Abstract
Using MonteCarlo computer simulations, we study the impact of matter fields on the geometry of a typical quantum universe in the causal dynamical triangulations (cdt) model of lattice quantum gravity. The quantum universe has the size of a few Planck lengths and the spatial topology of a three-torus. The matter fields are multicomponent scalar fields taking values in a torus with circumference δ in each spatial direction, which acts as a new parameter in the cdt model. Changing δ, we observe a phase transition caused by the scalar field. This discovery may have important consequences for quantum universes with nontrivial topology, since the phase transition can change the topology to a simply connected one.
Highlights
Introduction.—The problem of merging general relativity and quantum mechanics in a theory of quantum gravity has been approached from many directions, but no completely satisfactory formulation has yet been found
Using Monte Carlo computer simulations, we study the impact of matter fields on the geometry of a typical quantum universe in the causal dynamical triangulations (CDT) model of lattice quantum gravity
The question arises: what type of matter can be included in a particular approach and what impact does it have on the underlying geometric degrees of freedom? In this Letter we argue that the impact of matter can be quite dramatic even leading to a change of the topology of the Universe
Summary
We choose the target space N of the scalar field to have either Euclidean Rd or toroidal ðS1Þd topology, and we fix the flat metric hρσ 1⁄4 δρσ on N. Pffiffiffiffiffiffiffiffi d4x gðxÞ∂ν φσ ðxÞ∂νφσ ðxÞ; ð3Þ and the various components decouple for different σ because the target space metric is diagonal. For a particular sample geometry [g], quantum fluctuations of φσ will occur around a semiclassical solution φσ satisfying the Laplace equation. Let us start with a simple case where the target space of the scalar field is N 1⁄4 Rd. In CDT we consider the scalar field as located at the centers of equilateral simplexes, and the discrete counterpart of the action (3) takes a very simple form
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