  Ultraluminous X-ray sources (ULXs) are thought to be powerful X-ray binaries
(XRBs) and may contribute significantly to the redshift-dependent X-ray
emission from star forming galaxies. We have assembled a uniform sample of 259
ULXs over the redshift range z=0.002-0.51 to constrain their physical nature
and their contribution to the Cosmic X-Ray Background (CXB). The sample is
constructed by crossmatching galaxies from the Sloan Digital Sky Survey with
the Chandra Source Catalog and selecting off-nuclear X-ray sources after
applying astrometric corrections. The fraction of contaminants is ~30% and
shows no evolution with redshift. The host galaxy star formation rates (SFRs)
are systematically elevated relative to the parent sample when matched in host
stellar mass. The specific SFRs suggest a slight preference for high-mass XRBs,
and the X-ray luminosity scaling relations with host galaxy stellar mass and
SFR indicate that the highest redshift sources represent relatively luminous
XRB populations that dominate their host galaxy X-ray emission. The fraction of
galaxies hosting at least one ULX of a given luminosity increases with redshift
over the full range of our sample, as expected if ULXs are preferentially found
in galaxies with high SFRs and low metallicities. At z~0.5, the ULX X-ray flux
is consistent with the X-ray emission from star-forming galaxies. Moreover,
ULXs may account for up to ~40% of the integrated flux from XRBs in the normal
galaxy population out to z~0.5, suggesting they may contribute significantly to
the overall ionizing radiation from galaxies.
