A critical assessment of some inhomogeneous pressure Stephani models

We consider spherically symmetric inhomogeneous pressure Stephani universes, 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 have necessarily a radially dependent pressure. We consider a subclass of these models characterized by some inhomogeneity parameter $beta$. We show that also the velocity of sound, like the (effective) equation of state parameter, of comoving perfect fluids acquire away from the origin a time and radial dependent change proportional to $beta$. In order to produce a realistic universe accelerating at late times without dark energy component one must take $beta < 0$. The redshift gets a modified dependence on the scale factor $a(t)$ with a relative modification of $-9%$ peaking at $zsim 4$ and vanishing at the big-bang and today on our past lightcone. 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 for 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 $beta$ small enough.

Variations of the fine-structure constant $alpha$ in exotic singularity models

Various classes of exotic singularity models have been studied as possible mimic models for the observed recent acceleration of the universe. Here we further study one of these classes and, under the assumption that they are phenomenological toy models for the behavior of an underlying scalar field which also couples to the electromagnetic sector of the theory, obtain the corresponding behavior of the fine-structure constant $alpha$ for particular choices of model parameters that have been previously shown to be in reasonable agreement with cosmological observations. We then compare this predicted behavior with available measurements of $alpha$, thus constraining this putative coupling to electromagnetism. We find that values of the coupling which would provide a good fit to spectroscopic measurements of $alpha$ are in more than three-sigma tension with local atomic clock bounds. Future measurements by ESPRESSO and ELT-HIRES will provide a definitive test of these models.

How far is it to a sudden future singularity of pressure?

We discuss the constraints coming from current observations of type Ia supernovae on cosmological models which allow sudden future singularities of pressure (with the scale factor and the energy density regular). We show that such a sudden singularity may happen in the very near future (e.g. within ten million years) and its prediction at the present moment of cosmic evolution cannot be distinguished, with current observational data, from the prediction given by the standard quintessence scenario of future evolution. Fortunately, sudden future singularities are characterized by a momentary peak of infinite tidal forces only; there is no geodesic incompletness which means that the evolution of the universe may eventually be continued throughout until another ``more serious singularity such as Big-Crunch or Big-Rip.