Characterization of Lyman Alpha Spectra and Predictions of Structure Formation Models: A Flux Statistics Approach

In gravitational instability models, \lya absorption arises from a continuous fluctuating medium, so that spectra provide a non-linear one-dimensional ``map'' of the underlying density field. We characterise this continuous absorption using statistical measures applied to the distribution of absorbed flux. We describe two simple members of a family of statistics which we apply to simulated spectra in order to show their sensitivity as probes of cosmological parameters (H$_{0}$, $\Omega$, the initial power spectrum of matter fluctuations) and the physical state of the IGM. We make use of SPH simulation results to test the flux statistics, as well as presenting a preliminary application to Keck HIRES data.