In this seminar I will first quickly review the results of the canonical quantization of general relativity suggesting a fundamentally discrete nature of geometry at the Planck scale. This calls for a fundamental description that is combinatorial and discrete where the smooth spacetime description of QFT and general relativity would only be emergent from the collective behavior of the Planckian local structures. In this framework time and Lorentz invariance are still open issues. Nevertheless, discreteness helps, as we will discuss, understanding some of the enigmatic properties of semiclassical black holes: it clarifies the origin of black hole entropy and provides a natural perspective on the issue of information in black hole evaporation.

A natural consequence of the hypothesis that the smooth spacetime description is emergent is, I will argue in the second part, the possibility of energy diffusion from low energy degrees of freedom (effectively described by general relativity coupled to matter fields) to the underlying Planckian micro structure at the fundamental level. I will show that, in the context of cosmology, such effect leads to a novel perspective on the origin of dark energy. A phenomenological model that yields interesting quantitative estimates will be presented.