Redshift drift in a pressure-gradient cosmology

We derive a redshift drift formula for the spherically symmetric inhomogeneous pressure Stephani universes which are complementary to the spherically symmetric inhomogeneous density Lemaitre-Tolman-Bondi models. We show that there is a clear difference between redshift drift predictions for these two models as well as between the Stephani models and the standard Lambda CDM Friedmann models. The Stephani models have positive drift values at small redshift and behave qualitatively (but not quantitatively) as the Lambda CDM models at large redshift, while the drift for Lemaitre-Tolman-Bondi models is always negative. This prediction may perhaps be tested in future telescopes such as European Extremely Large Telescope (with its spectrograph Cosmic Dynamics Explorer), the Thirty Meter Telescope, the Giant Magellan Telescope, and especially, in gravitational wave interferometers Deci-Hertz Interferometer Gravitational Wave Observatory and Big Bang Observatory [K. Yagi and N. Seto, Phys. Rev. D 83, 044011 (2011).]. DOI: 10.1103/PhysRevD.87.063506