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.