This the second meeting of the "Windows on quantum gravity" series, held for the first time in 2008. The recent success of WMAP and Planck experiments triggered a new wave of interest in the foundations of primeval cosmology. In particular, since the inflationary process may involve very high energy scales, quantum gravity effects may play an important role in the construction of consistent scenarios. Those experiments also confirmed that the universe is currently undergoing an accelerated expansion. No satisfactory theoretical explanation for he latter is known, which may be a hint towards a mysterious relation to the other aspect of gravitation which is not completely understood: its quantum properties. In the near future, further experiments will hopefully clarify the way in which cosmological observations can help in our understanding of quantum gravity. With the previous motivations in mind, we will devote this workshop to discuss different models of gravity inspired by quantum gravity: GR, dilaton and scalar-tensor gravity, higher-derivative and F(R) gravity, Lorentz-symmetry broken gravity and string-inspired gravity. We aim at presenting an overview of the models and methods to study them. The emphasis will be in their possible role in cosmology - in particular possible quantum effects- to describe the early universe (inflation and alternatives thereof) and late-universe (dark energy).