Pressure gradients, shell-crossing singularities and acoustic oscillations - application to inhomogeneous cosmological models

Inhomogeneous cosmological models have recently become a very interesting alternative to standard cosmology. This is because these models are able to fit cosmological observations without the need for dark energy. However, due to inhomogeneity and pressureless matter content, these models can suffer from shell-crossing singularities. These singularities occur when two shells of dust collide with each other leading to infinite values of the density. In this Letter, we show that if inhomogeneous pressure is included then these singularities can be prevented from occurring over the period of structure formation. Thus, a simple incorporation of a gradient of pressure allows for more comprehensive studies of inhomogeneous cosmological models and their application to cosmology.