Equivalence of Models in Loop Quantum Cosmology and Group Field Theory

Baytaş, Bekir; Bojowald, Martin; Crowe, Sean

doi:10.3390/universe5020041

Cited by 9 publications

(14 citation statements)

References 48 publications

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“…This conformal invariance of the cosmological action under Mobius transformation in proper time, is distinct from the time reparametrization invariance, which is the remnant of the diffeomorphism invariance of general relativity in this cosmological setting. While previous works in classical and quantum cosmology have also noticed the existence of a conformal structure, such as [5][6][7][8][9], the realization of the conformal symmetry discussed in [1] is quite different.…”

Section: Introductionmentioning

confidence: 99%

“…One would then translate the Hamiltonian constraint and other observables into differential operators by applying the standard canonical quantization prescription withv andb quantized as multiplicative or derivative operators. One could also apply an9 Let us point out that there are hints of a more general conformal structure with a Virasoro algebra extending the sl(2, R) structure[18,19]. Virasoro group transformations act non-trivially on the potential, or in other words it looks possible to write the scalar field potential in terms of Virasoro generators.…”

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confidence: 99%

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Conformal structure of FLRW cosmology: spinorial representation and the $$ \mathfrak{so} $$ (2, 3) algebra of observables

Achour

Livine

2020

J. High Energ. Phys.

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It was recently shown that the homogeneous and isotropic cosmology of a massless scalar field coupled to general relativity exhibits a new hidden conformal invariance under Mobius transformation of the proper time, additionally to the invariance under time-reparamterization. The resulting Noether charges form a sl(2, R) Lie algebra, which encapsulates the whole kinematics and dynamics of the geometry. This allows to map FLRW cosmology onto conformal mechanics and formulate quantum cosmology in CFT 1 terms. Here, we show that this conformal structure is embedded in a larger so(3, 2) algebra of observables, which allows to present all the Dirac observables for the whole gravity plus matter sectors in a unified picture. Not only this allows one to quantize the system and its whole algebra of observables as a single irreducible representation of so(3, 2), but this also gives access to a scalar field operatorφ opening the door to the inclusion of non-trivial potentials for the scalar field. We expect this extended conformal structure to simplify the investigation of the quantum dynamics of inflationary cosmological backgrounds based on effective approaches to quantum cosmology.

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

Conformal structure of FLRW cosmology: spinorial representation and the $$ \mathfrak{so} $$ (2, 3) algebra of observables

Achour

Livine

2020

J. High Energ. Phys.

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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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“…I read this as a warning of an enlightened guru speaking to his present adherents and future believers: Safeguard your independent thinking before you become completely converted. We could include group field theory (GFT) [173][174][175][176] in the present considerations (only) to the extent that (partial) equivalence of models employed or results reported can be shown to exist between these two theories [177]. Of course we need to hear the views of the GFT community on this.…”

Section: Notesmentioning

confidence: 99%

Weyl Curvature Hypothesis in Light of Quantum Backreaction at Cosmological Singularities or Bounces

2021

Universe

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The Weyl curvature constitutes the radiative sector of the Riemann curvature tensor and gives a measure of the anisotropy and inhomogeneities of spacetime. Penrose’s 1979 Weyl curvature hypothesis (WCH) assumes that the universe began at a very low gravitational entropy state, corresponding to zero Weyl curvature, namely, the Friedmann–Lemaître–Robertson–Walker (FLRW) universe. This is a simple assumption with far-reaching implications. In classical general relativity, Belinsky, Khalatnikov and Lifshitz (BKL) showed in the 70s that the most general cosmological solutions of the Einstein equation are that of the inhomogeneous Kasner types, with intermittent alteration of the one direction of contraction (in the cosmological expansion phase), according to the mixmaster dynamics of Misner (M). How could WCH and BKL-M co-exist? An answer was provided in the 80s with the consideration of quantum field processes such as vacuum particle creation, which was copious at the Planck time (10−43 s), and their backreaction effects were shown to be so powerful as to rapidly damp away the irregularities in the geometry. It was proposed that the vaccum viscosity due to particle creation can act as an efficient transducer of gravitational entropy (large for BKL-M) to matter entropy, keeping the universe at that very early time in a state commensurate with the WCH. In this essay I expand the scope of that inquiry to a broader range, asking how the WCH would fare with various cosmological theories, from classical to semiclassical to quantum, focusing on their predictions near the cosmological singularities (past and future) or avoidance thereof, allowing the Universe to encounter different scenarios, such as undergoing a phase transition or a bounce. WCH is of special importance to cyclic cosmologies, because any slight irregularity toward the end of one cycle will generate greater anisotropy and inhomogeneities in the next cycle. We point out that regardless of what other processes may be present near the beginning and the end states of the universe, the backreaction effects of quantum field processes probably serve as the best guarantor of WCH because these vacuum processes are ubiquitous, powerful and efficient in dissipating the irregularities to effectively nudge the Universe to a near-zero Weyl curvature condition.

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Equivalence of Models in Loop Quantum Cosmology and Group Field Theory

Cited by 9 publications

References 48 publications

Conformal structure of FLRW cosmology: spinorial representation and the $$ \mathfrak{so} $$ (2, 3) algebra of observables

Conformal structure of FLRW cosmology: spinorial representation and the $$ \mathfrak{so} $$ (2, 3) algebra of observables

Phenomenological Implications of Modified Loop Cosmologies: An Overview

Weyl Curvature Hypothesis in Light of Quantum Backreaction at Cosmological Singularities or Bounces

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