Non-local gravity effects in cosmological dynamics probed by IceCube/KM3NeT signals and dark matter relic abundance

Non-local gravity terms have a relevant role in determining the cosmological dynamics. Here we consider curvature- and torsion-based cosmological models where non-local terms can be ``scalarised'' and then reduced under the standard of scalar-tensor gravity. In this context, we study the role of non-local cosmology with regards to the recent results reported by the IceCube/KM3NeT experiments, which revealed high-energy astrophysical neutrino fluxes up to energies of $220$\,PeV. Specifically, we consider the four-dimensional operator $y_{\alpha\chi}\bar L_\alpha H\chi$ in order to explain both the neutrino rate result and the abundance of dark matter in the Universe, provided that the cosmological background evolves according to non-local gravitational field equations. We show that different dynamical systems representing the evolution of the Universe can be highly sensitive to the parameters of non-local gravity at energies probed by IceCube/KM3NeT. In particular, we adopt power law solutions inferred by the existence of Noether symmetries in non-local cosmological models.