The unexpected dimness of Type Ia supernovae at redshifts z \lesssim 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 , 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 .