Abstract
Quantum effects derived through conformal anomaly lead to an inflationary model that can be either stable or unstable. The unstable version requires a large dimensionless coefficient of about $5\times 10^8$ in front of the $R^2$ term that results in the inflationary regime in the $R+R^2$ ("Starobinsky") model being a generic intermediate attractor. In this case the non-local terms in the effective action are practically irrelevant, and there is a 'graceful exit' to a low curvature matter-like dominated stage driven by high-frequency oscillations of $R$ -- scalarons, which later decay to pairs of all particles and antiparticles, with the amount of primordial scalar (density) perturbations required by observations. The stable version is a genuine generic attractor, so there is no exit from it. We discuss a possible transition from stable to unstable phases of inflation. It is shown that this transition is automatic if the sharp cut-off approximation is assumed for quantum corrections in the period of transition. Furthermore, we describe two different quantum mechanisms that may provide a required large $\,R^2$-term in the transition period.
Highlights
There are many solid results in quantum field theory (QFT) in curved space-time, concerning divergences and renormalization and to the evaluation of finite quantum corrections
It is worthwhile to discuss the situation in detail and see if the appearance of the large R2 term can be explained by the modified Spontaneous symmetry breaking (SSB) for a sufficiently low value of the Ricci scalar R
Equations (30) and (54) both lead to the approximately linear time dependence of H, which we can observe in the plot under discussion. It looks like the transition from stable to unstable phases is rather successful in the presence of a huge R2-term, since it leads to the known dynamics after this transition, and this is exactly the dynamics which passed some tests in comparison with observational data
Summary
There are many solid results in quantum field theory (QFT) in curved space-time, concerning divergences and renormalization and to the evaluation of finite quantum corrections (see, for example, [1,2,3,4,5] for introduction and further references, and [6,7] for a recent review). We assume that the unstable phase starts exactly at the point where the stable phase ends Another important issue discussed in this paper concerns quantum mechanisms to generate a large coefficient of the R2-term in the transition period from stable to unstable inflation. We demonstrate that this effect may take place because of a possible strong coupling between fields which may result in a large value of the parameters ξ of the non-minimal interaction of scalar fields with scalar curvature. In the last section we draw our conclusions and discuss further perspectives of the QFT-based approach to inflation
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