Is the cosmological constant screened in Liouville gravity with matter?

waleed a.j. addas;

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 λφ4 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 λφ4 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 λφ4 theory in comparison with the Sine–Gordon model, where it was possible.