Distance measurements as a probe of cosmic acceleration

A major recent development 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 d epends on the assumption that we know the equation of state for all mass-en ergy other than normal pressureless matter; popular models are based either on the cosmological constant or on the more general quintessence formulati on. However, this assertion also depends on a number of other assumptions, implicit in the derivation of the standard cosmological field equations: la rge-scale isotropy and homogeneity, the flatness of the Universe, and the v alidity 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 accele ration of the Universe is not possible unless one can define the precise na ture of the failure of any particular assumption. However a simple quantita tive investigation is possible and reveals a number of considerations about the relative importance of the different assumptions. In this paper we pre sent such an investigation. We find that the relationship between the dista nt-redshift relation and the sign of the deceleration parameter is fairly r obust 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 w ould not be close to zero in the currently favoured Omega (Lambda) = 1 - Om ega (matter) = 0.7 or 0.8 Universe, for example). Failures of two or more a ssumptions in concordance may have stronger effects.