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 ($w$).
