Non-vacuum initial states for the cosmological perturbations and the back-reaction problem of inflation

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In the framework of Inflationary theory, the assumption that the quantum state of the perturbations is a non-vacuum state leads to a difficulty: non-vacuum initial states imply, in general, a large energy density of inflaton field quanta, not of a cosmological term type, that could prevent the inflationary phase. In this short note, we discuss in detail why this is so, keeping an eye on possible non-Gaussian features due to considering generic non-vacuum initial states.