# Weinberg's No Go Theorem in Quantum Gravity

## TL;DR

This paper extends Weinberg's no go theorem to quantum gravity, demonstrating that the theorem's restrictions on flat solutions persist even when quantum effects are considered, thus posing a fundamental challenge to solving the cosmological constant problem.

## Contribution

The authors prove that Weinberg's no go theorem remains valid in quantum gravity using a general BRST invariance approach, independent of specific quantum gravity models.

## Key findings

- Weinberg's no go theorem applies in quantum gravity.
- The proof relies on BRST invariance, not model specifics.
- The theorem constrains solutions to the cosmological constant problem.

## Abstract

An important hurdle to be faced by any model proposing a resolution to the cosmological constant problem is Weinberg's venerable no go theorem. This theorem states that no local field equations including classical gravity can have a flat Minkowski solution for generic values of the parameters, in other words, the no go theorem forbids the existence of any solution to the cosmological constant problem within local field theories without fine tuning. Though the original Weinberg theorem is valid only in classical gravity, in this article we prove that this theorem holds even in quantum gravity. Our proof is very general since it makes use of the BRST invariance emerging after gauge-fixing of general coordinate invariance and does not depend on the detail of quantum gravity.