Matter Power Spectrum from the Lyman-Alpha Forest: Myth or Reality?

TL;DR

This work reexamines the Croft et al. Lyman-α forest inference of the matter power spectrum by sampling a broad range of prior cosmological models and quantifying the resulting systematic errors. The authors show that the recovered linear power spectrum is a biased, velocity-smoothed version of the true spectrum, expressible as $P_L^{obs}(k)=P_L^{fct}(k)\,Q_\text{Ω}\,Q_T\,Q_\tau$, where the factors encode dependence on density, temperature, and optical depth, and that peculiar velocities generate broad band-power windows, yielding correlated estimates across $k$. They assess missing physics—gas pressure, ionizing-background inhomogeneities, and shocks—and find gas pressure to be a small correction, while background fluctuations mainly bias baryon density without significantly altering $P_L$. The study concludes that Croft et al.'s measurement remains a powerful constraint on cosmological parameters and models of structure formation, provided model dependence and windowing are properly incorporated into analyses. Overall, the paper provides a framework to translate Lyman-α forest flux power into a robust, cosmology-dependent constraint on the matter power spectrum, with explicit guidance on systematic treatment and covariance.

Abstract

We investigate possible systematic errors in the recent measurement of the matter power spectrum from the Lyman-alpha forest by Croft et al. (2001). We find that for a large set of prior cosmological models the Croft et al. result holds quite well, with systematic errors being comparable to random ones, when a dependence of the recovered matter power spectrum on the cosmological parameters at z~3 is taken into account. We find that peculiar velocities cause the flux power spectrum to be smoothed over about 100-300 km/s, dependng on scale. Consequently, the recovered matter power spectrum is a smoothed version of the underlying true power spectrum. Uncertainties in the recovered power spectrum are thus correlated over about 100-300 km/s. As a side effect, we find that residual fluctuations in the ionizing background, while having almost no effect on the recovered matter power spectrum, significantly bias estimates of the baryon density from the Lyman-alpha forest data. We therefore conclude that the Croft et al. result provides a powerful new constraint on cosmological parameters and models of structure formation.

Figures (12)

• Figure 1: The flux power spectrum predicted by the Croft et al. CWB01 fiducial model, compared to the observed flux power spectrum from Croft et al. CWB01. The dotted line is the model averaged over 3 best realizations (roughly equivalent to 100 random realizations) while the solid line is averaged over 12 best realizations (roughly equivalent to 400 random realizations).
• Figure 2: The flux power spectrum from the Croft et al. CWB01 fiducial model ( solid line) and our reproduction of their result ( dashed line).
• Figure 3: ( a) The flux power spectrum and ( b) the recovered linear power spectrum $P_L^{\rm obs}$ in the Croft et al. CWB01 fiducial model (EdS cosmology; solid line), the same cosmological model with the Hubble constant rescaled to a value appropriate to a flat cosmology with $\Omega_{m,0}=0.4$ (just like in Croft et al.; dotted line)), and for the flat cosmological model with $\Omega_{m,0}=0.4$ ( dashed line). Thin solid lines in this and all following figures show the assumed linear power spectrum $P_L$ for the underlying cosmological model.
• Figure 4: The flux power spectrum ( a) and the recovered linear power spectrum ( b) in the Croft et al. CWB01 model with different assumed effective equations of state: $T_0=15{,}000\hbox{,K}$, $\gamma=1.6$ ( solid line, Croft et al. assumed values), $T_0=20{,}000\hbox{,K}$, $\gamma=1.2$ ( dotted line), $T_0=23{,}000\hbox{,K}$, $\gamma=1.2$ ( short-dashed line), $T_0=17{,}000\hbox{,K}$, $\gamma=1.2$ ( long-dashed line), $T_0=20{,}000\hbox{,K}$, $\gamma=1.4$ ( dot -- short-dashed line), and $T_0=20{,}000\hbox{,K}$, $\gamma=0.9$ ( dot -- long-dashed line). $T_0=20{,}000\hbox{,K}$, $\gamma=1.6$ ( short-dashed -- long-dashed line).
• Figure 5: The flux power spectrum ( a) and the recovered linear power spectrum ( b) in the Croft et al. model with different assumed values for the mean optical depth: $\tau=0.349$ ( solid line, Croft et al. assumed value), $\tau=0.260$ ( dotted line), $\tau=0.285$ ( short-dashed line), $\tau=0.315$ ( long-dashed line), $\tau=0.400$ ( dot -- short-dashed line).