Effects of Rastall parameter on perturbation of dark sectors of the Universe.

In recent years, Rastall gravity is undergoing a considerable surge in popularity. This theory purports to be a modified gravity theory with a non-conserved energy-momentum tensor ({\rm EMT}) and an unusual non-minimal coupling between matter and geometry. The present work looks for the evolution of homogeneous spherical perturbations within the Universe in the context of Rastall gravity. Using the spherical top hat collapse model we seek for exact solutions in linear regime for density contrast of dark matter (\rm DM) and dark energy ({\rm DE}). We find that the Rastall parameter affects crucially the dynamics of density contrasts for {\rm DM} and {\rm DE} and the fate of spherical collapse is different in comparison to the case of general relativity ({\rm GR}). Numerical solutions for perturbation equations in non-linear regime reveal that {\rm DE} perturbations could amplify the rate of growth of {\rm DM} perturbations depending on the values of Rastall parameter.