[Paper Review] Do we really see a cosmological constant in the supernovae data ?

Marie-Noëlle Célérier|ArXiv.org|Jul 15, 1999

Gamma-ray bursts and supernovaePhysics and Astronomy163 citations

TL;DR

This paper challenges the interpretation of Type Ia supernova data as definitive evidence for a positive cosmological constant, showing that large-scale inhomogeneity in a zero-Lambda universe can reproduce the observed magnitude-redshift relation. It proposes that current data cannot distinguish between a homogeneous universe with a cosmological constant and an inhomogeneous universe without one, emphasizing the need for higher-redshift, more accurate supernova data to test the Cosmological Principle and the nature of dark energy.

ABSTRACT

The magnitude-redshift relation is one of the tools for a direct observational approach to cosmology. The discovery of high redshift Type Ia supernovae (SNIa) and their use as ``standard candles'' has resurrected interest in this approach. Recently collected data 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. However, a straight reading of the published measurements, conducted with no a priori idea of which model would best describe our universe at least up to redshifts $z\sim 1$, does not exclude the possibility of ruling out the Cosmological Principle - and cosmological constant - hypotheses. It is therefore shown here how the large scale homogeneity of this part of the universe can be tested on our past light cone, using the magnitude-redshift relation, provided sufficiently accurate data from sources at redshifts approaching $z=1$ would be available. An exemple of an inhomogeneous model with zero cosmological constant reproducing the current observations is given. The presently published SNIa data can thus be interpreted as implying either a strictly positive cosmological constant in a homogeneous universe or large scale inhomogeneity with no constraint on $Λ$. An increase in the number and measurement accuracy of the candidate ``standard candles'' at very high redshift is therefore urgently needed, for progress in both fundamental issues of the Cosmological Principle and cosmological constant.

Motivation & Objective

• To assess whether the observed magnitude-redshift relation from high-redshift Type Ia supernovae truly implies a positive cosmological constant.
• To investigate whether the Cosmological Principle—specifically large-scale spatial homogeneity—can be observationally confirmed using supernova data.
• To explore alternative interpretations of the data that do not assume homogeneity, particularly inhomogeneous models with zero cosmological constant.
• To propose a method for testing large-scale homogeneity on the past light cone using high-precision supernova data at z ≈ 1.
• To highlight the critical need for improved data quality and quantity at high redshifts to resolve fundamental ambiguities in cosmological model selection.

Proposed method

• Analyzes the magnitude-redshift relation of Type Ia supernovae as a direct observational probe of cosmic geometry.
• Compares the predictions of Friedmann-Lemaître-Robertson-Walker (FLRW) models with those of Lemaître-Tolman-Bondi (LTB) inhomogeneous models.
• Uses the LTB model framework to construct a spherically symmetric, inhomogeneous universe with zero cosmological constant that reproduces the observed magnitude-redshift data.
• Applies the assumption of standard candle behavior for SNe Ia, while acknowledging potential systematic effects like progenitor evolution or dust extinction.
• Proposes a test of large-scale homogeneity based on the consistency of magnitude-redshift data across different redshift ranges, assuming sufficient data accuracy.
• Relies on the fact that while FLRW and LTB models can mimic the same distance-redshift relation, their underlying assumptions about symmetry and homogeneity differ fundamentally.

Experimental results

Research questions

• RQ1 Can the observed magnitude-redshift relation of high-redshift Type Ia supernovae be equally well explained by a homogeneous universe with a positive cosmological constant or by an inhomogeneous universe with zero cosmological constant?
• RQ2 To what extent can the current supernova data rule out the Cosmological Principle, given the observed isotropy of the CMBR and the Copernican assumption?
• RQ3 What observational criteria can be used to distinguish between a homogeneous FLRW model and an inhomogeneous LTB model based on supernova data alone?
• RQ4 How sensitive are the conclusions about the cosmological constant to assumptions about source evolution and distance measures?
• RQ5 What improvements in data quality and redshift coverage are necessary to definitively test the homogeneity of the universe on large scales?

Key findings

• The current supernova data do not rule out a zero cosmological constant in a large-scale inhomogeneous universe, as demonstrated by a constructed LTB model that fits the observations.
• A non-zero cosmological constant is not the only explanation for the observed magnitude-redshift relation; large-scale inhomogeneity can produce a similar effect.
• The Friedmann distance-redshift relation is necessary but not sufficient to confirm the Cosmological Principle, as inhomogeneous models can mimic it under specific conditions.
• The degeneracy between inhomogeneous and homogeneous models in fitting the magnitude-redshift relation implies that the data alone cannot distinguish between them without additional constraints.
• The possibility of a non-zero cosmological constant cannot be confirmed without first establishing large-scale homogeneity, and vice versa.
• An increase in the number and measurement accuracy of standard candles at redshifts approaching z=1 is essential to resolve the ambiguity between homogeneity and a cosmological constant.