Interacting bosonic dark energy and fermionic dark matter in Einstein scalar Gauss–Bonnet gravity

Abstract We explore a cosmological framework in which a Gauss–Bonnet (GB) coupled scalar field, acting as dark energy, interacts with a fermionic dark matter field through a coupling obtained from the point of view of particle physics. This setup is inspired by string/M-theory, and two representative scalar field potentials are investigated: exponential and power-law. A distinctive feature of the GB-coupled models is their potential to alter the propagation speed of gravitational waves (GWs), a property with significant implications in light of recent multi-messenger astrophysical observations. To account for this, we analyze models under two scenarios: one where the GW speed differs from that of light and the other where they are equal, but all consistent with current observational constraints. The dynamical evolution of the system is investigated by reformulating the field equations into an autonomous dynamical system, enabling a detailed analysis of the Universe’s long-term behavior, including the radiation-, matter- and dark energy-dominated epochs. We constrain the model parameters using a broad set of recent observational data, including mock high-redshift measurements from the Roman Space Telescope. Our findings indicate that both potentials yield cosmologies that are in excellent agreement with current data, closely tracking the expansion history predicted by the standard $$\Lambda $$ Λ CDM model, while still allowing room for subtle deviations that could be tested by future observations.