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The Lyman-alpha forest and WMAP year three

Matteo Viel, Martin G. Haehnelt, Antony Lewis

TL;DR

The study validates a joint analysis of WMAP3 with Lyman-α forest data to constrain the matter power spectrum across scales from ~1 Mpc/$h$ to horizon. By incorporating Lyman-α flux power spectra from VHS and SDSS into COSMOMC, it quantifies how small-scale information affects constraints on $\sigma_8$ and $n_s$, and tests for running. The results show that WMAP3 alone prefers a tilted spectrum with $n_s\approx0.95$ and $\sigma_8\approx0.74$, while Lyman-α data push the joint constraints toward $\sigma_8\approx0.78-0.86$ and $n_s\approx0.96$, with no strong evidence for running ($n_{\rm run}\approx -0.002 \pm 0.015$). The combined analysis, including additional CMB data and large-scale structure, yields $(\sigma_8, n_s) = (0.78\pm0.03, 0.96\pm0.01)$, demonstrating Lyman-α forest data provide valuable small-scale leverage while highlighting systematics as the main frontier for further improvement.

Abstract

A combined analysis of Cosmic Microwave Background (CMB) and Lyman-a forest data allows to constrain the matter power spectrum from small scales of about 1 Mpc/h all the way to the horizon scale. The long lever arm and complementarity provided by such an analysis has previously led to a significant tightening of the constraints on the shape and the amplitude of the power spectrum of primordial density fluctuations. We present here a combined analysis of the WMAP three year results with Lyman-a forest data. The amplitude of the matter power spectrum sigma_8 and the spectral index ns inferred from the joint analysis with high resolution Lyman-a forest data and low resolution Lyman-a forest data as analyzed by Viel & Haehnelt (2006) are consistent with the new WMAP results to within 1 sigma. The joint analysis with the mainly low resolution data as analysed by McDonald et al. (2005) suggests a value of sigma_8 which is ~ 2 sigma higher than that inferred from the WMAP three year data alone. The joint analysis of the three year WMAP and the Lyman-a forest data also does not favour a running of the spectral index. The best fit values for a combined analysis of the three year WMAP data, other CMB data, 2dF and the Lyman-a forest data are (sigma_8, ns) = (0.78\pm 0.03,0.96 \pm 0.01).

The Lyman-alpha forest and WMAP year three

TL;DR

The study validates a joint analysis of WMAP3 with Lyman-α forest data to constrain the matter power spectrum across scales from ~1 Mpc/ to horizon. By incorporating Lyman-α flux power spectra from VHS and SDSS into COSMOMC, it quantifies how small-scale information affects constraints on and , and tests for running. The results show that WMAP3 alone prefers a tilted spectrum with and , while Lyman-α data push the joint constraints toward and , with no strong evidence for running (). The combined analysis, including additional CMB data and large-scale structure, yields , demonstrating Lyman-α forest data provide valuable small-scale leverage while highlighting systematics as the main frontier for further improvement.

Abstract

A combined analysis of Cosmic Microwave Background (CMB) and Lyman-a forest data allows to constrain the matter power spectrum from small scales of about 1 Mpc/h all the way to the horizon scale. The long lever arm and complementarity provided by such an analysis has previously led to a significant tightening of the constraints on the shape and the amplitude of the power spectrum of primordial density fluctuations. We present here a combined analysis of the WMAP three year results with Lyman-a forest data. The amplitude of the matter power spectrum sigma_8 and the spectral index ns inferred from the joint analysis with high resolution Lyman-a forest data and low resolution Lyman-a forest data as analyzed by Viel & Haehnelt (2006) are consistent with the new WMAP results to within 1 sigma. The joint analysis with the mainly low resolution data as analysed by McDonald et al. (2005) suggests a value of sigma_8 which is ~ 2 sigma higher than that inferred from the WMAP three year data alone. The joint analysis of the three year WMAP and the Lyman-a forest data also does not favour a running of the spectral index. The best fit values for a combined analysis of the three year WMAP data, other CMB data, 2dF and the Lyman-a forest data are (sigma_8, ns) = (0.78\pm 0.03,0.96 \pm 0.01).

Paper Structure

This paper contains 8 sections, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. The data sets
  3. WMAP
  4. Lyman-$\alpha$ forest data sets
  5. Results
  6. Incorporating the Lyman-$\alpha$ data into COSMOMC
  7. Constraints on $\sigma_{8}$ and ${\hbox{{\it n}$_{\rm s}$}}$
  8. Conclusions

Figures (2)

  • Figure 1: $1$ and $2\sigma$ likelihoods for $\sigma_8$ and ${\hbox{{\it n}$_{\rm s}$}}$ marginalized over all other parameters. Left panel: Constraints are for WMAP1 only (green),the LUQAS+CROFT data sets as analysed by VHS (cyan) and the SDSS Lyman-$\alpha$ forest data of M05 (blue). The thick dashed white empty contours refer to WMAP1 + VHS, while the solid blue contours are for WMAP1 + SDSS. Right panel: As in the left panel but for the WMAP3 data set.
  • Figure 2: $1$- and $2\sigma$ likelihoods for $\sigma_8$ and ${\hbox{{\it n}$_{\rm s}$}}$ marginalized over all other parameters. Left panel: The blue contours show the constraints for SDSS only as analysed by M05 with an HST prior $72\pm 8$ km/s/Mpc (blue). The empty solid contours are for the SDSS data set as analysed by Viel:2005ha. The WMAP3 results are shown in green. Right panel: The combined analysis with WMAP3 using the same colour/line coding as in the left panel.