The effect of pressure gradients on luminosity distance - redshift
  relations
  Inhomogeneous cosmological models have had significant success in explaining
cosmological observations without the need for dark energy. Generally, these
models imply inhomogeneous matter distributions alter the observable relations
that are taken for granted when assuming the Universe evolves according to the
standard Friedmann equations. Moreover, it has recently been shown that both
inhomogeneous matter and pressure distributions are required in both early and
late stages of cosmological evolution. These associated pressure gradients are
required in the early Universe to sufficiently describe void formation, whilst
late-stage pressure gradients stop the appearance of anomalous singularities.
In this paper we investigate the effect of pressure gradients on cosmological
observations by deriving the luminosity distance - redshift relations in
spherically symmetric, inhomogeneous spacetimes endowed with a perfect fluid.
By applying this to a specific example for the energy density distribution and
using various equations of state, we are able to explicitly show that pressure
gradients may have a non-negligble effect on cosmological observations. In
particular, we show that a non-zero pressure gradient can imply significantly
different residual Hubble diagrams for $z\lesssim1$ compared to when the
pressure is ignored. This paper therefore highlights the need to properly
consider pressure gradients when interpreting cosmological observations.
