### Abstract

Original language | English |
---|---|

Article number | 135106 |

Journal | Physics Letters B |

Volume | 800 |

Early online date | 19 Nov 2019 |

DOIs | |

Publication status | Published - 10 Jan 2020 |

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*Physics Letters B*,

*800*, [135106]. https://doi.org/10.1016/j.physletb.2019.135106

**Quantization of time and the big bang via scale-invariant loop gravity.** / Wang, Charles H.-T.; Stankiewicz, Marcin.

Research output: Contribution to journal › Article

*Physics Letters B*, vol. 800, 135106. https://doi.org/10.1016/j.physletb.2019.135106

}

TY - JOUR

T1 - Quantization of time and the big bang via scale-invariant loop gravity

AU - Wang, Charles H.-T.

AU - Stankiewicz, Marcin

N1 - Acknowledgements The authors are grateful to Y. Adamu and D. Rodrigues for discussions and to the Carnegie Trust and Cruickshank Trust in Scotland for financial support.

PY - 2020/1/10

Y1 - 2020/1/10

N2 - We consider the background-independent quantization of a general scale-invariant theory of gravity with matter, which supports a conserved Weyl current recently suggested as a natural flow of time. For scalar-metric systems, a conformal class of Ashtekar-Barbero connection variables is constructed, which can be quantized using spin networks. Crucially, the quantum states become separable into the eigen states of the generator of the scale transformation and spin-network states in the Einstein frame. The eigen values consist of additional quantum numbers including a new type of fundamental frequency ω and energy E = ~ω with respect to a new local time τ carried by every spin-network vertex. The discretely distributed τ values as the “quanta of time” correspond to a functional time related to the integrated Weyl current in the classical theory. The Immirzi ambiguity of loop quantum geometry is removed by scale symmetry. To probe the quantum behaviour of the early Universe, the new formalism is applied to a scale-invariant homogenous and isotropic cosmological model coupled to a doublet of scalars with illustrative numerical simulations. The Einstein-frame volume is quantized in recently improved and regularized polymer representations with an arbitrary Immirzi parameter. The resulting unitary evolution of the quantum state of an expanding universe has a positive energy spectrum. A rescaling of the Immirzi parameter is equivalent to a translation in time without changing dynamics. The big bang can be identified in the past time limit when the expectation values of the Jordan-frame volume tend to zero. Remarkably, the quantized big bang is not replaced by a big bounce—a prevalent scenario in present loop quantum cosmology.

AB - We consider the background-independent quantization of a general scale-invariant theory of gravity with matter, which supports a conserved Weyl current recently suggested as a natural flow of time. For scalar-metric systems, a conformal class of Ashtekar-Barbero connection variables is constructed, which can be quantized using spin networks. Crucially, the quantum states become separable into the eigen states of the generator of the scale transformation and spin-network states in the Einstein frame. The eigen values consist of additional quantum numbers including a new type of fundamental frequency ω and energy E = ~ω with respect to a new local time τ carried by every spin-network vertex. The discretely distributed τ values as the “quanta of time” correspond to a functional time related to the integrated Weyl current in the classical theory. The Immirzi ambiguity of loop quantum geometry is removed by scale symmetry. To probe the quantum behaviour of the early Universe, the new formalism is applied to a scale-invariant homogenous and isotropic cosmological model coupled to a doublet of scalars with illustrative numerical simulations. The Einstein-frame volume is quantized in recently improved and regularized polymer representations with an arbitrary Immirzi parameter. The resulting unitary evolution of the quantum state of an expanding universe has a positive energy spectrum. A rescaling of the Immirzi parameter is equivalent to a translation in time without changing dynamics. The big bang can be identified in the past time limit when the expectation values of the Jordan-frame volume tend to zero. Remarkably, the quantized big bang is not replaced by a big bounce—a prevalent scenario in present loop quantum cosmology.

U2 - 10.1016/j.physletb.2019.135106

DO - 10.1016/j.physletb.2019.135106

M3 - Article

VL - 800

JO - Physics Letters B

JF - Physics Letters B

SN - 0370-2693

M1 - 135106

ER -