A Giant Metrewave Radio Telescope search for associated HI 21cm
  absorption in high-redshift flat-spectrum sources
  We report results from a Giant Metrewave Radio Telescope search for
"associated" redshifted HI 21cm absorption from 24 active galactic nuclei
(AGNs), at $1.1 < z < 3.6$, selected from the Caltech-Jodrell Bank
Flat-spectrum (CJF) sample. 22 out of 23 sources with usable data showed no
evidence of absorption, with typical $3\sigma$ optical depth detection limits
of $\approx 0.01$ at a velocity resolution of $\approx 30$~km~s$^{-1}$. A
single tentative absorption detection was obtained at $z \approx 3.530$ towards
TXS0604+728. If confirmed, this would be the highest redshift at which HI 21cm
absorption has ever been detected.
  Including 29 CJF sources with searches for redshifted HI 21cm absorption in
the literature, mostly at $z < 1$, we construct a sample of 52
uniformly-selected flat-spectrum sources. A Peto-Prentice two-sample test for
censored data finds (at $\approx 3\sigma$ significance) that the strength of HI
21cm absorption is weaker in the high-$z$ sample than in the low-$z$ sample,
this is the first statistically significant evidence for redshift evolution in
the strength of HI 21cm absorption in a uniformly selected AGN sample. However,
the two-sample test also finds that the HI 21cm absorption strength is higher
in AGNs with low ultraviolet or radio luminosities, at $\approx 3.4 \sigma$
significance. The fact that the higher-luminosity AGNs of the sample typically
lie at high redshifts implies that it is currently not possible to break the
degeneracy between AGN luminosity and redshift evolution as the primary cause
of the low HI 21cm opacities in high-redshift, high-luminosity active galactic
nuclei.
