  The unexpected dimness of Type Ia supernovae at redshifts z >~ 1 has over the
past 7 years been seen as an indication that the expansion of the universe is
accelerating. A new model cosmology, the "fractal bubble model", has been
proposed by one of us [gr-qc/0503099], based on the idea that our observed
universe resides in an underdense bubble remnant from a primordial epoch of
cosmic inflation, together with a new solution for averaging in an
inhomogeneous universe. Although there is no cosmic acceleration, it is claimed
that the luminosity distance of type Ia supernovae data will nonetheless fit
the new model, since it mimics a Milne universe at low redshifts. In this paper
the hypothesis is tested statistically against the available type Ia supernovae
data by both chi-square and Bayesian methods. While the standard model with
cosmological constant Omega_Lambda = 1-Omega_m is favoured by a Bayesian
analysis with wide priors, the comparison depends strongly on the priors chosen
for the density parameter, Omega_m. The fractal bubble model gives better
agreement generally for Omega_m<0.2. It also gives reasonably good fits for all
the range, Omega_m=0.01-0.55, allowing the possibility of a viable cosmology
with just baryonic matter, or alternatively with both baryonic matter and
additional cold dark matter.
