Generalized cosmological constant from gauging Maxwell-conformal algebra

TL;DR

This paper constructs a conformally invariant gravity theory by gauging the Maxwell-conformal algebra, resulting in a model that naturally includes Einstein-Hilbert and cosmological terms without extra scalar fields.

Contribution

It introduces a novel conformally invariant gravity framework based on Maxwell-conformal algebra gauging, avoiding the need for compensator scalar fields.

Findings

The gravitational action contains Einstein-Hilbert and cosmological terms derived from algebra curvatures.

The theory reduces to a Brans-Dicke-like model under specific conditions.

A generalized Einstein equation with a coordinate-dependent cosmological term is obtained.

Abstract

The Maxwell extension of the conformal algebra is presented. With the help of gauging the Maxwell-conformal group, a conformally invariant theory of gravity is constructed. In contrast to the conventional conformally invariant actions, our gravitational action contains the Einstein-Hilbert term without introducing any additional (compensator) scalar field to satisfy the local scale invariance. This is achieved by using the curvatures of the algebra. In a special condition, we show that the resulting action is reduced to the Brans-Dicke like theory of gravity. We subsequently find the generalized Einstein field equation together with a coordinate dependent cosmological term and additional contributions.