Requiem to "Proof of Inflation" or Sourced Fluctuations in a Non-Singular Bounce

Abstract: Popular wisdom suggests that measuring the tensor to scalar ratio $r$ on CMB scales is a "proof of inflation" since one generic prediction is a scale-invariant tensor spectrum while alternatives predict $r$ that is many orders of magnitude below the sensitivity of future experiments. A bouncing Universe with sourced fluctuations allows for nearly scale-invariant spectra of both scalar and tensor perturbations challenging this point of view. Past works have analyzed the model until the bounce, under the assumption that the bounce will not change the final predictions. In this work, we discard this assumption. We explicitly follow the evolution of the Universe and fluctuations across the bounce until reheating. The evolution is stable, and the existence of the sourced fluctuations does not destroy the bounce. The bounce enhances the scalar spectrum while leaving the tensor spectrum unchanged. The enhancement depends on the duration of the bounce - a shorter bounce implies a larger enhancement. The model matches current observations and predicts any viable tensor-to-scalar ratio $r\lesssim 10^{-2}$, which may be observed in upcoming CMB experiments. Hence, a measurement of $r$ will no longer be a "proof of inflation'', and a Sourced Bounce is a viable paradigm with distinct predictions.