The Hubble Diagram of Type Ia Supernovae in Non-Uniform Pressure Universes

We use the redshift-magnitude relation, as derived by Da̧browski (1995), for the two exact non-uniform pressure spherically symmetric Stephani universes with the observer positioned at the center of symmetry, to test the agreement of these models with recent observations of high redshift type Ia supernovae (SNIa), as reported in Perlmutter et al. (1997). By a particular choice of model parameters, we show that these models can give an excellent fit to the observed redshifts and (corrected) B band apparent magnitudes of the Perlmutter et al. data, but for an age of the Universe which is typically about two Gyr – and may be more than three Gyr – greater than in the corresponding Friedmann model, for which non-negative values of the deceleration parameter appear to be favoured by the data. We show that this age increase is obtained for a wide range of the non-uniform pressure parameters of the Stephani models. We claim this paper is the first attempt to compare inhomogeneous models of the universe with real astronomical data. Several recent calibrations of the Hubble parameter, from the Hubble diagram of SNIa and other distance indicators, indicate a value of H0 ≃ 65, and a Hubble time of ∼ 15 Gyr. Based on this value for H0 and assuming Λ ≥ 0, the P97 data would imply a Friedmann age of at most 13 Gyr and in fact a best-fit (for q0 = 0.5) age of only 10 Gyr. Our Stephani models, on the other hand, can give a good fit to the P97 data with an age of up to 15 Gyr. The Stephani models considered here could, therefore, significantly alleviate the conflict between recent cosmological and astrophysical age predictions. The choice of model parameters is quite robust: in order to obtain a good fit to the current P97 data,