Probing large-scale structure with large samples of X-ray selected AGN:
  I Baryonic acoustic oscillations
  We investigate the potential of large X-ray-selected AGN samples for
detecting baryonic acoustic oscillations (BAO). Though AGN selection in X-ray
band is very clean and efficient, it does not provide redshift information, and
thus needs to be complemented with an optical follow-up. The main focus of this
study is (i) to find the requirements needed for the quality of the optical
follow-up and (ii) to formulate the optimal strategy of the X-ray survey, in
order to detect the BAO. We demonstrate that redshift accuracy of
$\sigma_0=10^{-2}$ at $z=1$ and the catastrophic failure rate of $f_{\rm
fail}\lesssim 30\%$ are sufficient for a reliable detection of BAO in future
X-ray surveys. Spectroscopic quality redshifts ($\sigma_0=10^{-3}$ and $f_{\rm
fail}\sim 0$) will boost the confidence level of the BAO detection by a factor
of $\sim 2$. For meaningful detection of BAO, X-ray surveys of moderate depth
of $F_{\rm lim}\sim {\rm few~} 10^{-15}$ erg/s/cm$^2$ covering sky area from a
few hundred to $\sim$ten thousand square degrees are required. The optimal
strategy for the BAO detection does not necessarily require full sky coverage.
For example, in a 1000-day long survey by an eROSITA type telescope, an optimal
strategy would be to survey a sky area of $\sim 9000$ deg$^2$, yielding a $\sim
16\sigma$ BAO detection. A similar detection will be achieved by ATHENA+ or
WFXT class telescopes in a survey with a duration of 100 days, covering a
similar sky area. XMM-Newton can achieve a marginal BAO detection in a 100-day
survey covering $\sim 400$ deg$^2$. These surveys would demand a
moderate-to-high cost in terms the optical follow-ups, requiring determination
of redshifts of $\sim 10^5$ (XMM-Newton) to $\sim 3\times 10^6$ objects
(eROSITA, ATHENA+, and WFXT) in these sky areas.
