The Large-Scale Structure of the Universe in One Dimension
  (Abridged) I investigate statistical properties of one-dimensional fields in the universe such as the Lyman alpha forest and inverted line-of-sight densities. Because of gravitational clustering, the cosmic density field is already quite non-Gaussian on scales below 10 Mpc/h at redshift z=3. The covariance of the one-dimensional mass power spectrum 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. 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. Finally, I provide a method for inverting Lyman alpha forests and obtaining line-of-sight densities, so that statistics can be measured from one-dimensional density fields directly. 
Hu Zhan