According to the most popular scenario, the early Universe should have experienced an accelerated expansion phase, called Cosmological Inflation, after which the standard Big Bang Cosmology would have taken place giving rise to the radiation-dominated epoch. However, the details of the inflationary scenario are far to be completely understood. Thus, in this paper we study if possible additional (exotic) cosmological phases could delay the beginning of the standard Big Bang history and alter some theoretical predictions related to the inflationary cosmological perturbations, like, for instance, the order of magnitude of the tensor-to-scalar ratio r.A post-publication change was made to this article on 4 Jun 2020 to correct the title on the webpage.