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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.