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Testing Cosmological Models With A $\lya$ Forest Statistic: The High End Of The Optical Depth Distribution

We pay particular attention to the high end of the $\lya$ optical depth distribution of a quasar spectrum. Based on the flux distribution (Miralda-Escudé et al 1996), a simple yet seemingly cosmological model -differentiating statistic, $Δ_{τ_0}$ -- the cumulative probability of a quasar spectrum with $\lya$ optical depth greater than a high value $τ_0$ -- is emphasized. It is shown that two different models -- the cold dark matter model with a cosmological constant and the mixed hot and cold dark matter model, both normalized to COBE and local galaxy cluster abundance -- yield quite different values of $Δ_{τ_0}$: 0.13 of the former versus 0.058 of the latter for $τ_0=3.0$ at $z=3$. Moreover, it is argued that $Δ_{τ_0}$ may be fairly robust to compute theoretically because it does not seem to depend sensitively on small variations of simulations parameters such as radiation field, cooling, feedback process, radiative transfer, resolution and simulation volume within the plausible ranges of the concerned quantities. Furthermore, it is illustrated that $Δ_{τ_0}$ can be obtained sufficiently accurately from currently available observed quasar spectra for $τ_0\sim 3.0-4.0$, when observational noise is properly taken into account. We anticipate that analyses of observations of quasar $\lya$ absorption spectra over a range of redshift may be able to constrain the redshift evolution of the amplitude of the density fluctuations on small-to-intermediate scales, therefore providing an independent constraint on $Ω_0$, $Ω_{0,HDM}$ and $Λ_0$.