Quantum gravity and the cosmological constant: Lessons from two-dimensional dilaton gravity

In the investigation and resolution of the cosmological constant problem, the inclusion of the dynamics of quantum gravity can be a crucial step. In this work we suggest that the quantum constraints in a canonical theory of gravity can provide a way of addressing the issue: we consider the case of two-dimensional quantum dilaton gravity nonminimally coupled to a $U(1)$ gauge field, in the presence of an arbitrary number of massless scalar matter fields, intended also as an effective description of highly symmetrical higher-dimensional models. We are able to quantize the system nonperturbatively and obtain an expression for the cosmological constant $\Lambda$ in terms of the quantum physical states, in a generalization of the usual quantum field theory approach. We discuss the role of the classical and quantum gravitational contributions to $\Lambda$ and present a partial spectrum of values for it.

Figure 1

Positive (left) and negative (right) values of the cosmological constant lie on discrete levels ranging, in absolute value, from ${10}^{-10}$ to ${10}^{-39}$ with the choices ${\hslash }_{*}=1$, $\xi ={10}^{-4}$, $q{P}^2=1$. The horizontal axis simply labels sequentially the values.