  Observations of Type Ia supernovae (SNe Ia) reveal correlations between their
luminosities and light-curve shapes, and between their spectral sequence and
photometric sequence. Assuming SNe Ia do not evolve at different redshifts, the
Hubble diagram of SNe Ia may indicate an accelerating Universe, the signature
of a cosmological constant or other forms of dark energy. Several studies raise
concerns about the evolution of SNe Ia (e.g., the peculiarity rate, the
risetime, and the color of SNe Ia at different redshifts), but all these
studies suffer from the difficulties of obtaining high-quality spectroscopy and
photometry for SNe Ia at high redshifts. There are also some troubling cases of
SNe Ia that provide counterexamples to the observed correlations, suggesting
that a secondary parameter is necessary to describe the whole SN Ia family.
Understanding SNe Ia both observationally and theoretically will be the key to
boosting confidence in the SN Ia cosmological results.
