The influence of metagalactic ultra-violet background fluctuations on
  the high-redshift Ly$\alpha$ forest
  Under the assumption that galaxies and Quasi-Stellar Objects (QSOs) dominate
the metagalactic ultra-violet (UV) background, it is shown that at high
redshifts fluctuations in the UV background are dominated by QSO shot noise and
have an auto-correlation length of a few to several comoving Mpcs, depending on
the bright end of the QSO luminosity function. The correlations create long
range spatial coherence in the neutral hydrogen fraction. Using a semi-analytic
model, it is demonstrated that the coherence may account for the broad
distribution in effective optical depths measured in the Ly$\alpha$ forest
spectra of background QSOs, for line-of-sight segments of comoving length
$50h^{-1}$ Mpc at redshifts $5<z<6$. Capturing the fluctuations in a numerical
simulation requires a comoving box size of $\sim1h^{-1}$ Gpc, although a box
half this size may be adequate if sufficient random realizations of the QSO
population are performed.
