External priors for the next generation of CMB experiments

Planned cosmic microwave background (CMB) experiments can dramatically improve what we know about neutrino physics, inflation, and dark energy. The low level of noise, together with improved angular resolution, will increase the signal to noise of the CMB polarized signal as well as the reconstructed lensing potential of high redshift large scale structure. Projected constraints on cosmological parameters are extremely tight, but these can be improved even further with information from external experiments. Here, we examine quantitatively the extent to which external priors can lead to improvement in projected constraints from a CMB-Stage IV (S4) experiment on neutrino and dark energy properties. We find that CMB S4 constraints on neutrino mass could be strongly enhanced by external constraints on the cold dark matter density $\Omega_{c}h^{2}$ and the Hubble constant $H_{0}$. If polarization on the largest scales ($\ell<50$) will not be measured, an external prior on the primordial amplitude $A_{s}$ or the optical depth $\tau$ will also be important. A CMB constraint on the number of relativistic degrees of freedom, $N_{\rm eff}$, will benefit from an external prior on the spectral index $n_{s}$ and the baryon energy density $\Omega_{b}h^{2}$. Finally, an external prior on $H_{0}$ will help constrain the dark energy equation of state ($w$).