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

Julien Lesgourgues, Matteo Viel+2 more|arXiv (Cornell University)|May 4, 2007

Astronomy and Astrophysical Research3 citations

TL;DR

This study combines 3D weak lensing (COSMOS), Lyman-alpha forest flux power spectrum (SDSS/LUQAS), and WMAP CMB data using a Markov Chain Monte Carlo approach to tightly constrain cosmological parameters in a LambdaCDM framework. The joint analysis yields σ₈ = 0.800 ± 0.023, nₛ = 0.971 ± 0.011, and Ωₘ = 0.247 ± 0.016, significantly reducing uncertainties and breaking degeneracies inherent in individual probes.

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).

Motivation & Objective

• To improve constraints on the amplitude and shape of the matter power spectrum in the standard LambdaCDM model.
• To break the σ₈–Ωₘ degeneracy present in weak lensing data alone by incorporating Lyman-alpha forest measurements.
• To combine independent cosmological probes—3D weak lensing, Ly-alpha forest, and CMB anisotropies—for a more robust and precise parameter estimation.
• To test the consistency of cosmological parameters inferred from different scales and physical processes.

Proposed method

• A Markov Chain Monte Carlo (MCMC) approach is used to jointly analyze multiple cosmological datasets.
• The 3D weak gravitational lensing shear field from the COSMOS survey provides constraints on small-scale matter clustering.
• Low- and high-resolution Lyman-alpha forest flux power spectra from SDSS and LUQAS are used to probe intermediate-scale matter power on the Ly-alpha forest redshift range.
• Cosmic Microwave Background (CMB) temperature and polarization anisotropies from WMAP Year 3 provide large-scale constraints on cosmological parameters.
• The joint likelihood analysis combines these datasets to simultaneously constrain σ₈, nₛ, Ωₘ, and possible running of the spectral index n_run.
• The analysis assumes a flat ΛCDM model and evaluates parameter degeneracies, particularly between σ₈ and Ωₘ.

Experimental results

Research questions

• RQ1 How do the constraints on the matter power spectrum amplitude σ₈ from Lyman-alpha forest and weak lensing data compare, and can they be combined to break degeneracies?
• RQ2 What is the impact of combining Lyman-alpha forest, weak lensing, and CMB data on the precision of cosmological parameter estimation?
• RQ3 Does the joint analysis favor a value of σ₈ that is consistent with WMAP Year 3 CMB data or deviates from it?
• RQ4 To what extent does the Lyman-alpha forest data improve constraints on Ωₘ and σ₈ compared to weak lensing alone?
• RQ5 What are the joint constraints on the spectral index nₛ and its possible running n_run when all three datasets are combined?

Key findings

• The Lyman-alpha forest and 3D weak lensing data show good agreement in constraining the matter power spectrum amplitude on intermediate and small scales.
• Incorporating Lyman-alpha forest data breaks the σ₈–Ωₘ degeneracy present in weak lensing results, yielding σ₈ = 0.876 ± 0.048 for COSMOS and SDSS Ly-alpha data alone.
• The value of σ₈ derived from COSMOS and Ly-alpha data is somewhat larger than that preferred by WMAP Year 3 CMB data.
• The joint analysis of all three datasets—COSMOS, SDSS Ly-alpha, and WMAP—significantly tightens constraints, yielding σ₈ = 0.800 ± 0.023.
• The joint constraints are nₛ = 0.971 ± 0.011 for the spectral index of primordial density fluctuations and Ωₘ = 0.247 ± 0.016 for the matter density.
• Assuming no running of the spectral index, the joint analysis yields a precise determination of cosmological parameters with reduced uncertainties.