the constraints on sigma_8, the spectral index of primordial density fluctuation n_s, a possible running of the spectral index n_run and the matter density Omega_m. Assuming no running, the joint constraints for COSMOS, SDSS and WMAP are sigma_8 = 0.800 +- 0.023, n_s = 0.971 +- 0.011, Omega_m = 0.247 +- 0.016 (1-sigma error bars).

A combined analysis of 3D Weak Lensing, Lyman-alpha forest and WMAP year three data

TL;DR

This paper tackles the problem of constraining the amplitude and shape of the matter power spectrum within the standard LambdaCDM framework by combining three cosmological probes: CMB temperature and polarization from WMAP3, three-dimensional weak lensing from the COSMOS survey, and LyAlpha forest flux power spectra from VHS and SDSS. The authors employ Markov Chain Monte Carlo with CAMB-based linear power spectra, non-linear Halofit corrections, and hydrodynamical simulations to perform a joint analysis, marginalizing over extensive nuisance parameters. They find that LyAlpha forest and weak lensing prefer a higher amplitude of structure on small and intermediate scales than the WMAP3 CMB data alone, with joint analyses yielding around 0.80–0.82, near 0.96–0.97, and consistent with zero. The study demonstrates that combining diverse data sets breaks parameter degeneracies and provides more precise constraints, reinforcing the LambdaCDM model and showcasing the value of multi-probe cosmology for probing small-scale structure and potential running of the spectral index.

Abstract

We present constraints on the amplitude and shape of the matter power spectrum and the density of dark matter within the framework of a standard LambdaCDM model. We use a Markov Chain Monte Carlo approach to combine independent measurements of the three dimensional weak gravitational lensing shear field by the COSMOS survey, of low and high resolution Ly-alpha forest flux power spectrum by SDSS and LUQAS, and of Cosmic Microwave Background temperature and polarization anisotropies by WMAP. We note good agreement between the amplitude of the matter power spectrum on intermediate and small scales as inferred from Ly-alpha forest and lensing data. The Ly-alpha forest data helps to break the sigma_8-Omega_m degeneracy characteristic of weak lensing results, yielding sigma_8 = 0.876 +- 0.048 for COSMOS plus Ly-alpha SDSS data. This is somewhat larger than the value preferred by the WMAP year three CMB data. Combining all three data sets significantly tightens the constraints on sigma_8, the spectral index of primordial density fluctuation n_s, a possible running of the spectral index n_run and the matter density Omega_m. Assuming no running, the joint constraints for COSMOS, SDSS and WMAP are sigma_8 = 0.800 +- 0.023, n_s = 0.971 +- 0.011, Omega_m = 0.247 +- 0.016 (1-sigma error bars).

Paper Structure

This paper contains 6 sections, 2 equations, 2 figures, 4 tables.

Table of Contents

  1. Introduction
  2. The data sets
  3. Ly$\alpha\ $ forest data
  4. Weak lensing data
  5. Results
  6. Conclusions

Figures (2)

  • Figure 1: 1-$\sigma$ and 2-$\sigma$ contours of the marginalized likelihood in the $\sigma_8-\Omega_{\rm 0m}$ plane (left) and $\sigma_8-n_{\mathrm{s}}$ plane (right) for each data set separately: WMAP (red), weak lensing (orange), Ly$\alpha\ $ forest from VHS Viel:2004bf (blue) and from SDSS as analyzed by Viel:2005ha (green).
  • Figure 2: 1-$\sigma$ and 2-$\sigma$ contours of the marginalized likelihood in the $\sigma_8-\Omega_{\rm 0m}$ plane (left column) and $\sigma_8-n_{\mathrm{s}}$ plane (right column) for various combinations of data sets from COSMOS (WL), WMAP, and Ly$\alpha\ $ forest data from VHS Viel:2004bf (LyaVHS, upper panels) and SDSS as analyzed by Viel:2005ha (LyaSDSS-d, lower panels).