Modeling Science Return from the Lunar Crater Radio Telescope on the Far Side of the Moon

The era following the separation of CMB photons from matter, until the emergence of the first stars and galaxies, is known as the Cosmic Dark Ages. The study of the electromagnetic radiation emitted by neutral hydrogen at the 21~cm rest wavelength is the only way to explore this significant phase of the history of the Universe, offering opportunities to investigate essential questions about dark matter physics, the standard cosmological model, and inflation. Due to cosmological redshift, this signal is now only observable at frequencies that cannot be accessed from the surface of the Earth due to ionospheric absorption and reflection. With the Lunar Crater Radio Telescope (LCRT), we aim at carrying out unprecedented measurements of the sky-averaged redshifted signal spectrum in the 4.7-47 MHz band, by deploying a 350m-diameter parabolic reflector mesh inside a lunar crater on the far side of the Moon and suspending a receiver at its focus. This work discusses the feasibility of the LCRT science goals through the development of a science model, with emphasis on post-processing techniques to extract the Dark Ages signal from the galactic foreground dominating the expected raw data. This model can be used to vary critical instrument and mission parameters to understand their effect on the quality of the retrieved signal.