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

We use the redshift-magnitude relation, as derived by Dbrowski, for the two exact non-uniform pressure spherically symmetric Stephani universes with the observer positioned at the center of symmetry in order to test the agreement of these models with recent observations of high-redshift Type Ia supernovae (SN Ia's). 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 data, but for an age of the universe that is typically about 2 Gyr—and may be more than 3 Gyr—greater than in the corresponding Friedmann model, for which nonnegative values of the deceleration parameter appear to be favored 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 that 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 SN Ia's 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 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 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 data, one requires only that the non-uniform pressure parameter a in one of the models be negative and satisfy |a| ≲ 3 km2 s-2 Mpc-1. This limit gives a value for the acceleration scalar u̇ of order | u̇ |≲0.66×10−10r Mpc-1, where r is the radial coordinate in the model. Thus, although the pressure is not zero at the center of symmetry, r = 0, the effect of acceleration is nondetectable at the center, since the acceleration scalar vanishes there. However, the effect of the nonuniform pressure on the redshift-magnitude relation is clearly seen, since neighboring galaxies are not situated at the center, and they necessarily experience acceleration. By allowing slightly larger negative values of a one may fine-tune the model to give an even better fit to the data.