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Our goals are (i) to search for BAO and large‐scale structure in current quasi‐stellar object (QSO) survey data and (ii) to use these and simulation/forecast results to assess the science case for a new, ≳10 times larger, QSO survey. We first combine the Sloan Digital Sky Survey (SDSS), 2dF QSO Redshift Survey (2QZ) and 2dF‐SDSS LRG and QSO (2SLAQ) surveys to form a survey of ≈60 000 QSOs. We find a hint of a peak in the QSO two‐point correlation function, ξ( s ), at the same scale (≈105  h  −1  Mpc) as detected by Eisenstein et al. in their sample of Data Release 5 (DR5) Luminous Red Galaxies (LRGs) but only at low statistical significance. We then compare these data with QSO mock catalogues from the Hubble Volume  N ‐body light‐cone simulation used by Hoyle et al. and find that both routes give statistical error estimates that are consistent at ≈100  h  −1  Mpc scales. Mock catalogues are then used to estimate the nominal survey size needed for a 3–4σ detection of the Baryon Acoustic Oscillations (BAO) peak. We find that a redshift survey of ≈250 000  z  &lt; 2.2 QSOs is required over ≈3000 deg 2 . This is further confirmed by static lognormal simulations where the BAO are clearly detectable in the QSO power spectrum and correlation function. The nominal survey would on its own produce the first detection of, for example, discontinuous dark energy evolution in the so far uncharted 1 &lt;  z  &lt; 2.2 redshift range. We further find that a survey with ≈50 per cent higher QSO sky densities and 50 per cent bigger area will give an ≈6σ BAO detection, leading to an error ≈60 per cent of the size of the BOSS error on the dark energy evolution parameter,  w   a  .  Another important aim of a QSO survey is to place new limits on primordial non‐Gaussianity at large scales. In particular, it is important to test tentative evidence we have found for the evolution of the linear form of the combined SDSS+2QZ+2SLAQ QSO ξ( s ) at  z ≈ 1.6, which may be caused by the existence of non‐Gaussian clustering features at high redshift. Such a QSO survey will also determine the gravitational growth rate at  z ≈ 1.6 via redshift‐space distortions, allow lensing tomography via QSO magnification bias while also measuring the exact luminosity dependence of small‐scale QSO clustering.

Measuring BAO and non‐Gaussianity via QSO clustering