Inflation from a massive scalar field and scalar perturbations of the metric

In the framework of chaotic inflation we study the case of a massive scalar field using a semiclassical approach. We derive the energy density fluctuations in the infrared sector generated by matter field and gauge-invariant metric fluctuations by means of a different method. We find that the super Hubble density fluctuations increase during inflation for a massive scalar field, in agreement with the result obtained in a previous work in which a power-law expanding universe was considered