Evolution of cold gas at 2<z<5: a blind search for HI and OH absorption lines towards mid-infrared color selected radio-loud AGNs

We present results from a spectroscopically blind search for associated and intervening HI 21-cm and OH 18-cm absorption lines towards 88 AGNs at $2\le z\le5$ using the upgraded Giant Metrewave Radio Telescope (uGMRT). The sample of AGNs with 1.4 GHz spectral luminosity in the range, $10^{27 - 29.3}$ W/Hz, is selected using mid-infrared colors and closely resembles the distribution of the underlying quasar population. The search for associated or proximate absorption, defined to be within 3000 km/s of the AGN redshift, led to one HI 21-cm absorption detection (M1540-1453; $z_{abs}$= 2.1139). This is only the fourth known absorption at $z>2$. The detection rate ($1.6^{+3.8}_{-1.4}$%) suggests low covering factor of cold neutral medium (CNM; T$\sim$100 K) associated with these powerful AGNs. The intervening absorption line search, with a sensitivity to detect CNM in damped Ly$\alpha$ systems (DLAs), has comoving absorption path lengths of $\Delta$X = 130.1 and 167.7 for HI and OH, respectively. The corresponding number of absorber per unit comoving path lengths are $\le$0.014 and $\le$0.011, respectively. The former is at least 4.5 times lower than that of DLAs and consistent with the CNM cross-section estimated using H$_2$ and CI absorbers at $z>2$. Our AGN sample is optically fainter compared to the quasars used to search for DLAs in the past. In our optical spectra obtained using the Southern African Large Telescope (SALT) and the Nordic Optical Telescope (NOT), we detect 5 intervening (redshift path$\sim9.3$) and 2 proximate DLAs. This is slightly excessive compared to the statistics based on optically selected quasars. The non-detection of HI 21-cm absorption from these DLAs suggests small CNM covering fraction around galaxies at $z>2$.