The large-scale structure of the universe in one dimension

I investigate statistical properties of one-dimensional fields in the universe such as the Lyα forest (Lyα absorptions in the quasar spectrum) and inverted line-of-sight densities. The Lyα 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 Lyα forests and obtaining line-of-sight densities, so that statistics can be measured from one-dimensional density fields directly