Hybrid quantization of an inflationary universe

Fernández-Méndez, Mikel; Marugán, Guillermo A. Mena; Olmedo, Javier

doi:10.1103/physrevd.86.024003

Cited by 154 publications

(217 citation statements)

References 66 publications

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“…The structure of the physical states (3.16) and the properties of Θ (namely its self-adjointness and positive definiteness) also imply the equivalence between the physical inner product and the gravitational kinematical inner product on constant A γ slices 19) which allows us to interpret A γ as an emergent time and use it as an evolution parameter. We can thus define the dynamics as the unitary mapping…”

Section: Deparametrizationmentioning

confidence: 99%

“…The classical dynamics of this model is generated by the Hamiltonian constraint term in the canonical action 19) where the gravitational and matter terms are given by (2.18) and (2.14) respectively. The physical trajectories lie on the surface…”

Section: Classical Dynamicsmentioning

confidence: 99%

“…Most recently cosmological perturbations have also been studied in LQC, first from an effective theory standpoint [18] and then in quantum treatments following various approaches: a "hybrid" quantization (i.e., the LQC of the homogeneous background and a Fock quantization of the perturbative degrees of freedom) [19] (see also [20]) and by the LQC treatment of a discretization of the flat FLRW space-time with scalar perturbations [21]. These works have allowed the study of the dynamics of cosmological perturbations in the Planck regime in some of the most interesting cosmological scenarios -those that generate a scale-invariant power spectrum of scalar perturbationsnamely inflation [22], the matter bounce [23] and the ekpyrotic universe [24].…”

Section: Introductionmentioning

confidence: 99%

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Loop quantum cosmology of a radiation-dominated flat FLRW universe

2014

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We study the loop quantum cosmology of a flat Friedmann-Lemaître-Robertson-Walker spacetime with a Maxwell field. We show that many of the qualitative properties derived for the case of a massless scalar field also hold for a Maxwell field. In particular, the big-bang singularity is replaced by a quantum bounce, and the operator corresponding to the matter energy density is bounded above by the same critical energy density. We also numerically study the evolution of wave functions that are sharply peaked in the low energy regime, and derive effective equations which very closely approximate the full quantum dynamics of sharply peaked states at all times, including the near-bounce epoch. In the process, the analytical and numerical methods originally used to study the dynamics in LQC for the case of a massless scalar field are substantially improved to handle the difficulties (that generically arise for matter content other than a massless scalar field) related to the presence of a Maxwell field.

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Section: Deparametrizationmentioning

confidence: 99%

Section: Classical Dynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Loop quantum cosmology of a radiation-dominated flat FLRW universe

2014

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“…Finally, let us emphasize that this particle production is due to the quantum evolution of the vacuum in the Euclidean regime, a phenomenon which is apparently independent of the amplification of modes [40] that has also been confirmed recently in the effective description of inhomogeneous models in hybrid LQC [41], systems in which the cosmological background always remains Lorentzian and a bounce in the expansion occurs.…”

Section: Discussionmentioning

confidence: 99%

Uniqueness of the Fock quantization of scalar fields and processes with signature change in cosmology

Gomar

Marugán

2014

Phys. Rev. D

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We study scalar fields subject to an equation of the Klein-Gordon type in nonstationary spacetimes, such as those found in cosmology, assuming that all the relevant spatial dependence is contained in the Laplacian. We show that the field description -with a specific canonical pair-and the Fock representation for the quantization of the field are fixed indeed in a unique way (except for unitary transformations that do not affect the physical predictions) if we adopt the combined criterion of (a) imposing the invariance of the vacuum under the group of spatial symmetries of the field equations and (b) requiring a unitary implementation of the dynamics in the quantum theory. Besides, we provide a spacetime interpretation of the field equations as those corresponding to a scalar field in a cosmological spacetime that is conformally ultrastatic. In addition, in the privileged Fock quantization, we investigate the generalization of the evolution of physical states from the hyperbolic dynamical regime to an elliptic regime. In order to do this, we contemplate the possibility of processes with signature change in the spacetime where the field propagates and discuss the behavior of the background geometry when the change happens, proving that the spacetime metric degenerates. Finally, we argue that this kind of signature change leads naturally to a phenomenon of particle creation, with exponential production.

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“…As it is known how to include inflation in LQC [24,25], it is important now to study how quantum gravity effects could affect the standard inflationary predictions. Some work has already been done in this direction, see for example [15,26].…”

Section: Discussionmentioning

confidence: 99%

The Matter Bounce Scenario in Loop Quantum Cosmology

Wilson-Ewing

2016

Proceedings of Frontiers of Fundamental Physics 14 — PoS(FFP14)

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In the matter bounce scenario, a dust-dominated contracting space-time generates scale-invariant perturbations that, assuming a nonsingular bouncing cosmology, propagate to the expanding branch and set appropriate initial conditions for the radiation-dominated era. Since this scenario depends on the presence of a bounce, it seems appropriate to consider it in the context of loop quantum cosmology where a bouncing universe naturally arises. For a pressureless collapsing universe in loop quantum cosmology, the predicted power spectrum of the scalar perturbations after the bounce is scale-invariant and the tensor to scalar ratio is negligibly small. A slight red tilt can be given to the scale-invariance of the scalar perturbations by a scalar field whose equation of state is P = −ǫρ, where ǫ is a small positive number. Then, the power spectrum for tensor perturbations is also almost scale-invariant with the same red tilt as the scalar perturbations, and the tensor to scalar ratio is expected to be r ≈ 9 × 10 −4 . Finally, for the predicted amplitude of the scalar perturbations to agree with observations, the critical density in loop quantum cosmology must be of the order ρc ∼ 10 −9 ρ Pl .

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Hybrid quantization of an inflationary universe

Cited by 154 publications

References 66 publications

Loop quantum cosmology of a radiation-dominated flat FLRW universe

Loop quantum cosmology of a radiation-dominated flat FLRW universe

Uniqueness of the Fock quantization of scalar fields and processes with signature change in cosmology

The Matter Bounce Scenario in Loop Quantum Cosmology

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