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The Nancy Grace Roman Space Telescope (RST), with its field of view and highsensitivity will make surveys of cosmological large-scale structure possible athigh redshifts. We investigate the possibility of detecting Baryon AcousticOscillations (BAO) at redshifts $z>7.6$ for use as a standard ruler. We usedata from the hydrodynamic simulation \textsc{BlueTides} in conjunction withthe gigaparsec-scale Outer Rim simulation and a model for patchy reionizationto create mock RST High Latitude Survey grism data for Lyman-alpha emissionline selected galaxies at redshifts $z=7.4$ to $z=10$, covering 2280 squaredegrees. We measure the monopoles of galaxies in the mock catalogues and fitthe BAO features. We find that for a line flux of $L = 7\times 10^{-17} \ {\rmerg/s/cm}^{2}$, the $5 \sigma$ detection limit for the current design, the BAOfeature is partially detectable (measured in three out of four survey quadrantsanalysed independently). The resulting root mean square error on the angulardiameter distance to $z=7.7$ is 7.9$\%$. If we improve the detectionsensitivity by a factor of two (i.e. $L = 3.5\times 10^{-17} \ {\rmerg/s/cm}^{2}$), the distance error reduces to $1.4\%$. We caution that manymore factors are yet to be modelled, including dust obscuration, the dampingwing due to the intergalactic medium, and low redshift interlopers. If theseissues do not strongly affect the results, or different observationaltechniques (such as use of multiple lines) can mitigate them, RST or similarinstruments may be able to constrain the angular diameter distance to the highredshift Universe.

On the possibility of Baryon Acoustic Oscillation measurements at redshift $z>7.6$ with the Roman Space Telescope