Spinodal decomposition and inflation: Dynamics and metric perturbations

Abstract

We analyse the dynamics of spinodal decomposition in inflationary cosmology using the closed time path formalism of out of equilibrium quantum field theory combined with the non-perturbative Hartree approximation. In addition to a general analysis, we compute the detailed evolution of two inflationary models of particular importance: λΦ 4 new inflation and natural inflation. We compute the metric fluctuations resulting from inflationary phase transitions in the slow roll approximation, showing that there exists a regime for which quantum fluctuations of the inflaton field result in a significant deviation in the predictions of the spectrum of primordial density perturbations from standard results. We provide case examples for which a blue tilt to the power spectrum (i.e. ns > 1) results from the evolution of a single inflaton field, and demonstrate that field fluctuations may result in a scalar amplitude of fluctuations significantly below standard predictions, resulting in a slight alleviation of the inflationary fine tuning problem. We show explicitly that the metric perturbation spectrum resulting from inflation depends upon the state at the outset of the inflationary phase.

Spinodal Instabilities and Super-Planckian Excursions in Natural Inflation

“…In fact, due to the continuing influx of unstable modes during inflation, the two-point function will become nonperturbatively large [21]. How can we tame this growth so as to be able to understand how the fluctuations influence the evolution of the zero mode?…”

“…The main observation leading us to this result is that the potential in Eq. (1) has regions where the frequency ω k for modes of comoving wave number k is imaginary; these give rise to spinodal instabilities [21]. The equation of motion for these modes is given by d…”

Electroweak-scale inflation, inflaton–Higgs mixing and the scalar spectral index

“…It turns out that both regularizations give very similar results and for definiteness we shall continue with the first one, (32).…”

“…More sophisticated methods (e.g. Hartree or 2PI [32,33]) are available, but they are a lot more complicated. In the inflationary domain the one-loop potential is complex due to the tree potential being unstable, and we shall concentrate on its real part.…”

Erratum: False vacuum decay by self-consistent bounces in four dimensions [Phys. Rev. D75, 045001 (2007)]

“…False vacuum decay may initiate inflation, or it may happen after inflation, if the universe gets trapped in one of the local minima of the Higgs potential in Grand Unified Theories. The false vacuum may decay by spinodal decomposition [4,5,6] if the minimum becomes a maximum by a change of the effective potential, e.g., with decreasing temperature or cosmological expansion, or triggered by another field (inflaton) [7]. If this does not happen it may decay by an over-the-barrier transition at finite temperature, the process of bubble nucleation, or it may tunnel to the true vacuum, a process that is described semiclassically by bounce solutions of the associated Euclidean theory.…”