# On the cosmological constant problem

## TL;DR

This paper proposes a novel approach to the cosmological constant problem by deriving a constraint from the Einstein-Hilbert action that prevents vacuum energy from gravitating, leading to a natural explanation for the observed acceleration of the universe.

## Contribution

It introduces a new variation of the Einstein-Hilbert action that constrains the Ricci scalar, resulting in a self-consistent emergence of the cosmological constant from matter inhomogeneities.

## Key findings

- Predicts a present-day cosmological constant density parameter of approximately 0.704.
- Provides a mechanism for late-time cosmic acceleration without fine-tuning.
- Suggests a natural explanation for the coincidence of matter and dark energy densities.

## Abstract

An additional variation of the Einstein-Hilbert action with respect to the Planck mass provides a constraint on the average Ricci scalar that prevents vacuum energy from gravitating. Consideration of the evolution of the inhomogeneous matter distribution in the Universe with evaluation of the averaging constraint on disconnected matter cells that ultimately form isolated gravitationally bound structures yields a backreaction effect that self-consistently produces the cosmological constant of the background. A uniform prior on our location in the formation of these isolated structures implies a mean expectation for the present cosmological constant energy density parameter of $\Omega_{\Lambda}=0.704$, giving rise to a late-time acceleration of the cosmic expansion and a coincident current energy density of matter.