Gravitational-wave background in bouncing models from semi-classical, quantum and string gravity

We study the primordial spectra and the gravitational-wave background (GWB) of three models of semi-classical, quantum or string gravity where the big bang is replaced by a bounce and the primordial tensor spectrum is blue: ekpyrotic universe with fast-rolling Galileons, string-gas cosmology with Atick-Witten conjecture and pre-big-bang cosmology. We find that the ekpyrotic scenario with Galileons does not produce a GWB amplitude detectable by present or third-generation interferometers, while the Atick-Witten-based string-gas model is ruled out in its present form for violating the big-bang-nucleosynthesis bound, contrary to the original string-gas scenario. In contrast, the GWB of the pre-big-bang scenario falls within the sensitivity window of both LISA and Einstein Telescope, where it takes the form of a single or a broken power law depending on the choice of parameters. The latter will be tightly constrained by both detectors.