The use of astronomical observations to directly determine the space-time geometry of our universe is a long time proposed instrument (Sandage 1961, Kristian & Sachs 1966, Ellis et al. 1985). First presented as an ideal program which could be realised "in principle", it has of late become a new field in cosmology, due to recent tremendous progress in instrumental technology.
The magnitude-redshift relation is one of the tools for a direct observational approach. The discovery of high redshift () Type Ia supernovae (SNIa), and of their potential use as "standard candles" (Phillips 1993, Riess et al. 1995, Hamuy et al. 1995, 1996a, 1996b, Perlmutter et al. 1997, Tripp 1998, Jha et al. 1999) has resurrected interest in this approach. Recently collected data, from ongoing systematic searches, have been used to address the problem of measuring the cosmological parameters of the universe. Analysed in the framework of homogeneous models, they have yielded, as a primary result, a strictly positive cosmological constant, many orders of magnitude smaller than the energy of the vacuum expected in standard particle physics models, as proposed by Riess et al. (1998), hereafter refered to as R98, and by Perlmutter et al. (1999), hereafter refered to as P99.
A non zero cosmological constant was long ago proposed as a possible interpretation of magnitude-redshift observations of cluster galaxies and quasars by Solheim (1966). But the accuracy of the data was not then sufficient to probe this hypothesis.
Anything that contributes to the energy density of the vacuum acts just like a cosmological constant. Analysed in the framework of Friedmann models of the universe, this can be viewed as an argument in favor of a zero cosmological constant, since some unknown symmetry of particle physics theory could presumably cancel the vacuum energy density (see e.g., Weinberg 1989). If the value of the cosmological constant was confirmed to be in the range favored by the SNIa announced results, it would be necessary to explain how it is so small, yet non zero. As such a result would have a revolutionary impact on our understanding of the fundamental laws of physics, it is of tremendous importance to check the different available interpretations.
Provided every other source of potential bias or systematic uncertainties has been correctly taken into account, one of the most vulnerable points of the data collecting procedure is the difference in the absolute magnitude of the supernovae due to an evolution of their progenitors. This point is discussed at length in R98 and P99 who conclude that their results cannot be markedly affected by this effect. Other authors (Drell et al. 1999, Dominguez et al. 1999) claim contrary evidence that high and low redshift supernovae observed so far, substantially differ from one another, and thus contest their use as "standard candles". A progressive dimming of the SNIa by intergalactic dust has also been proposed as a possible systematic effect that could mimic the behaviour of cosmic acceleration, and thus allow cosmologies without a cosmological constant (Aguirre 1999). This important problem is not treated in the present work, where the working assumption is made that the SNIa data actually measure the magnitude-redshift relation up to the precisions claimed in R98 and P99.
The theoretical interpretation is another matter which has to be dealt with carefully to avoid a priori assertions which would lead to incorrect results.
P98 discuss the possibility that the magnitude-redshift relation they find from the analysis of their data is due, not to a cosmological constant, but to an evolving field of unknown nature that contributes to the total energy density of the universe (see e.g., Steinhardt 1996, Caldwell et al. 1998, Garnavich et al. 1998). This entity, which can have an equation-of-state ratio different from that of the cosmological constant, would lead to a different expansion history.
It is proposed here to focus on a less exotic alternative, namely the possibility of large scale inhomogeneity of the part of the universe which can be probed with SNIa measurements.
Large scale spatial homogeneity of the universe is a belief most commonly shared by current cosmologists. It procceeds from a hypothesis brought to the status of Cosmological Principle by Einstein (1917). Its justification is based on two arguments:
Since a matter distribution which is seen isotropic from everywhere implies homogeneity, the Cosmological Principle follows. However, of the two above arguments, only the first is observation grounded. The second, purely philosophical, has never been verified, and cannot thus constitute acceptable evidence.
As will be shown in Sect. 2, the claim for a strictly positive cosmological constant from SNIa data procceeds from an a priori homogeneity assumption. This, and the central role played in the whole cosmological field by the Cosmological Principle, is sufficient motivation to examine to which extent this Principle can be observationally tested.
As has been stressed by Ellis (1979), the situation is completly different within and outside our past light cone. For models exhibiting particle horizons, there are regions of the universe, outside our past light cone, from which we cannot receive any information at the present time. There is thus no way we can observationally verify the spatial homogeneity of such far out regions.
The possibility of direct verification on our past light cone has been studied by Partovi and Mashhoon (1984). These authors have explored the extent to which it is possible to distinguish between large scale homogeneous and inhomogeneous spherically symmetrical models, using magnitude-redshift data. Owing to the then state of observational technique, they concluded this distinction could not be performed.
Analyses of galaxy redshift surveys have recently received increased attention. A controversy over whether the universe is smooth on large scale (Guzzo 1997, Cappi et al. 1998, Martinez et al. 1998 , Scaramella et al. 1998, Wu et al. 1999) or presents an unbounded fractal hierarchy (Sylos Labini et al. 1996, Sylos Labini et al. 1998) has developed and waits for the next generation of wider and deeper galaxy catalogues which may provide a more conclusive answer (Martinez 1999).
The supernovae data have already been investigated for what they can tell about (in)homogeneity. Kim et al. (1997) used the first seven SNIa discovered by the Supernova Cosmology Project at and compared them to a nearby sample at to declare the ruling out of the hypothesis of a locally underdense bubble. The nearby sample has also been examined for evidence of a local "Hubble Bubble" by Zehavi et al. (1998). The marginal signal identified by these authors is very sensitive to the cosmological model retained. Its value has been estimated for an Einstein-de Sitter universe, but would be less significant, and could be considered as included in the limits calculated by Kim et al., for the type of models proposed by R98 and P99.
At another redshift extreme, Starkman et al. (1999) have shown that the segment of the universe sampled by the current supernovae data is not large enough to determine the overall properties of the expansion. But these authors only consider the Einstein-de Sitter homogeneous case to complete their caculations.
It will however be shown, in Sect. 2, that in the near future, we would in principle, be able to probe homogeneity on scales up to, at least . In principle here means provided the evolution effect comes under control, as well as any other bias or systematic effect. But, as long as the relevance of the homogeneous models used by R98 and P99 as a framework for their data analyses is not verified, any claim to cosmological parameter measurements remains premature. Furthermore, a straight reading of the presently published results does not exclude a ruling out of the homogeneity hypothesis. It is moreover shown, in Sects. 3 and 4, that large scale inhomogeneity can mimic a cosmological constant in an homogeneous universe up to the precision achieved by current measurements.
© European Southern Observatory (ESO) 2000
Online publication: December 8, 1999