A reduction of order two for infinite-order Lagrangians

Jaén, Xavier; Llosa, Josep; Molina, Alfred

doi:10.1103/physrevd.34.2302

Cited by 87 publications

(102 citation statements)

References 8 publications

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“…For the loop quantized model it is more complicated to introduce adiabaticity relative to free solutions because free quantum variables (27)- (32) are not simply proportional to powers of the expectation values as in the Wheeler-DeWitt case. The most direct possibility is to introduce the free solutions as explicitly time dependent functions G a,n V =0 (φ).…”

Section: Non-adiabaticity Relative To Free Solutionsmentioning

confidence: 99%

“…In the free case, its implementation resulted in selecting the cosh-solution for p and ruling out the sinh solution, proving the bounce under the assumption of a semiclassical state at large volume. (The integration constants A and B must have equal sign in (27) if c 1 is not too large and negative.) Perturbatively, the reality condition becomes…”

Section: (J +J)mentioning

confidence: 99%

“…Perturbed equations of motion are more complicated than for the Wheeler-DeWitt model, but we can focus on a few dominant terms. Moreover, we can assume A = B in (27), (28) since we would just need to shift our internal time otherwise. We keep the classical perturbation, given by p…”

Section: Wheeler-dewitt Modelmentioning

confidence: 99%

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Effective equations for isotropic quantum cosmology including matter

2007

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Effective equations often provide powerful tools to develop a systematic understanding of detailed properties of a quantum system. This is especially helpful in quantum cosmology where several conceptual and technical difficulties associated with the full quantum equations can be avoided in this way. Here, effective equations for Wheeler-DeWitt and loop quantizations of spatially flat, isotropic cosmological models sourced by a massive or interacting scalar are derived and studied. The resulting systems are remarkably different from that given for a free, massless scalar. This has implications for the coherence of evolving states and the realization of a bounce in loop quantum cosmology.

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Section: Non-adiabaticity Relative To Free Solutionsmentioning

confidence: 99%

Section: (J +J)mentioning

confidence: 99%

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Effective equations for isotropic quantum cosmology including matter

2007

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“…An additional challenge arises because the presence of dimension five operators encoding the corrections to QED in the MP model make the theory of the HOTD type. At least at the perturbative level, it is well known that HOTD theories, besides the obvious property of having additional degrees of freedom with respect to the lower order ones, give rise to Hamiltonians which are not positive definite, irrespectively of the interaction terms [4,5]. In fact, a perturbation of electrodynamics should not introduce additional degrees of freedom, so that a careful strategy is required to define an adequate perturbative procedure in the LIV parameters.…”

Section: Introductionmentioning

confidence: 99%

Quantum corrections in the Myers-Pospelov model: a progress report

Urrutia¹

2008

Proceedings of From Quantum to Emergent Gravity: Theory and Phenomenology — PoS(QG-Ph)

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The Myers-Pospelov (MP) model is an effective field theory (EFT), including dimension five operators, which describes the phenomenology of active Lorentz invariance violation produced by a preferred reference frame. We concentrate here in the case of the modified electrodynamics. The point of view taken in this work is that the Lorentz violating part of the action in the MP model, which includes higher order time derivative (HOTD) operators, is to be considered as a perturbation over the dynamics described by standard Electrodynamics, particularly in the quantum case. HOTD theories, besides incorporating additional degrees of freedom, suffer from well known difficulties in their quantization, among which one finds Hamiltonians which are not bounded from below. Thus, in order to cope with these challenges it will be necessary to deal with a modified perturbation theory which is well described in the literature. We apply such methods to this specific model providing a quantization of the free sector of the theory by identifying the modified normal mode expansions of the fields together with the modified propagators and the interaction terms. The calculation of interacting processes, together with radiative corrections, is beyond the scope of the present article and will be deferred for future publications. From Quantum to Emergent Gravity: Theory and Phenomenology

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“…There are several problems with higher derivative theories [17,18], e.g., need for additional initial conditions in a formulation of a cauchy problem, existence of run away solutions, and whether solutions obtained from R + βR 2 gravity reduce to solutions of Einstein's gravity as β → 0. In order to resolve these issues, the author has recently proposed an alternate approach to R + βR 2 gravity in which βR 2 is treated as a backreaction on Einstein's gravity [19].…”

mentioning

confidence: 99%

Strong energy condition inR+R2gravity

Kung

1996

Phys. Rev. D

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A reduction of order two for infinite-order Lagrangians

Cited by 87 publications

References 8 publications

Effective equations for isotropic quantum cosmology including matter

Effective equations for isotropic quantum cosmology including matter

Quantum corrections in the Myers-Pospelov model: a progress report

Strong energy condition inR+R2gravity

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