Testing Cosmological Models with a Lyman Alpha Cloud Statistic: The Fraction of a Quasar Spectrum with High Lyman Alpha Optical Depth

We propose a simple yet powerful statistic, $\Delta_{\tau_0}$, which is the fraction of a quasar spectrum with Lyman alpha optical depth greater than $\tau_0$ and can be easily applied to existing observations as well as simulations. It is shown that two different models --- the cold dark matter model with a cosmological constant and the mixed hot and cold dard matter model, both normalized to COBE and local galaxy cluster abundance --- yield quite different values of $\Delta_{\tau_0}$: 0.11 in the former versus 0.040 in the latter for $\tau_0=4.0$ at $z=3$. It is argued that the statistic may be fairly robust to compute theoretically as well as observationally. It is explained that it is relatively insensitive to details of Lyman alpha clouds simulations such as radiation field, cooling, feedback process, radiative transfer, simulation resolution and simulation volume within plausible ranges of the concerned quantities. Analyses of observations of quasar Lyman alpha 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 constrain $\Omega_0$, $\Omega_{0,HDM}$ and $\Lambda_0$.