Abstract
A model proposed some years ago by Hartle to study the back reaction in a cosmological model due to the creation of massless non-conformally coupled particles is reexamined. The model consists of a spatially flat FRW spacetime with a classical source made of two perfect fluids one a radiative fluid and the other a baryonic fluid with the equation of state of dust, and it is assumed that the ratio of baryons to photons is small. The back-reaction equations for the cosmological scale factor are derived using a CTP (closed time path) effective action method. Making use of the connection, in the semiclassical context, between the CTP effective action and the influence functional in quantum statistical mechanics, improved back-reaction equations are derived which take into account the fluctuations of the stress-energy tensor of the quantum field. These new dynamical equations are real and causal and predict stochastic fluctuations for the cosmological scale factor.
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