We quantify the prospects for using emission lines from rotational transitions of the CO molecule to perform an `intensity mapping observation at high redshift during the Epoch of Reionization (EoR). The aim of CO intensity mapping is to observe the combined CO emission from many unresolved galaxies, to measure the spatial fluctuations in this emission, and use this as a tracer of large scale structure at very early times in the history of our Universe. This measurement would help determine the properties of molecular clouds -- the sites of star formation -- in the very galaxies that reionize the Universe. We further consider the possibility of cross-correlating CO intensity maps with future observations of the redshifted 21 cm line. The cross spectrum is less sensitive to foreground contamination than the auto power spectra, and can therefore help confirm the high redshift origin of each signal. Furthermore, the cross spectrum measurement would help extract key information about the EoR, especially regarding the size distribution of ionized regions. We discuss uncertainties in predicting the CO signal at high redshift, and discuss strategies for improving these predictions. Under favorable assumptions, and feasible specifications for a CO survey mapping the CO(2-1) and CO(1-0) lines, the power spectrum of CO emission fluctuations and its cross spectrum with future 21 cm measurements from the MWA are detectable at high significance.
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