Quasimatter domination parameters in bouncing cosmologies

A fine set of parameters is introduced for bouncing cosmologies in order to describe the nearly matter-dominated phase, and which play the same role that the usual slow-roll parameters play in inflationary cosmology. It is shown that, as in the inflation case, the spectral index and the running parameter for scalar perturbations in bouncing cosmologies can be best expressed in terms of these small parameters. Further, they explicitly exhibit the duality that exists between a nearly matter-dominated universe in its contracting phase and the quasi–de Sitter regime in the expanding one. The results obtained also confirm and extend the known evidence that the spectral index for an exactly matter-dominated universe (i.e., a pressureless universe) in the contracting phase is, in fact, the same as the spectral index for an exact de Sitter regime in the expanding phase. Finally, in both the inflationary and the matter bounce scenarios, the theoretical values of the spectral index and of the running parameter are compared with their experimental counterparts, obtained from the most recent Planck data, with the result that the bouncing models discussed here fit accurate astronomical observations well.