N-cutoff regularization for fields on hyperbolic space

We apply a novel background independent regularization scheme, the N-cutoffs, to self-consistently quantize scalar and metric fluctuations on the maximally symmetric but noncompact hyperbolic space. For quantum matter fields on a classical background or full quantum Einstein gravity (regarded here as an effective field theory) treated in the background field formalism, the N-cutoff is an ultraviolet regularization of the fields’ mode content that is independent of the background hyperbolic space metric. For each N>0, the regularized system backreacts on the geometry to dynamically determine the self-consistent background metric. The limit in which the regularization is removed then automatically yields the “physically correct” spacetime on which the resulting quantum field theory lives. When self-consistently quantized with the N-cutoff, we find that without any fine-tuning of parameters, the vacuum fluctuations of scalar and (linearized) graviton fields do not lead to the usual cosmological constant problem of a curvature singularity. Instead, the presence of increasingly many field modes tends to reduce the negative curvature of hyperbolic space, leading to vanishing values in the limit of removing the cutoff. Published by the American Physical Society 2024