An overview of the anomaly-induced inflation

Shapiro, Ilya L.

doi:10.1016/s0920-5632(03)02431-9

Cited by 7 publications

(18 citation statements)

References 21 publications

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“…The basic principles of the anomaly-induced inflation has been explained in [ 1] (see also references and notations therein).…”

mentioning

confidence: 99%

“…The 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].…”

mentioning

confidence: 99%

“…Let us remember that the corresponding equations of motion (see, e.g. [ 4,1]) include the fourth derivative terms and therefore the stability of the solution (4) with respect to the small perturbations of the conformal factor σ(t) = ln a(t) can not be seen as a trivial occurrence. It may happen that some run-away type solution is stable instead.…”

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confidence: 99%

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Stability issues in the modified starobinsky model

Pelinson

Shapiro

Takakura

2004

Nuclear Physics B - Proceedings Supplements

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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...

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“…The basic principles of the anomaly-induced inflation has been explained in [ 1] (see also references and notations therein).…”

mentioning

confidence: 99%

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confidence: 99%

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Stability issues in the modified starobinsky model

Pelinson

Shapiro

Takakura

2004

Nuclear Physics B - Proceedings Supplements

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“…[50] and references therein, the parameter ε is not considered to be a free parameter, but it is rather taken as determined by the field content of the QFT model, just like the parameter γ in (3.20). This is motivated by the fact that most common computational schemes for regularising the quantum stress-energy tensor yield the same result for ε, which is thus taken to be the correct value.…”

Section: Deviations From the Standard Model And Theirmentioning

confidence: 99%

Cosmological Applications

Hack¹

2015

Cosmological Applications of Algebraic Quantum Field Theory in Curved Spacetimes

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In this chapter we discuss two cosmological applications of algebraic quantum field theory in curved spacetimes. In the Standard Model of Cosmologythe ΛCDM-model-the matter-energy content of the universe on large scales is modelled by a classical stress-energy tensor of perfect fluid form. Motivated by the fact that this matter-energy is considered to have a microscopic description in terms of a quantum field theory, we demonstrate as a first application how the classical perfect fluid stress-energy tensor in the ΛCDM-model may be derived within quantum field theory on curved spacetimes by showing that there exist quantum states on cosmological spacetimes in which the expectation value of the quantum stress-energy tensor is qualitatively and quantitatively of the form assumed in the ΛCDM-model up to corrections which may have interesting phenomenological implications. In the simplest models of Inflation, it is assumed that a classical scalar field on a cosmological spacetime coupled to the metric via the Einstein equations drives an exponential phase of expansion in the early universe. As a second application, the standard approach to the quantization of the perturbations of this coupled system, which makes heavy use of the symmetries of cosmological spacetimes, is re-examined by comparing it with a more fundamental approach which consists of quantizing the perturbations of a scalar field and the metric field in a gauge-invariant manner on general backgrounds and then considering the symmetric cosmological backgrounds as a special case. A Brief Introduction to CosmologyAccording to the well-known cosmological principle, our universe is homogeneous and isotropic. This postulate implies that, on large scales, the cosmos looks 'the same' everywhere and in all directions, see [61, Chap. 5] for a precise definition and a discussion of these issues. A remarkable confirmation of the isotropy of our universe is the fact that the temperature of the Cosmic Microwave Background (CMB) is isotropic up to relative fluctuations of the order 10 −5 [1]. Based on the cosmological principle, we shall regard Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes as the curved manifolds describing our universe on large scales, where here 'large' means scales of the size of galaxy superclusters, i.e. around 10 8 light-years or

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“…When rewriting equation of motion (39) in terms of ǫ and noting that ǫ should diverge exactly at the branching point, one finds: We probe the dependence on scale by changing the numerical value attached to λ in equation (28). If we decrease λ, then also Λ decreases which results in a smaller H C 0 .…”

Section: A Case I: Unrestricted Value Of B ′′mentioning

confidence: 99%

Effect of the trace anomaly on the cosmological constant

Koksma

Prokopec

2008

Phys. Rev. D

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It has been argued that the quantum (conformal) trace anomaly could potentially provide us with a dynamical explanation of the cosmological constant problem. In this paper, however, we show by means of a semiclassical analysis that the trace anomaly does not affect the cosmological constant. We construct the effective action of the conformal anomaly for flat FLRW spacetimes consisting of local quadratic geometric curvature invariants. Counterterms are thus expected to influence the numerical value of the coefficients in the trace anomaly and we must therefore allow these parameters to vary. We calculate the evolution of the Hubble parameter in quasi de Sitter spacetime, where we restrict our Hubble parameter to vary slowly in time, and in FLRW spacetimes. We show dynamically that a Universe consisting of matter with a constant equation of state, a cosmological constant and the quantum trace anomaly evolves either to the classical de Sitter attractor or to a quantum trace anomaly driven one. When considering the trace anomaly truncated to quasi de Sitter spacetime, we find a region in parameter space where the quantum attractor destabilises. When considering the exact expression of the trace anomaly, a stability analysis shows that whenever the trace anomaly driven attractor is stable, the classical de Sitter attractor is unstable, and vice versa. Semiclassically, the trace anomaly does not affect the classical late time de Sitter attractor and hence it does not solve the cosmological constant problem.PACS numbers: 98.80.-k, 04.62.+v, 95.36.+x

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An overview of the anomaly-induced inflation

Cited by 7 publications

References 21 publications

Stability issues in the modified starobinsky model

Stability issues in the modified starobinsky model

Cosmological Applications

Effect of the trace anomaly on the cosmological constant

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