Abstract
The physics during the inflationary stage of the universe is of quantum nature involvingextremely high energy densities. Moreover, it is out of equilibrium on a fastly expanding dynamical geometry. We present in these lectures non-perturbative out of equilibrium field theoretical methods in cosmological universes. Wethen study the non-linear dynamics of quantum fields in matter and radiation dominated FRW and de Sitter universes. For a variety of initial conditions, we compute the evolution of the quantum inflaton field, its large quantum fluctuations and the equation of state. We investigate the explosive particle production due to spinodal instabilities and parametric amplification in FRW and de Sitter universes with and without symmetry breaking. We show howthe particle production is sensitive to the expansion of the universe. In the large N limit for symmetry breaking scenarios, we determine generic late time fields behavior for any flat FRW and de Sitter cosmology. We show that the amplitude of the quantum fluctuations falloff in FRW with the square of the scale factor while the order parameter approaches a minimum of the potential in the same manner. We present a complete and numerically accessible renormalization scheme for the equation of motion and the energy momentum tensor in flat cosmologies. Furthermore, we consider an O(N) inflaton model coupled self-consistently to gravity in the semiclassical approximation, where the field is subject to ‘new inflation’ type initial conditions. Westudy the dynamics self-consistently and non-perturbatively with non-equilibrium field theory methods in the large N limit. We find that spinodal instabilities drive the growth of non-perturbatively large quantum fluctuations which shut off the inflationary growth of the scale factor. We find that a very specific combination of these large quantum fluctuations plus the inflaton zero mode assemble into a new effective field. This new field behaves classically and it is the object which actually rolls down. The metric perturbations during inflation are computed using this effective field and the Bardeen variable for superhorizon modes during inflation. We compute the amplitude and index for the spectrum of scalar density and tensor perturbations and argue that in all models of this type the spinodal instabilities are responsible for a ‘red’ spectrum of primordial scalar density perturbations.
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Boyanovsky, D., de Vega, H.J. (2001). Out of Equilibrium Fields In Selfconsistent Inflationary Dynamics. Density Fluctuations. In: Sánchez, N.G. (eds) Current Topics in Astrofundamental Physics: The Cosmic Microwave Background. NATO Science Series, vol 562. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0748-1_3
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