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

## TL;DR

This paper investigates the theoretical limitations of gravitational models that aim to neutralize vacuum energy effects on spacetime, revealing fundamental obstructions and proposing potential pathways to achieve self-tuning.

## Contribution

It extends Weinberg's no go theorem by analyzing field theoretic completions and identifies new obstructions to self-tuning, proposing two novel approaches to overcome these challenges.

## Key findings

- Transition from self-tuning to General Relativity is generally obstructed by fundamental principles.
- A unitary field configuration on anti-de Sitter space can achieve the desired transition.
- Vacuum energy sequestering offers a promising alternative pathway.

## Abstract

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. We complement Weinberg's no go theorem by studying field theoretic completions of self-adjustment allowing for broken translations as well as other generalisations, and identify new obstructions. Our analysis uses a very general Kallen-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 on shorter scales is generically not possible. We search for novel ways around our obstructions and highlight two interesting possibilities. The first is an example of a unitary field configuration on anti-de Sitter space with the desired transition from self-tuning to GR. A second example is motivated by vacuum energy sequestering.