Observable Primordial Gravitational Waves from Modified Gravity

We investigate the production of primordial gravitational waves (GWs) in modified gravity models formulated within the Palatini approach. Our framework introduces a non-minimal coupling between the inflaton and gravity, includes higher-order curvature terms, and employs a runaway inflaton potential with reheating driven by inflaton–radiation interactions induced by cosmological expansion. We analyze GW generation during hyperkination, kination, and reheating, finding that the GW energy density is generally enhanced during kination across all models as a function of the order of the non-minimal coupling. A key result is that in Palatini R² gravity, this enhancement is truncated by a short-lived hyperkination phase, yielding a flat GW spectrum consistent with BBN constraints and preventing overproduction. This mechanism highlights the relevance of higher-order curvature terms, opening a wide and viable parameter space. We further discuss observational prospects for detecting such signals with ongoing and future GW experiments, including implications for the minimal Starobinsky model. A detection of these signatures would not only confirm a robust prediction of inflation but also provide compelling evidence for modified gravity.