Higgs inflation and vacuum stability
  Inflation is nowadays a well-established paradigm consistent with all the
observations. The precise nature of the inflaton is however unknown and its
role could be played by any candidate able to imitate a scalar condensate in
the slow-roll regime. The discovery of a fundamental scalar in the LHC provides
the less speculative candidate. Could the Higgs field itself be responsible for
inflation? Do we really need to advocate new physics to explain the properties
of the Universe at large scales? Which is the relation between the Standard
Model parameters and the inflationary observables? What happens if our vacuum
becomes unstable below the scale of inflation? We present an overview of Higgs
inflation trying to provide answers to the previous questions with special
emphasis on the vacuum stability issue.
