  A major recent evelopment in observational cosmology has been an accurate
measurement of the luminosity distance-redshift relation out to redshifts z=0.8
from Type Ia supernova standard candles. The results have been argued as
evidence for cosmic acceleration. It is well known that this assertion depends
on the assumption that we know the equation of state for all mass-energy other
than normal pressureless matter; popular models are based on either the
cosmological constant or on the more general quintessence formulation. But this
assertion also depends on a number of other assumptions, implicit in the
derivation of the standard cosmological field equations: large-scale isotropy
and homogeneity, the flatness of the Universe, and the validity of general
relativity on cosmological scales (where it has not been tested). A detailed
examination of the effects of these assumptions on the interplay between the
luminosity distance-redshift relation and the acceleration of the Universe is
not possible unless one can define the precise nature of the failure of any
particular assumption. However a simple quantitative investigation is possible
and reveals a number of considerations about the relative importance of the
different assumptions. In this paper we present such an investigation. We find
that the relationship between the distant-redshift relation and the sign of the
deceleration parameter is fairly robust and is unaffected if only one of the
assumptions that we investigate is invalid so long as the deceleration
parameter is not close to zero (it would not be close to zero in the
currently-favored Omega_Lambda = 1 - Omega_matter = 0.7 or 0.8 Universe, for
example). Failures of two or more assumptions in concordance may have stronger
effects.
