Abstract
We consider the backgroundindependent quantization of a general scaleinvariant theory of gravity with matter, which supports a conserved Weyl current recently suggested as a natural flow of time. For scalarmetric systems, a conformal class of AshtekarBarbero 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 spinnetwork 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 spinnetwork 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 scaleinvariant homogenous and isotropic cosmological model coupled to a doublet of scalars with illustrative numerical simulations. The Einsteinframe 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 Jordanframe volume tend to zero. Remarkably, the quantized big bang is not replaced by a big bounce—a prevalent scenario in present loop quantum cosmology.
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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Profiles

Charles Wang
Person: Academic