Exact solutions in bouncing cosmology

We discuss the effects of a (possibly) negative (1+z)6 type contribution to the Friedmann equation in a spatially flat universe. No definite answer can be given as to the presence and magnitude of a particular mechanism, because any test using the general relation H(z) is able to estimate only the total of all sources of such a term. That is why we describe four possibilities: (1) geometric effects of loop quantum cosmology, (2) braneworld cosmology, (3) metric-affine gravity, and (4) cosmology with spinning fluid. We find the exact solutions for the models with ρ2 correction in terms of elementary functions, and show all evolutional paths on their phase plane. Instead of the initial singularity, the generic feature is now a bounce.