Abstract
Loop quantum gravity is believed to eliminate singularities such as the big bang and big crunch singularity. This belief is based on studies of so-called loop quantum cosmology which concerns symmetry-reduced models of quantum gravity. In this paper, the problem of singularities is analysed in the context of the Bohmian formulation of loop quantum cosmology. In this formulation there is an actual metric in addition to the wave function, which evolves stochastically (rather than deterministically as the case of the particle evolution in non-relativistic Bohmian mechanics). Thus a singularity occurs whenever this actual metric is singular. It is shown that in the loop quantum cosmology for a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker space-time with arbitrary constant spatial curvature and cosmological constant, coupled to a massless homogeneous scalar field, a big bang or big crunch singularity is never obtained. This should be contrasted with the fact that in the Bohmian formulation of the Wheeler-DeWitt theory singularities may exist.
Highlights
According to general relativity space-time singularities such as a big bang or big crunch are generic
Since there is merely the wave function, one might even consider the question about space-time singularities as off-target, since it is the dynamics of the wave function that needs to be well-defined
We explore the question of singularities in the mini-superspace model of a FLRW space-time coupled to a homogeneous scalar field in the context of Bohmian mechanics
Summary
Loop quantum gravity is believed to eliminate singularities such as the big bang and big crunch singularity. It is shown that in the loop quantum cosmology for a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker space-time with arbitrary constant spatial curvature and cosmological constant, coupled to a massless homogeneous scalar field, a big bang or big crunch singularity is never obtained This should be contrasted with the fact that in the Bohmian formulation of the Wheeler-DeWitt theory singularities may exist. There is the problem of what it means to have a space-time singularity In both theories, the universe is described solely by a wave function, but there is no actual metric. We just need to assume that the wave function is such that the Bohmian dynamics is well-defined Since it is rather unclear what the Wheeler-DeWitt equation means in the context of standard quantum mechanics, there is no straightforward comparison between the Bohmian predictions and those of standard quantum theory possible.
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