In this follow-up work to the High Energy Physics Community Summer Study 2013 (HEP CSS 2013, a.k.a. Snowmass), we explore the scientific capabilities of a future Stage-IV Cosmic Microwave Background polarization experiment (CMB-S4) under various assumptions on detector count, resolution, and sky coverage. We use the Fisher matrix technique to calculate the expected uncertainties in cosmological parameters in $ u Lambda$CDM that are especially relevant to the physics of fundamental interactions, including neutrino masses, effective number of relativistic species, dark-energy equation of state, dark-matter annihilation, and inflationary parameters. To further chart the landscape of future cosmology probes, we include forecasted results from the Baryon Acoustic Oscillation (BAO) signal as measured by DESI to constrain parameters that would benefit from low redshift information. We find the following best 1-sigma constraints: $sigma$ constraints: $sigma(M_{ u})= 15$ meV, $sigma(N_{rm eff})= 0.0156$, Dark energy Figure of Merit = 303, $sigma(p_{ann})= 0.00588times3times10^{-26}$ cm$^3$/s/GeV, $sigma(Omega_K)= 0.00074$, $sigma(n_s)= 0.00110$, $sigma(alpha_s)= 0.00145$, and $sigma(r)= 0.00009$. We also detail the dependences of the parameter constraints on detector count, resolution, and sky coverage.
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