The quantum cosmological constant

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 L and Chern-Simons time; the consequences of which will be discussed elsewhere.