General covariance violation and the gravitational dark matter. I. Scalar graviton

TL;DR

This paper explores how minimal violations of general covariance, specifically unimodular gravity, can produce a massive scalar graviton that acts as gravitational dark matter, with implications for cosmology.

Contribution

It introduces a formalism for a scalar graviton arising from covariance violation and discusses its potential role as dark matter in cosmological models.

Findings

Scalar graviton emerges from covariance violation.

Formalism for perfect fluid in scalar graviton environment.

Implications for cosmology briefly discussed.

Abstract

The violation of the general covariance is proposed as a resource of the gravitational dark matter. The minimal violation of the covariance to the unimodular one is associated with the massive scalar graviton as the simplest representative of such a matter. The Lagrangian formalism for the continuous medium, the perfect fluid in particular, in the scalar graviton environment is developed. The implications for cosmology are shortly indicated.