Is cosmological constant screened in Liouville gravity with matter?

TL;DR

This paper investigates whether infrared quantum effects in Liouville gravity with matter can lead to screening of the cosmological constant, finding that it does in two-dimensional de-Sitter space due to sign differences.

Contribution

It demonstrates that the cosmological constant is screened in Liouville gravity with matter in 2D de-Sitter space, contrasting with higher-dimensional cases, and introduces time-dependent infrared counter-terms for robustness.

Findings

Cosmological constant is screened in 2D Liouville gravity.

Screening effect is due to sign difference in cosmological constants.

Infrared counter-terms help analyze de-Sitter invariance restoration.

Abstract

There has been a proposal that infrared quantum effects of massless interacting field theories in de-Sitter space may provide time-dependent screening of the cosmological constant. As a concrete model of the proposal, we study the three loop corrections to the energy-momentum tensor of massless $\lambda \phi^4$ theory in the background of classical Liouville gravity in $D=2$ dimensional de-Sitter space. We find that the cosmological constant is screened in sharp contrast to the massless $\lambda \phi^4$ theory in $D=4$ dimensions due to the sign difference between the cosmological constant of the Liouville gravity and that of the Einstein gravity. To argue for the robustness of our prediction, we introduce the concept of time-dependent infrared counter-terms and examine if they recover the de-Sitter invariance in the $\lambda \phi^4$ theory in comparison with the Sine-Gordon model where it was possible.