Some physical implications of regularization ambiguities in SU(2) gauge-invariant loop quantum cosmology

Liegener, Klaus; Singh, Parampreet

doi:10.1103/physrevd.100.124049

Cited by 12 publications

(22 citation statements)

References 80 publications

(227 reference statements)

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“…Finally, one can hope that these insights into the cosmological model help to deal with the vast regularization ambiguities of the full theory. Some of these ambiguities and their physical implications are studied in our companion paper [47].…”

Section: Discussionmentioning

confidence: 99%

New loop quantum cosmology modifications from gauge-covariant fluxes

Liegener

Singh

2019

Phys. Rev. D

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Loop quantum cosmology is a symmetry reduced quantization of cosmological spacetimes based on loop quantum gravity. While it has been succsessful in resolution of various cosmological singularities and connecting Planck scale physics to phenomenology, its connection with loop quantum gravity has remained elusive. It is therefore important to integrate more and more features of the full theory into this framework and understand the reliability of physical predictions. In particular, if one wishes to connect the effective Hamiltonian in loop quantum cosmology to an expectation value of the scalar constraint operator in suitable coherent states for the full theory, one has to go beyond the standard setting of loop quantum cosmology. One possibility is to introduce gauge-covariant fluxes, which become necessary because the presence of a finite regularization parameter causes functions build out of the standard discretized variables to be in general not gauge invariant. Following the construction of gauge-covariant fluxes pioneered by Thiemann in [1], we show that the physics of loop quantum cosmology is affected in a non-trivial way. The bounce turns out to be generically asymmetric with a rescaling of the Newton's constant in the pre-bounce branch. Gauge-covariant fluxes result in a higher order quantum difference equation in comparison to loop quantum cosmology. Even the behavior of matter, which behaves innocuously in loop quantum cosmology, is enriched resulting in an effective non-minimal coupling. These effects are shown to be common to different choices of regularization parameters.

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Section: Discussionmentioning

confidence: 99%

New loop quantum cosmology modifications from gauge-covariant fluxes

Liegener

Singh

2019

Phys. Rev. D

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“…In this subsection, we consider effective dynamics resulting from two loop quantizations of the classical Hamiltonian (2.17). The first is based on using holonomy and triad variables as in standard LQC [7,58], and the second is based on a recently studied quantization of holonomy and gauge-covariant fluxes [47][48][49]. In addition to the effective Hamiltonian and the equations of motion in each case, we also discuss analytical solutions in the first case and define useful variables for unravelling the dynamics of the collapsing dust cloud through numerical results when analytical solutions are not available.…”

Section: A Quantum Gravity Modified Dynamical Equationsmentioning

confidence: 99%

“…While this strategy works for loop quantization of symmetry reduced models, one needs to go beyond this approach if one wishes to obtain an effective Hamiltonian with loop quantum modifications from loop quantum gravity using suitable coherent states. A possibility in this direction requires an introduction of gauge-covariant fluxes, first introduced by Thiemann [50], which have been recently implemented in loop quantization of cosmological spacetimes [47][48][49]. It tuns out that the corresponding quantum effects can be incorporated into the effective Hamiltonian by making the substitution √ ε x → √ ε x sinc (δ x k x /2) in the classical Hamiltonian (2.17), which, together with the holonomy corrections in k x , gives rise to the following effective Hamiltonian,…”

Section: Non-singular Evolution In Holonomy and Gauge-covariant Flux ...mentioning

confidence: 99%

“…One prominent approach to relate these models to LQG is via coherent states to approximate certain sectors of LQG. But, this is challenging for quantizations, as ones discussed above, which are based on a fixed discretized lattice and flux variables (for a discussion see [47][48][49]). A resolution is to use gauge-covariant flux variables on a discretized fixed lattice [50].…”

Section: Introductionmentioning

confidence: 99%

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Non-singular quantum gravitational dynamics of an LTB dust shell model: the role of quantization prescriptions

Giesel,

Li,

Singh

2021

Preprint

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We study some consequences of the loop quantization of the outermost dust shell in the Lemaître-Tolman-Bondi spacetime with a homogeneous dust density using different quantization strategies motivated by loop quantum gravity. Prior work has dealt with loop quantizing this model by employing holonomies and the triads, following the procedure in standard loop quantum cosmology. In this work we compare this quantization with the one in which holonomies and gauge-covariant fluxes are used. While both of the quantization schemes resolve the central singularity, they lead to different mass gaps at which a trapped surface forms. This trapped surface which is matched to an exterior generalized Vaidya spacetime disappears when the density of the dust shell is in the Planck regime. We find that the quantization based on holonomies and gauge-covariant fluxes generically results in an asymmetric evolution of the dust shell in which the effective mass associated with the white hole as seen by an external observer is 2/π of the one for the black hole. This effective difference in masses results from difference in the classical limits in pre-and post-bounce regimes in the two quantizations. This distinctive feature rules out formation of any black hole-white hole twin in presence of gauge-covariant flux modifications which is in contrast to the quantization using holonomies and triads where the gravitational collapse always leads to a black hole-white hole twins. In another striking difference, for the quantization based on holonomies and gauge-covariant fluxes there can be situations in which during a non-singular collapse only a black hole forms without a white hole.

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“…As a consequence, the two branches of the Universe (pre and post-bounce) tend, in general, to different classical trajectories. Even though this is the first time that an asymmetric bounce has resulted from this quantization procedure, we note that other prescriptions within the context of LQC have been found to generate an asymmetry between the pre and post-bounce epochs [30][31][32][33].…”

Section: The Effect Of the Constant Potential In The Bounce Scenario mentioning

confidence: 74%

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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Some physical implications of regularization ambiguities in SU(2) gauge-invariant loop quantum cosmology

Cited by 12 publications

References 80 publications

New loop quantum cosmology modifications from gauge-covariant fluxes

New loop quantum cosmology modifications from gauge-covariant fluxes

Non-singular quantum gravitational dynamics of an LTB dust shell model: the role of quantization prescriptions

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

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