Abstract
We present an extension of general relativity in which the cosmological constant becomes dynamical and turns out to be conjugate to the Chern–Simons invariant of the Ashtekar connection on a spatial slicing. The latter has been proposed Soo and Smolin as a time variable for quantum gravity: the Chern–Simons time. In the quantum theory, the inverse cosmological constant and Chern–Simons time will then become conjugate operators. The “Kodama state” gets a new interpretation as a family of transition functions. These results imply an uncertainty relation between Λ and Chern–Simons time; the consequences of which will be discussed elsewhere.
Highlights
The long-standing cosmological constant problem comes in many guises
If the data on acceleration continues to be consistent with a plain cosmological constant, rather than a more general form of dark energy, the new cosmological constant problem becomes a question of extreme fine-tuning
Quantum tunneling is a nonperturbative process and any perturbative expansion in the vicinity of the tunneling barrier would be blind to tunneling. It is in this context, we would like to address the issue of both the IR and UV versions of the cosmological constant problems (We will not address the issue of phase transitions in this work, and how it might impart on the problem)
Summary
The long-standing cosmological constant problem comes in many guises. Before the observation of cosmic acceleration, the search had been to seek a theory where all contributions to the cosmological constant summed up to zero. Quantum tunneling is a nonperturbative process and any perturbative expansion in the vicinity of the tunneling barrier would be blind to tunneling It is in this context, we would like to address the issue of both the IR and UV versions of the cosmological constant problems (We will not address the issue of phase transitions in this work, and how it might impart on the problem). Even ignoring details of the dynamics at the classical level, we can see that a quantum uncertainty principle would always be in action, rendering Lambda and Chern–Simons time [1], complementary variables This may possibly leads to deep implications for quantum cosmology and quantum gravity, which we outline, and take up again elsewhere. There the conjugate measure of time is four volume to the past of a three slice
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