In the past, various types of galaxies were proposed as standard candle candidates, but it has been found that any cosmological dependences exhibited by these galaxies are dominated by the process of galactic evolution (see, e.g., Tinsley & Gunn 1976). In contrast, a supernova event contains additional information (e.g. light-curve decline rates, and variations of colour and spectral features with declining light) which can be scrutinised for evidence of evolution as a function of look-back time. Additionally, SNe Ia are theorised to result from the thermonuclear explosion of a carbon-oxygen white dwarf which has accreted material until it reaches the Chandrasekhar mass; if true, the uniformity of mass and similarity of chemical composition for SN Ia progenitors could explain why these supernovae are particularly good standard candles. As supernovae are rare, short-lived, and unpredictable, extensive searches have been mounted using large-aperture telescopes and search techniques that guarantee finding batches of high-redshift supernovae (see, e.g., Perlmutter et al. 1997B), allowing follow-up searches to be scheduled so that the SN Ia light curves and spectra can be monitored.
The basic approach to determining cosmological parameters from
supernova observations is contained in the relation between the
apparent magnitude m, the absolute magnitude M, and the
intervening luminosity distance 
:
This can be rewritten in terms of a 
-free luminosity distance
:
where defining 
means that
determining 
removes all dependence from the
cosmological density parameters. At a
given redshift z, this equation will constrain 
and
to an elongated confidence
region, the slope of which changes with redshift. Thus by making
several measurements over a
range of z, one can in principle isolate and
separately. This is a point stressed by Perlmutter
et al. (1997);
unless 
the luminosity distance is not
a function of merely the deceleration parameter 
but of
and independently:
where 
is defined as sinh(x), x, and sin(x) for
, 
, and 
, respectively.
