Gravitational theory without the cosmological constant problem, symmetries of space-filling branes and higher dimensions

TL;DR

This paper proposes a first-order formalism for gravitational theory that naturally solves the cosmological constant problem by introducing a local symmetry linked to space-filling branes, especially effective in higher dimensions.

Contribution

It introduces a novel formulation of gravity with a measure of integration symmetry, connecting space-filling branes and higher-dimensional models to address the cosmological constant problem.

Findings

The theory solves the cosmological constant problem without fine-tuning.

Higher-dimensional compactifications generate scalar and gauge fields.

Four-dimensional space remains effectively zero cosmological constant.

Abstract

We showed that the principle of nongravitating vacuum energy, when formulated in the first order formalism, solves the cosmological constant problem. The most appealing formulation of the theory displays a local symmetry associated with the arbitrariness of the measure of integration. This can be motivated by thinking of this theory as a direct coupling of physical degrees of freedom with a "space - filling brane" and in this case such local symmetry is related to space-filling brane gauge invariance. The model is formulated in the first order formalism using the metric and the connection as independent dynamical variables. An additional symmetry (Einstein - Kaufman symmetry) allows to eliminate the torsion which appears due to the introduction of the new measure of integration. The most successful model that implements these ideas is realized in a six or higher dimensional space-time. The compactification of extra dimensions into a sphere gives the possibility of generating scalar masses and potentials, gauge fields and fermionic masses. It turns out that remaining four dimensional space-time must have effective zero cosmological constant.