| I investigate statistical properties of one-dimensional fields in the universe such as the Lyalpha forest (Lyalpha absorptions in the quasar spectrum) and inverted line-of-sight densities. The Lyalpha forest has opened a great window for studying the large-scale structure of the universe, because it can probe the cosmic density field over a wide range of redshift at relatively high resolution, which has not been easily accessible with other types of observations.; The power spectrum completely characterizes Gaussian random fields. However, because of gravitational clustering, the cosmic density field is already quite non-Gaussian on scales below 10 h-1Mpc at redshift z = 3. I analyze the covariance of the one-dimensional mass power spectrum, which involves a fourth-order statistic, the trispectrum. The covariance indicates that Fourier modes in the cosmic density field are highly correlated and that the variance of the measured one-dimensional mass power spectrum is much higher than the expectation for Gaussian random fields. It is found that rare high-density structures contribute significantly to the covariance. The window function due to the length of lines of sight introduces additional correlations between different Fourier modes.; In practice, one observes quasar spectra instead of one-dimensional density fields. As such, flux power spectrum has been the basis of many works. I show that the nonlinear transform between density and flux quenches the fluctuations so that the flux power spectrum is less sensitive to cosmological parameters than the one-dimensional mass power spectrum. The covariance of the flux power spectrum is nearly Gaussian, which suggests that higher-order statistics may be less effective for the flux.; Finally, I provide a method for inverting Lyalpha forests and obtaining line-of-sight densities, so that statistics can be measured from one-dimensional density fields directly. |
