Abstract. We analyze various phases of inflation based on the anomaly-induced effective action of gravity (modified Starobinsky model), taking the cosmological constant Λ and k = 0, ±1 topologies into account. The total number of the inflationary e-folds may be enormous, but at the last 65 of them the inflation greatly slows down due to the contributions of the massive particles. For the supersymmetric particle content, the stability of inflation holds from the initial point at the sub-Planck scale until the supersymmetry breaks down. After that the universe enters into the unstable regime with the eventual transition into the stable FRW-like evolution with small positive cosmological constant. It is remarkable, that all this follows automatically, without fine-tuning of any sort, independent on the values of Λ and k. Finally, we consider the stability under the metric perturbations during the last 65 e-folds of inflation and find that the amplitude of the ones with the wavenumber below a certain cutoff has an acceptable range.
Inspired in some works about quantization of dissipative systems, in particular of the damped harmonic oscillator[1, 2, 3], we consider the dissipative system of a charge interacting with its own radiation, which originates the radiation damping (RD). Using the indirect Lagrangian representation we obtained a Lagrangian formalism with a Chern-Simons-like term. A Hamiltonian analysis is also done, what leads to the quantization of the system.
In this paper, the analog of Maxwell electromagnetism for hydrodynamic turbulence, the metafluid dynamics, is extended in order to reformulate the metafluid dynamics as a gauge field theory. That analogy opens up the possibility to investigate this theory as a constrained system. Having this possibility in mind, we propose a Lagrangian to describe this new theory of turbulence and, subsequently, analyze it from the symplectic point of view. From this analysis, a hidden gauge symmetry is revealed, providing a clear interpretation and meaning of the physics behind the metafluid theory. Also, the geometrical interpretation to the gauge symmetries is discussed.
We discuss the stability of the anomaly-induced inflation (modified Starobinsky model) with respect to the arbitrary choice of initial data and with respect to the small perturbations of the conformal factor and tensor modes of the metric in the later period of inflation and, partially, in the present Universe.The basic principles of the anomaly-induced inflation has been explained in [ 1] (see also references and notations therein).The advantage of this inflationary model is that it requires smaller amount of the cosmological phenomenology than the usual inflaton models. To some extent, this model is mainly based on the principles of quantum field theory. In particlar, the simplest inflationary solution follows from the anomaly-induced quantum correction to the vacuum actionΓ[g µν ] which is a solution of the equationThe coefficients w, b, c are defined in [ 1], C 2 is a square of the Weyl tensor and E is an integrand of the Gauss-Bonnet topological term. This equation admits an explicit solution [ 2]. It is easy to see that this solution contains an ambiguity because an arbitrary conformal functional S c [g µν ] plays the role of the "integration constant" for the Eq. (1). However, this "integration constant" does not affect the equation for the conformal factor of the metric and in this respect the initial inflationary solution follows from the exact effective action. The tempered form of expansion which is observed at the later inflationary phase is not exact, but it has quite a robust background.The stability of the inflationary solution from the initial stage until the graceful exit and the stability of the classical solution in the theory with loop corrections represent a strong consistency test of the model. Let us start from the initial stage of inflation, when the particle content N 0 , N 1/2 N 1 (number of scalar, fermion and vector fields) of the theory provides the stabilityof the exponential solutionof Starobinsky [ 3]. According to [ 4], the condition (2) is independent on the cosmological constant and on the choice of the metric k = 0 or k = ±1. For the sake of simplicity we consider k = 0 and also assume that the cosmological constant is small during inflation, such that the last is driven by the quantum effects only. The original Starobinsky model deals with the unstable case. The initial data are chosen very close to the exponential solution (3) such that the inflation lasts long enough. Using the 0-0 component of the Einstein equations with quantum correction, Starobinsky constructed the phase diagram of the theory. This phase diagram represent several distinct attractors, FRW behaviour is one of them and others represent physically unacceptable run-away type solutions. In the modified version of the model [ 1], the inflation starts in the stable phase (2). In this case the phase diagram, dual to the one of [ 3], has the form shown at the Figure1. This phase portrait indicates to the unique stable solution (3). Therefore the anomaly-induced inflation does not depend on the choice of initial d...
Improving the beginning steps of a previous work, we settle the dual embedding method (DEM) as an alternative and efficient method for obtaining dual equivalent actions also in D = 3. We show that we can obtain dual equivalent actions which were previously obtained in the literature using the gauging iterative Noether dualization method (NDM). We believe that, with the arbitrariness property of the zero mode, the DEM is more profound since it can reveal a whole family of dual equivalent actions. The result confirms the one obtained previously which is important since it has the same structure that appears in the Abelian Higgs model with an anomalous magnetic interaction.
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