CMB Science: Opportunities for a Cryogenic Filter-Bank Spectrometer

Cosmic microwave background (CMB) spectral science is experiencing a renewed interest after the impressive result of COBE-FIRAS in the early Nineties. In 2011, the PIXIE proposal contributed to reopen the prospect of measuring deviations from a perfect 2.725 K planckian spectrum. Both COBE-FIRAS and PIXIE are differential Fourier transform spectrometers (FTSes) capable to operate in the null condition across 2 frequency decades (in the case of PIXIE, the frequency span is 30 GHz-6 THz). We discuss a complementary strategy to observe CMB spectral distortions at frequencies lower than 250 GHz, down to the Rayleigh-Jeans tail of the spectrum. The throughput advantage that makes the FTS capable of achieving exquisite sensitivity via multimode operation becomes limited at lower frequencies. We demonstrate that an array of 100 cryogenic planar filter-bank spectrometers coupled to single mode antennas, on a purely statistical ground, can perform better than an FTS between tens of GHz and 200 GHz (a relevant frequency window for cosmology) in the hypothesis that (1) both instruments have the same frequency resolution and (2) both instruments are operated at the photon noise limit (with the FTS frequency band extending from tens of GHz up to 1 THz). We discuss possible limitations of these hypotheses, and the constraints that have to be fulfilled (mainly in terms of efficiency) in order to operate a cryogenic filter-bank spectrometer close to its ultimate sensitivity limit.