Semiclassical limit of new path integral formulation from reduced phase space loop quantum gravity

Han, Muxin; Liu, Hongguang

doi:10.1103/physrevd.102.024083

Cited by 28 publications

(37 citation statements)

References 66 publications

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“…Motivated by the above considerations, recently various modified LQC models have been proposed, see, for example (Alesci and Cianfrani, 2013;Alesci and Cianfrani, 2015;Alesci et al, 2017;Oriti, 2017;Oriti et al, 2017;Wilson-Ewing, 2017;Engle and Vilensky, 2018;Gerhardt et al, 2018;Wilson-Ewing, 2018;Baytas et al, 2019;Engle and Vilensky, 2019;Neuser et al, 2019;Olmedo and Alesci, 2019;Han and Liu, 2020a;Han and Liu, 2020b;Han et al, 2020;Li et al, 2020b), and references therein. In this brief review, we have restricted ourselves only to mLQC-I and mLQC-II (Yang et al, 2009;Dapor and Liegener, 2018a;Dapor and Liegener, 2018b), as they are the ones that have been extensively studied in the literature not only the dynamics of the homogeneous Universe (Li et al, 2018a;Li et al, 2018b;Saini and Singh, 2019a;Saini and Singh, 2019b;García-Quismondo and Mena Marugán, 2019;Li et al, 2019;, but also the cosmological perturbations (Agullo, 2018;Castelló Gomar et al, 2020;Li et al, 2020a;Li et al, 2020b).…”

Section: Discussionmentioning

confidence: 99%

Phenomenological Implications of Modified Loop Cosmologies: An Overview

Singh

Wang

2021

Front. Astron. Space Sci.

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In this paper, we first provide a brief review of the effective dynamics of two recently well-studied models of modified loop quantum cosmologies (mLQCs), which arise from different regularizations of the Hamiltonian constraint and show the robustness of a generic resolution of the big bang singularity, replaced by a quantum bounce due to non-perturbative Planck scale effects. As in loop quantum cosmology (LQC), in these modified models the slow-roll inflation happens generically. We consider the cosmological perturbations following the dressed and hybrid approaches and clarify some subtle issues regarding the ambiguity of the extension of the effective potential of the scalar perturbations across the quantum bounce, and the choice of initial conditions. Both of the modified regularizations yield primordial power spectra that are consistent with current observations for the Starobinsky potential within the framework of either the dressed or the hybrid approach. But differences in primordial power spectra are identified among the mLQCs and LQC. In addition, for mLQC-I, striking differences arise between the dressed and hybrid approaches in the infrared and oscillatory regimes. While the differences between the two modified models can be attributed to differences in the Planck scale physics, the permissible choices of the initial conditions and the differences between the two perturbation approaches have been reported for the first time. All these differences, due to either the different regularizations or the different perturbation approaches in principle can be observed in terms of non-Gaussianities.

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Section: Discussionmentioning

confidence: 99%

Phenomenological Implications of Modified Loop Cosmologies: An Overview

Singh

Wang

2021

Front. Astron. Space Sci.

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“…where e I , e J , e K have been re-oriented to be outgoing at v, ǫ IJK = sgn[det(e I ∧ e J ∧ e K )], α IJ is the minimal loop around a plaquette containing e I and e J [17,18], which begins at v via e I and gets back to v through e J . With the same notations, the Lorentzian part is given by…”

Section: E(γ)|mentioning

confidence: 99%

“…This operator is manifestly Hermitian and therefore admits a self-adjoint extension. Based on this Hamiltonian operator, the effective dynamics from the coherent state path integral has been studied for a cubic graph γ in [14,17]. We now give a brief review of this effective dynamics.…”

Section: Effective Dynamics From Coherent State Path Integralmentioning

confidence: 99%

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The effective dynamics of weak coupling loop quantum gravity

Long,

2021

Preprint

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By taking the limit that Newton's Gravitational constant tends to zero, the weak coupling loop quantum gravity can be formulated as a U (1) 3 gauge theory instead of the original SU (2) gauge theory. In this paper, a parametrization of the SU (2) holonomy-flux variables by the U (1) 3 holonomy-flux variables is introduced, and the Hamiltonian operator based on this parametrization is obtained for the weak coupling loop quantum gravity. It is shown that the effective dynamics obtained from the coherent state path integrals in U (1) 3 and SU (2) loop quantum gravity respectively are consistent to each other in the weak coupling limit, provided that the expectation values of the Hamiltonian operators on the coherent states in these two theories coincide with their classical expressions respectively.

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“…Especially, it has been shown that the heat-kernel coherent state of SU (2) possesses a well-behaved peakedness property in the phase space T * SU (2), and the "Ehrenfest property" of this coherent state guarantee the coincidence between the expectation values of the elementary operators Ô and the classical evaluations of O in the phase space. Based on these properties of the heat-kernel coherent state of SU (2), the semi-classical limit of (1+3)-dimensional LQG is studied from a variety of perspectives [13][14][15][16]. Apart from the heat-kernel coherent state, another type of coherent state in (1+3)-dimensional LQG is introduced and applied to analyze the asymptotics of the EPRL spin foam model [17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Twisted geometry coherent states in all dimensional loop quantum gravity: I. Construction and Peakedness properties

Long,

Zhang,

Zhang

2021

Preprint

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A new family of coherent states for all dimensional loop quantum gravity are proposed, which is based on the generalized twisted geometry parametrization of the phase space of SO(D + 1) connection theory. We prove that this family of coherent states provide an over-complete basis of the Hilbert space in which edge simplicity constraint is solved. Moreover, according to our explicit calculation, the expectation values of holonomy and flux operators with respect to this family of coherent states coincide with the corresponding classical values given by the labels of the coherent states, up to some gauge degrees of freedom. Besides, we study the peakedness properties of this family of coherent states, including the peakedness of the wave functions of this family of coherent states in holonomy, momentum and phase space representations. It turns out that the peakedness in these various representations and the (relative) uncertainty of the expectation values of the operators are well controlled by the semi-classical parameter t. Therefore, this family of coherent states can serve as a candidate for the semi-classical analysis of all dimensional loop quantum gravity.

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Semiclassical limit of new path integral formulation from reduced phase space loop quantum gravity

Cited by 28 publications

References 66 publications

Phenomenological Implications of Modified Loop Cosmologies: An Overview

Phenomenological Implications of Modified Loop Cosmologies: An Overview

The effective dynamics of weak coupling loop quantum gravity

Twisted geometry coherent states in all dimensional loop quantum gravity: I. Construction and Peakedness properties

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