Sensitivity forecasts for the cosmological recombination radiation in
  the presence of foregrounds
  The cosmological recombination radiation (CRR) is one of the inevitable
$\Lambda$CDM spectral distortions of the cosmic microwave background (CMB).
While it shows a rich spectral structure across dm-mm wavelengths, it is also
one of the smallest signals to target. Here we carry out a detailed forecast
for the expected sensitivity levels required to not only detect but also
extract cosmological information from the CRR in the presence of foregrounds.
We use ${\tt CosmoSpec}$ to compute the CRR including all important radiative
transfer effects and modifications to the recombination dynamics. We confirm
that detections of the overall CRR signal are possible with spectrometer
concepts like ${\it SuperPIXIE}$. However, for real exploitation of the
cosmological information, a $\simeq 50$ times more sensitive spectrometer is
required. While extremely futuristic, this could provide independent
constraints on the primordial helium abundance, $Y_p$, and probe the presence
of extra relativistic degrees of freedom during BBN and recombination.
Significantly improving the constraints on other cosmological parameters
requires even higher sensitivity (another factor of $\simeq 5$) when
considering a combination of a CMB spectrometer with existing CMB data. To a
large part this is due to astrophysical foregrounds which interestingly do not
degrade the constraints on $Y_p$ and $N_{\rm eff}$ as much. A future CMB
spectrometer could thus open a novel way of probing non-standard BBN scenarios,
dark radiation and sterile neutrinos. In addition, inflation physics could be
indirectly probed using the CRR in combination with existing and forthcoming
CMB anisotropy data.
