Astron. Astrophys. 353, 63-71 (2000)

5. Conclusion and discussion

The interpretation of recently published data from high redshift SNIa surveys, devoted to the measurement of the magnitude-redshift relation, has been re-examined with no a priori idea about which model would best describe our universe, at least up to redshifts .

It has been shown that a straight reading of these data does not exclude the possibility of ruling out the Cosmological Principle.

A method of testing large scale homogeneity on our past light cone, provided sufficiently accurate data from "standard candles" at redshifts approaching would be available, has been proposed. This method could be applied using the SNIa data, provided every source of potential bias or systematic uncertainties would be correctly taken into account. An evolution of the progenitors is generally considered as one of the more likely sources of potential systematic errors in the analysis of the supernovae data. Mustapha et al. (1997) have made the point that, given isotropic observations about us, homogeneity cannot be proved without either a model independent theory of source evolution, or distance measures that are independent of source evolution. If a perceptible evolution effect was to be put forward, its impact on the SNIa data would thus have to be evaluated with a model independent method, before using them as a test for homogeneity.

An example of an inhomogeneous model with a zero cosmological constant reproducing the current observations has been given. However, a vanishing cosmological constant is a minimal feature here imposed on the model only to prove that is not necessary to fulfill the observational constraints. A non zero would only add a new free parameter in the LTB equations and would not alter the following primary statement: the presently published SNIa data can be interpreted as implying either a strictly positive cosmological constant in an homogeneous universe or large scale inhomogeneity with no constraint on .

The choice of over-simple inhomogeneous models as examples can, of course, be questioned. The most naive assumptions of spherical symmetry and centered observer, which have been discussed in other works (see e.g. Célérier & Schneider 1998, Célérier 1999), have been mainly retained for simplification purpose, but do not distort the above conclusions. It could be actually interesting to probe the possibility of an off-center observer (see e.g. Humphreys et al. 1997) with the SNIa data. Spherical symmetry is grounded on the observed quasi-anisotropy of the CMBR temperature, and can thus be considered as a sufficiently good working approximation.

The possibility of testing finer features of the model depends on observational improvements. But before aiming at such ambitious goals, it is of the utmost importance to complete the large scale homogeneity test. A previous increase in the number and measurement accuracy of the candidate "standard candles" at very high redshifts is therefore urgently needed, for progress in both fundamental issues of the Cosmological Principle and of the cosmological constant.

It has been shown however that LTB models are highly degenerate with respect to any magnitude-redshift relation, but this is not the case for FLRW models. The best way to prove large scale inhomogeneity would therefore be to disprove homogeneity. Conversely, the best way to prove a non zero cosmological constant would be to prove large scale homogeneity. But, as the Friedmann distance-redshift relation is a necessary but not a sufficient condition for homogeneity, its observed verification would not, in principle, be enough to support the Cosmological Principle. Even if this would imply a fine tuning of its parameters, the possibility for an inhomogeneous universe to mimic such a relation could not be excluded.

To consolidate the robustness of the future magnitude-redshift tests, it would therefore be worth confronting their results with the full range of available cosmological data. The most recent attempt to do so is the work by Bahcall et al. (1999) who conclude that the analysed observations can be considered as consistent with the standard Big-Bang picture of the expansion of the universe, but do not discuss the homogeneity hypothesis. A cross-check with a model independent analysis of the CMBR anisotropy would, for instance, likely yield a substantial improvement, as the CMBR data are known to provide orthogonal constraints on the models parameters.

© European Southern Observatory (ESO) 2000

Online publication: December 8, 1999
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