  (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.
