On the possibility of Baryon Acoustic Oscillation measurements at redshift $z>7.6$ with WFIRST

The Wide Field Infrared Survey Telescope (WFIRST), with its field of view and high sensitivity will make surveys of cosmological large-scale structure possible at high redshifts. We investigate the possibility of detecting Baryon Acoustic Oscillations (BAO) at redshifts $z>7.6$ for use as a standard ruler. We use data from the hydrodynamic simulation \textsc{BlueTides} in conjunction with the gigaparsec-scale Outer Rim simulation and a model for patchy reionization to create mock WFIRST High Latitude Survey grism data for \lya\ emission line selected galaxies at redshifts $z=7.4$ to $z=10$, covering 2280 square degrees. We measure the monopoles of galaxies in the mock catalogues and fit the BAO features. We find that for a line flux of $L = 7\times 10^{-17} \ {\rm erg/s/cm}^{2}$, the $5 \sigma$ detection limit for the current design, the BAO feature is partially detectable (measured in three out of four survey quadrants analysed independently). The resulting root mean square error on the angular diameter distance to $z=7.7$ is 7.9$\%$. If we improve the detection sensitivity by a factor of two (i.e. $L = 3.5\times 10^{-17} \ {\rm erg/s/cm}^{2}$), the distance error reduces to $1.4\%$. We caution that many more factors are yet to be modelled, including dust obscuration, the damping wing due to the intergalactic medium, and low redshift interlopers. If these issues do not strongly affect the results, or different observational techniques (such as use of multiple lines) can mitigate them, WFIRST or similar instruments may be able to constrain the angular diameter distance to the high redshift Universe.