On the stability of the anomaly-induced inflation

Pelinson, Ana; Shapiro, Ilya L.; Takakura, F. I.

doi:10.1016/s0550-3213(02)00999-9

Cited by 89 publications

(201 citation statements)

References 45 publications

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“…If one includes a cosmological constant, the theory of anomaly induced inflation is plagued by instabilities, which we will also come to address. The Modified Starobinsky Model as advocated by [41,42,43], takes advantage of these instabilities to account for a graceful exit from inflation. It is argued that supersymmetry breaking changes the degrees of freedom such that it destabilises the quantum anomaly driven attractor and simultaneously stabilises the classical de Sitter attractor.…”

Section: The Modified Starobinsky Modelmentioning

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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Section: The Modified Starobinsky Modelmentioning

confidence: 99%

Effect of the trace anomaly on the cosmological constant

Koksma

Prokopec

2008

Phys. Rev. D

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“…Indeed, the last option is completely equivalent to taking the trace of (1). The resulting equation has, for k = 0 FRW metric, the following form (since the cases k = ±1 are quite similar [ 8] we will not consider them here):…”

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confidence: 99%

“…According to the method of [ 14,8] the leading effect of the particle masses is that the Planck mass and the cosmological constant in the equation (4) and in the solution (6) must be replaced by the variable expressions…”

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An overview of the anomaly-induced inflation

Shapiro¹

2004

Nuclear Physics B - Proceedings Supplements

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The anomaly-induced inflation (modified Starobinsky model) is based on the application of the effective quantum field theory approach to the Early Universe. We present a brief general review of this model with a special attention to the existing difficulties and unsolved problems.The original version of the anomaly-induced inflation [ 1,2,3,4] is the cosmological model which takes into account the vacuum quantum effects of the free, massless and conformally coupled to metric matter fields [ 5]. The quantum correction to the Einstein equation with cosmological constantproduces a non-trivial effect because the anomalous trace of the stress tensoris non-zero. If the matter fields are absent, there are the following equivalent ways to study the cosmological solution of (1): using the (0-0)-component [ 1,2] or via the anomaly-induced effective action [ 6,7]. Indeed, the last option is completely equivalent to taking the trace of (1). The resulting equation has, for k = 0 FRW metric, the following form (since the cases k = ±1 are quite similar [ 8] we will not consider them here):The equation above has a remarkable particular solutionwhere (motivated by the recent supernova data [ 9], we consider only positive cosmological constant in the low-energy regime)As far as Λ ≪ M 2 P , we meet two very different solutionsThe first solution is exactly the classical one, which one meets in the theory without quantum corrections, while the second one H S is the inflationary solution of Starobinsky. The phase portrait of the theory may look very different depending on the sign of the coefficient c [ 8]. The inflationary solution is stable for a positive c and is unstable in the case c < 0. In the last case there are several stable points (attractors), one of which corresponds to the FRW evolution. The original Starobinsky model deals only with the unstable solution. In this case one has to choose the initial conditions in a very special way. First of all, they must be very close to the exact exponential solution (5), such that the inflation lasts long enough. Moreover the choice of the initial condition has to provide that, after the inflationary phase ends, the Universe will approach the attractor corresponding to the FRW solution, and not to the other (physically unacceptable) attractor. All the matter content of the Universe is

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“…The equation governing the behaviour of gravitational waves in the anomaly-induced model, in terms of the cosmic time t, is [ 3] …”

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Gravitational waves in an anomaly-induced inflation

Fabris¹,

Pelinson²,

Shapiro³

et al. 2004

Nuclear Physics B - Proceedings Supplements

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The behaviour of gravitational waves in the anomaly-induced inflationary phase is studied. The metric perturbations exhibit a stable behaviour, with a very moderate growth in the amplitude of the waves. The spectral indice is computed, revealing an almost flat spectrum.The goal of the present study is to analyze the fate of gravitational waves in a background defined by an inflationary scenario created by a trace anomaly induced by quantum effects generated by matter fields in the primordial Universe [ 1]. This model is a generalization of the Starobinsky model [ 2], where a similar mechanism has been developed. The counterterms necessary to avoid divergences in the quantization of these conformal quantum fields in a FriedmannRobertson-Walker background leads to a higher derivative action with a trace anomaly. Details of the model may be found in [ 1]. An important point concerns the fact that an inflationary phase may be obtained with this effective gravitational action. When all fields are massless, this inflationary phase is an eternal de Sitter phase, where many of the traditional problems of the inflationary scenario appear. However, if massive conformal fields are included, the inflationary phase has more complicated form. A detailed analysis of the massive case reveals that a huge amplification of the scale factor may be obtained, of the order of 10 10 e-folds. However, from the observational point of view, only the last 65 − 70 e-folds are relevant. During this final period, the behaviour of the scale factor may be approximated by an exponential function, the Hubble parameter being constant. It is possible that a transition to the FRW standard scenario may be achieved solving the graceful exit problem [ 4].The equation governing the behaviour of gravitational waves in the anomaly-induced model, in terms of the cosmic time t, is [ 3]withHere the quantities with tildes are pure numbers:whileb 4 depends on the multiplet content of the matter fields:where N 0 , N 1/2 and N 1 are the scalar, fermionic and vectorial numbers of matter fields. For example, in the minimal standard model, N 0 = 4, N 1/2 = 24 and N 1 = 12, leading to b 4 ∼ 0.2. As usual, H =ȧ/a is the Hubble parameter. The parameters described above take those value in the last 65 e-fold. In this case, the background model enters in a quasi-de Sitter and the scale factor behaves essentially as a ∼ e Ht (5)

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On the stability of the anomaly-induced inflation

Cited by 89 publications

References 45 publications

Effect of the trace anomaly on the cosmological constant

Effect of the trace anomaly on the cosmological constant

An overview of the anomaly-induced inflation

Gravitational waves in an anomaly-induced inflation

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