Solvable loop quantum cosmology: Domain of the volume observable and semiclassical states

Martín-Benito, Mercedes; Neves, Rita B.

doi:10.1103/physrevd.99.043525

Cited by 5 publications

(4 citation statements)

References 27 publications

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“…The problem with finding suitable states in the volume domain was already mentioned in [20]. Indeed, for both WDW and these LQC models we will prove that there are basically no states such that expectation value of the volume is finite under the evolution (see section 2 for notation).…”

Section: Introductionmentioning

confidence: 73%

The volume operator in loop quantum cosmology

Kaminski

2019

Preprint

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We show that for basically all states, the evolution of the expectation value of the volume operator in Wheeler-DeWitt and various homogenous isotropic loop quantum comology (LQC) models (k = 0, coupled to massless scalar field and without cosmological constant) is ill-defined. The expectation value of the volume operator become instantonously infinite during the evolution. The effect is produced by a very long tail in the volume spectrum, that is however semiclassically small and beyond reach of numerical simulations (that is why it went unnoticed so far). This is not necessarily problem of theory but rather it suggests that one should be extremely careful with unbounded observables.

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Section: Introductionmentioning

confidence: 73%

The volume operator in loop quantum cosmology

Kaminski

2019

Preprint

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“…For completeness, we end this section noticing that the aforementioned issue is avoided as well in the especial cases ε = 2, 4 of the sLQC model, and in the so-called sMMO prescription [36,38] for any choice of its superselection sectors (which have the same form as in the MMO model). We refer again to the appendix for details.…”

Section: Avoidance Of the Issuementioning

confidence: 99%

On the evolution of the volume in Loop Quantum Cosmology

Navascués

2024

Class. Quantum Grav.

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The dynamics of the expectation value of the volume is one of the key ingredients behind the replacement of the Big Bang singularity by a bounce in Loop Quantum Cosmology. As such, it is of great importance that this quantity is mathematically well-defined in the space of physical states of the theory. A number of caveats have been raised about such a definition entering in conflict with the quantum evolution of states, motivated by the situation found in quantum geometrodynamics. We show that there are ways around these caveats, all of which are related to the existence of quantization prescriptions leading to a nondegenerate curvature operator in Loop Quantum Cosmology. Interestingly, the properties of the curvature operator that may allow for a good behavior of the volume are only possible thanks to the discreteness of the geometry characteristic of the loop quantization procedure.

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“…With a constant potential, it is straightforward to compute I 1 (x, φ) as defined in (29). This is followed by a manipulation of E(x, φ) of (31) in order to identify the v n functions that appear in V of (30).…”

Section: Constant Potentialmentioning

confidence: 99%

“…As investigated in [29], the relation between the profiles ψ(k) of the v-representation and the profiles F(k) of the solvable representation is given by…”

Section: Constant Potentialmentioning

confidence: 99%

The Effect of a Positive Cosmological Constant on the Bounce of Loop Quantum Cosmology

Martín-Benito

Neves

2020

Mathematics

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We provide an analytical solution to the quantum dynamics of a flat Friedmann-Lemaître-Robertson-Walker model with a massless scalar field in the presence of a small and positive cosmological constant, in the context of Loop Quantum Cosmology. We use a perturbative treatment with respect to the model without a cosmological constant, which is exactly solvable. Our solution is approximate, but it is precisely valid at the high curvature regime where quantum gravity corrections are important. We compute explicitly the evolution of the expectation value of the volume. For semiclassical states characterized by a Gaussian spectral profile, the introduction of a positive cosmological constant displaces the bounce of the solvable model to lower volumes and to higher values of the scalar field. These displacements are state dependent, and in particular, they depend on the peak of the Gaussian profile, which measures the momentum of the scalar field. Moreover, for those semiclassical states, the bounce remains symmetric, as in the vanishing cosmological constant case. However, we show that the behavior of the volume is more intricate for generic states, leading in general to a non-symmetric bounce.

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Solvable loop quantum cosmology: Domain of the volume observable and semiclassical states

Cited by 5 publications

References 27 publications

The volume operator in loop quantum cosmology

The volume operator in loop quantum cosmology

On the evolution of the volume in Loop Quantum Cosmology

The Effect of a Positive Cosmological Constant on the Bounce of Loop Quantum Cosmology

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