Modeling the Radio Foreground for detection of CMB spectral distortions from Cosmic Dawn and Epoch of Reionization

Cosmic baryon evolution during the Cosmic Dawn and Reionization results in redshifted 21-cm spectral distortions in the cosmic microwave background (CMB). These encode information about the nature and timing of first sources over redshifts 30-6 and appear at meter wavelengths as a tiny CMB distortion along with the Galactic and extragalactic radio sky, which is orders of magnitude brighter. Therefore, detection requires precise methods to model foregrounds. We present a method of foreground fitting using maximally smooth (MS) functions. We demonstrate the usefulness of MS functions over traditionally used polynomials to separate foregrounds from the Epoch of Reionization (EoR) signal. We also examine the level of spectral complexity in plausible foregrounds using GMOSS, a physically motivated model of the radio sky, and find that they are indeed smooth and can be modeled by MS functions to levels sufficient to discern the vanilla model of the EoR signal. We show that MS functions are loss resistant and robustly preserve EoR signal strength and turning points in the residuals. Finally, we demonstrate that in using a well-calibrated spectral radiometer and modeling foregrounds with MS functions, the global EoR signal can be detected with a Bayesian approach with 90\% confidence in 10 minutes' integration.