Does loop quantum gravity imply Λ=0?

Abstract

We suggest that in a recently proposed framework for quantum gravity, where Vassiliev invariants span the the space of states, the latter is dramatically reduced if one has a non-vanishing cosmological constant. This naturally suggests that the initial state of the universe should have been one with Λ = 0.CGPG-98/3-5 gr-qc/9803097 For a long time the problem of the value of the cosmological constant has been viewed as an important open issue in cosmology. The observed value of the constant is quite low (smaller than 10 −120 in Planck units), and most fieldtheoretic mechanisms for generation of a cosmological constant predict a much higher value. Although one can set the constant to zero by hand, this amounts to a highly artificial fine-tuning. It has therefore been viewed as desirable to find a fundamental mechanism that could set its value to either zero or a very small value. Quantum gravity has been suggested in the past as a possible mechanism. The original proposal is due to Coleman [1], and a recent attractive revision of this proposal was introduced by Carlip [2]. In both proposals the discussion was made at the level of the path integral formulation of quantum gravity. There have also been proposals for "screening" of the cosmological constant in perturbative approaches to quantum gravity [3]. Here we would like to suggest that similar conclusions can be reached when constructing the canonical quantum theory of general relativity.Canonical quantum gravity was considered for a long time as an intellectual wasteland. The complexity of the constraint equations barred the implementation of even the earlier steps of a canonical quantization program. This made the status whole canonical approach look quite naive, since it could not even begin to grasp with the physics of quantum gravity. The general situation of the canonical approach to quantum gravity started to get better with the introduction of the Ashtekar new variables [4]; but still important difficulties remain before a canonical quantization can be completed. More specifically, the issues of observables and the "problem of time" are still important obstacles to the completion of the canonical quantization program. In spite of this, it has become recently clear that one is in fact able to make use of the formalism to come up with interesting physical predictions, in spite of it being incomplete. This is perhaps better displayed by the recent calculations of black hole entropy [5][6][7][8], which yield physical predictions in spite of not addressing the issues mentioned above. The intention of this note is to show that one can, within the canonical approach, reach certain conclusions about the value of the cosmological constant, again without having a complete formalism. Contrary to the arguments about black hole entropy, those that involve the cosmological constant require, as we will see, a somewhat detailed use of the dynamics of the theory, namely the Hamiltonian constraint. Unfortunately, although progress towards a consistent and physically meanin...

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