Stable analytic bounce in non-local Einstein-Gauss-Bonnet cosmology

We consider the most general quadratic in curvature stringy-motivated non-local action for the modified Einstein's gravity. We present exact analytic cosmological solutions including the bouncing ones and develop the relevant techniques for the further study of these types of models. We also elaborate on the perturbation formalism and argue that the found bouncing solution is stable during the bounce phase.