Probing dark energy with supernovae: Exploiting complementarity with the cosmic microwave background

A primary goal for cosmology and particle physics over the coming decade will be to unravel the nature of the dark energy that drives the accelerated expansion of the Universe. In particular, the determination of the equation-of-state of dark energy $w\equiv p/\rho$ and its time variation $dw/dz$ will be critical for developing a theoretical understanding of the new physics behind this phenomenon. Type Ia supernovae (SNe) and cosmic microwave background (CMB) anisotropy are each sensitive to the dark energy equation of state. SNe alone can determine $w\left(z\right)\mathrm{}$ with some precision, while CMB anisotropy alone cannot because of a strong degeneracy between the matter density ${\Omega }_M$ and $w.\mathrm{}$ However, we show that the Planck CMB mission can significantly improve the power of a deep SNe survey to probe w and especially $dw/dz.\mathrm{}$ Because CMB constraints are nearly orthogonal to SNe constraints in the ${\Omega }_M-w$ plane, for constraining $w\left(z\right)\mathrm{}$ Planck is more useful than precise determination of ${\Omega }_M.$ We discuss how the CMB/SNe complementarity impacts strategies for the redshift distribution of a supernova survey to determine $w\left(z\right)\mathrm{}$ and conclude that a well-designed sample should include a substantial number of supernovae out to redshifts $z\sim 2.$