A quasi-matter bounce equivalent to Starobinsky inflation

Abstract

In this paper we construct a bounce model that mimics the Starobinsky inflationary model. Our construction relies on Wands' duality, which shows that the Mukhanov-Sasaki equation has a symmetry transformation by changing appropriately its time-dependent mass term. One of the advantages of this constructive method is that one can control every contribution to the primordial power spectrum and check how far we can emulate a given primordial model with a different scenario. In particular, we show that mapping the Starobinsky inflation into a quasi-matter bounce gives the correct relation between the scalar spectral index $n_s-1$ and the tensor-to-scalar ratio $r$.