Because of their intrinsic brightness, supernovae make excellent cosmological probes. We describe the spectral-fitting expanding atmosphere method (SEAM) for obtaining distances to Type IIP supernovae (SNe IIP) and present a distance to SN 1999em for which a Cepheid distance exists. Our models give results consistent with the Cepheid distance, even though we have not attempted to tune the underlying hydrodynamical model but have simply chosen the best fits. This is in contradistinction to the expanding photosphere method (EPM), which yields a distance to SN 1999em that is 50 percent smaller than the Cepheid distance. We emphasize the differences between the SEAM and the EPM. We show that the dilution factors used in the EPM analysis were systematically too small at later epochs. We also show that the EPM blackbody assumption is suspect. Since SNe IIP are visible to redshifts as high as z<~;6, with the James Webb Space Telescope, the SEAM may be a valuable probe of the early universe.

Type Ia supernovae have played a crucial role in the discovery of the dark energy, via the measurement of their light curves and the determination of the peak brightness via fitting templates to the observed lightcurve shape. Two spectroscopic indicators are also known to be well correlated with peak luminosity. Since the spectroscopic luminosity indicators are obtained directly from observed spectra, they will have different systematic errors than do measurements using photometry. Additionally, these spectroscopic indicators may be useful for studies of effects of evolution or age of the SNe~;Ia progenitor population. We present several new variants of such spectroscopic indicators which are easy to automate and which minimize the effects of noise. We show that these spectroscopic indicators can be measured by proposed JDEM missions such as snap and JEDI.

Supernova 1987A remains the most well-studied supernova to date. Observations produced excellent broad-band photometric and spectroscopic coverage over a wide wavelength range at all epochs. We model the observed spectra from Day 1 to Day 81 using a hydrodynamical model. We show that good agreement can be obtained at times up to about 60 days, if we allow for extended nickel mixing. Later than about 60 days the observed Balmer lines become stronger than our models can reproduce. We show that this is likely due to a more complicated distribution of gamma-rays than we allow for in our spherically symmetric calculations. We present synthetic light curves in UBVRIJHK and a synthetic bolometric light curve. Using this broad baseline of detailed spectroscopic models we find a distance modulus mu = 18.5 +/- 0.2 using the SEAM method of determining distances to supernovae. We find that the explosion time agrees with that of the neutrino burst and is constrained at 68 percent confidence to within +/- 0.9 days. We argue that the weak Balmer lines of our detailed model calculations casts doubt on the accuracy of the purely photometric EPM method. We also suggest that Type IIP supernovae will be most useful as distance indicators at early times due to a variety of effects.