Einstein-Gauss-Bonnet (EGB) model is recently restudied in order to analyze new consequences in gravitation, modifying appropriately the Einstein-Hilbert action. The consequences in EGB cosmology are mainly geometric, with higher order values in the Hubble parameter. In this vein this paper is devoted to contribute with extra evidences about its pros and cons of the model from a cosmological point of view. We start constraining the characteristic parameter, $α$, of the EGB model when a cosmological constant as the catalyst for the acceleration is considered. The constrictions are developed at the background cosmology using Observational Hubble Data, Baryon Acoustic Oscillations, Supernovaes of the Ia type, Strong Lensing Systems and the recent compilation of HII Galaxies. Additionally, we implement a statefinder analysis where we found not only a late acceleration but also an early Universe acceleration which is associated with the parameter $α$. Based on our results of the lensing systems, the Universe evolution never reaches a non accelerated phase, instead it is always presented in an accelerated state, being a possible fault that afflicts the EGB model.
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 this type of models. We also elaborate on the perturbation formalism and argue that the found bouncing solution is stable during the bounce phase.
