Critical assessment of some inhomogeneous pressure Stephani models

We consider spherically symmetric inhomogeneous pressure Stephani universes, with the center of symmetry being our location. The main feature of these models is that comoving observers do not follow geodesics. In particular, comoving perfect fluids necessarily have a radially dependent pressure. We consider a subclass of these models characterized by some inhomogeneity parameter β . We show also that the velocity of sound of comoving perfect fluids, like the (effective) equation of state parameter, acquires away from the origin a time- and radial-dependent change proportional to β . In order to produce a realistic universe accelerating at late times without a dark energy component, one must take β <0 . The redshift acquires a modified dependence on the scale factor a (t ) with a relative modification of -9 %, peaking at z ∼4 and vanishing at the big bang and today on our past light cone. The equation of state parameter and the speed of sound of dustlike matter (corresponding to a vanishing pressure at the center of symmetry r =0 ) behave in a similar way, and away from the center of symmetry they become negative—a property usually encountered in the dark energy component only. In order to mimic the observed late-time accelerated expansion, the matter component must significantly depart from standard dust, presumably ruling this subclass of Stephani models out as a realistic cosmology. The only way to accept these models is to keep all standard matter components of the universe, including dark energy, and take an inhomogeneity parameter β that is sufficiently small.