Title: Gravitational self-tuning of the vacuum energy: obstructions and ways around —
Gravitational models of self-tuning are those in which vacuum energy has no observable effect on spacetime curvature even though it is a priori unsuppressed below the cut-off, thereby avoiding the cosmological constant problem. According to a famous argument by Weinberg, consistent field theoretic realisations of self-tuning are notoriously hard to find. We complement Weinberg’s argument by using a very general spectral decomposition of the exchange amplitude for conserved sources of energy-momentum, and identify new obstructions. Specifically, we exploit Lorentz invariance and unitarity to show that a transition from self-tuning of long wavelength sources to near General Relativity on shorter scales is generically not possible. In particular, these findings question the phenomenological prospects of different extra dimensional implementations of self-tuning. We search for novel ways around our obstructions and highlight different interesting possibilities. One is motivated by vacuum energy sequestering.