On the possibility of Baryon Acoustic Oscillation measurements at
  redshift $z>7.6$ with the Roman Space Telescope
  The Nancy Grace Roman Space Telescope (RST), 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 RST High Latitude Survey grism data for Lyman-alpha 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, RST or similar
instruments may be able to constrain the angular diameter distance to the high
redshift Universe.
