Aspects of string phenomenology in particle physics and cosmology

I discuss possible connections between several scales in particle physics and cosmology, such the the electroweak, inflation, dark energy and Planck scales. In particular, I discuss the physics of extra dimensions and low scale gravity that are motivated from the problem of mass hierarchy, providing an alternative to low energy supersymmetry. I describe their realization in type I string theory with D-branes and I present the main experimental predictions in particle accelerators and their implications in cosmology. I also show that low-mass-scale string compactifications, with a generic D-brane configuration that realizes the Standard Model by open strings, can explain the relatively broad peak in the diphoton invariant mass spectrum at 750 GeV recently reported by the ATLAS and CMS collaborations