Evolution of Density Perturbations in a Slowly Contracting Universe

One focus of research in cosmology regards the growth of structure in the universe, i.e., how we end up with stars, galaxies, galaxy clusters, and large-scale structure in a universe that appears homogeneous and isotropic on large scales. Using cosmological perturbation theory, we investigate the evolution of density perturbations corresponding to a universe that is slowly contracting as proposed in 2019 by A. Ijjas and P. J. Steinhardt, testing with and comparing different values for the equation-of-state parameter in the context of Newtonian gravity. This allows for the comparison of the growth of large-scale structure in scenarios including a matter-dominated expanding universe, a dark-energy-dominated expanding universe, and now, an ekpyrotic scalar-field-dominated contracting universe. These predictions become observationally useful in the context of two-point correlation functions to describe clustering. It is valuable to discriminate between various cosmological models to understand both the distant past and the ultimate fate of our universe.