Bouncing universes

Bouncing models correspond to situations wherein the universe initially goes through a period of contraction until the scale factor reaches a certain minimum value before transiting to the expanding phase. They offer an alternative to inflation to overcome the horizon problem, as they permit well motivated initial conditions to be imposed on the perturbations at early times during the contracting phase. In this talk, divided into two parts, I discuss two different phenomena in bouncing universes. In the first part, I discuss the generation of the tensor bi-spectrum in bouncing scenarios. We analytically evaluate the tensor bi-spectrum in a matter bounce for an arbitrary triangular configuration of the wave vectors and show that, over scales of cosmological interest, the non-Gaussianity parameter that characterizes the amplitude of the tensor bi-spectrum is quite small when compared to the corresponding values in de Sitter inflation. We also explicitly show that the consistency condition governing the tensor bi-spectrum is violated in the matter bounce. In the second part, I consider the generation of magnetic fields in bouncing models. We illustrate that scale invariant magnetic fields of observable strengths today can be generated in a class of bounces for suitable non-minimal couplings. We also show that the power spectrum of the magnetic field remains invariant under a two parameter family of transformations of the non-minimal coupling function. I conclude by highlighting the issues associated with bouncing models.