Gravitational Mechanisms to Self-Tune the Cosmological Constant: Obstructions and Ways Forward.

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 cutoff. We complement Weinberg's no-go theorem by studying field-theoretic completions of self-adjustment allowing for broken translations as well as other generalizations, and identify new obstructions. Our analysis uses a very general Källén-Lehmann spectral representation of the exchange amplitude for conserved sources of energy-momentum and exploits unitarity and Lorentz invariance to show that a transition from self-tuning of long wavelength sources to near general relativity (GR) on shorter scales is generically not possible.