After the Higgs boson has been discovered, the Standard Model of particle physics became a confirmed theory, potentially valid up to the Planck scale and allowing one to trace the evolution of the Universe from the inflationary stage till the present days. We discuss the relation between the results from the LHC and the inflationary cosmology. We overview the Higgs inflation, and its relation to the possible metastability of the electroweak vacuum. A short overview of the bounds on the metastability of the electroweak vacuum in the models with inflation not related to the Higgs boson is presented. (C) 2015 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.