Generalized Einstein theory with fundamental cosmological stress tensor

TL;DR

This paper generalizes Einstein's theory by incorporating a cosmological stress tensor, derived through variational principles and diffeomorphism restrictions, interpreting gravity as a cosmological fluid.

Contribution

It introduces a new generalized Einstein theory that includes a cosmological stress tensor based on variational principles and symmetry restrictions.

Findings

Derivation of a generalized Einstein equation with a cosmological stress tensor

Interpretation of gravity as a cosmological fluid

Field equations correspond to the stress tensor of the theory

Abstract

Careful analysis of parametrized variational principles in mechanics and field theory leads to a generalization of Einstein theory that includes a cosmological stress tensor. This generalization also follows by restricting variations of the metric in the Hilbert action to spacetime diffeomorphisms. The equation of motion for the generalized theory is the twice-contracted Bianchi identity while the field equations constitute the stress tensor of the theory. Gravity is interpreted as a cosmological fluid.