Quantized cosmological constant in 1+1 dimensional quantum gravity with coupled scalar matter

Abstract

A two dimensional matter coupled model of quantum gravity is studied in the Dirac approach to constrained dynamics in the presence of a cosmological constant. It is shown that after partial fixing to the conformal gauge the requirement of a quantum realization of the conformal algebra for physical quantum states of the fields naturally constrains the cosmological constant to take values in a well determined and mostly discrete spectrum. Furthermore the contribution of the quantum fluctuations of the single dynamical degree of freedom in the gravitational sector, namely the conformal mode, to the cosmological constant is negative, in contrast to the positive contributions of the quantum fluctuations of the matter fields, possibly opening an avenue towards addressing the cosmological constant problem in a more general context.

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

“…Two interesting examples of a cosmological constant determined by the symmetries in quantum gravity are given by one-dimensional gravity [8] and two-dimensional Liouville gravity [5], in the presence of scalar matter. In both cases the presence of diffeomorphisms constraints was exploited to obtain a set of equations that determine the value of the cosmological constant in terms of the physical quantum states.…”

“…This choice is not the most intuitive but it has the advantage of providing us with complete control on the single coefficients of each field, so that specific quantum states are easily selected for the purpose of a spectrum analysis 7 . 6 We refer to [5,7] for details. 7 In the simple example of two decoupled systems, A and B, with an Hilbert space basis |n and |m respectively, the easiest way to write a general state has the form |ψg = n,m ψ(n, m)|n |m .…”

“…Most of the technical results are contained in [5][6][7]. This paper is organized as follows: in Section II we present a general mechanism that can determine the cosmological constant in a quantum theory of gravity.…”

“…It is interesting to note that such a cancellation occurs only in the presence of a Maxwell field. As discussed in[5,7], if the Maxwell field is not present at the classical level there is no Liouville potential of the Y field. Therefore there is no need to fix a quantum correction to the coupling constant in the Y sector, while quantum corrections to ξ are still allowed.…”

Cleaning up the cosmological constant

“…Typically, such approaches will fall foul of Weinberg's famous "no-go" theorem [4], although there are ways around that, as evidenced by the SLED proposal [5] and the cosmology of the Fab Four [6]. Other recent attempts to address the cosmological constant problem include [7,8,9,10,11]. However, for the most part, advocates of the ΛCDM model are inclined to sweep the troublesome vacuum energy under the carpet.…”