Carbon ionization states and the cosmic far-UV background with HeII
  absorption
  We constrain the spectrum of the cosmic ultraviolet background radiation by
fitting the observed abundance ratios carbon ions at $z\sim 2\hbox{--}3$ with
those expected from different models of the background radiation. We use the
recently calculated modulation of the background radiation between 3 and 4 Ryd
due to resonant line absorption by intergalactic HeII, and determine the ratios
of CIII to CIV expected at these redshifts, as functions of metallicity, gas
density and temperature. Our analysis of the observed ratios shows that
'delayed reionization' models, which assume a large fraction of HeII at
$z\sim3$, is not favored by data. Our results suggest that HeII reionization
was inhomogeneous, consistent with the predictions from recent simulations.
