Quantitative Spectroscopy of Supernovae for Dark Energy Studies

Detailed quantitative spectroscopy of Type Ia supernovae (SNe~Ia) provides crucial information needed to minimize systematic effects in both ongoing SNe Ia observational programs such as the Nearby Supernova Factory, ESSENCE, and the SuperNova Legacy Survey (SNLS) and in proposed JDEM missions such as SNAP, JEDI, and DESTINY. Quantitative spectroscopy is mandatory to quantify and understand the observational strategy of comparing ``like versus like''. It allows us to explore evolutionary effects, from variations in progenitor metallicity to variations in progenitor age, to variations in dust with cosmological epoch. It also allows us to interpret and quantify the effects of asphericity, as well as different amounts of mixing in the thermonuclear explosion.