Gravitational Theory without the Cosmological Constant Problem

TL;DR

This paper introduces a novel gravitational theory that eliminates the cosmological constant problem by modifying the measure of integration using scalar fields, ensuring vacuum energy does not induce a cosmological term, and explores its implications for unification.

Contribution

It develops a new first-order formalism-based gravitational theory with a modified measure that naturally cancels the cosmological constant, linking internal diffeomorphism invariance to force unification.

Findings

The theory enforces a vanishing cosmological constant in vacuum.

It maintains consistency with diffeomorphism invariance under certain matter models.

The approach suggests a connection to force unification akin to Kaluza-Klein theories.

Abstract

We develop the principle of nongravitating vacuum energy, which is implemented by changing the measure of integration from $\sqrt{-g}d^{D}x$ to an integration in an internal space of $D$ scalar fields $\phi_{a}$. As a consequence of such a choice of the measure, the matter Lagrangian $L_{m}$ can be changed by adding a constant while no cosmological term is induced. Here we develop this idea to build a new theory which is formulated through the first order formalism, i.e. using vielbein $e_{a}^{\mu}$ and spin connection $\omega_{\mu}^{ab}$ (a,b=1,2,...D) as independent variables. The equations obtained from the variation of $e_{a}^{\mu}$ and the fields $\phi_{a}$ imply the existence of a nontrivial constraint. This approach can be made consistent with invariance under arbitrary diffeomorphisms in the internal space of scalar fields $\phi_{a}$ (as well as in ordinary space-time), provided that the matter model is chosen so as to satisfy the above mentioned constraint. If the matter model is not chosen so as to satisfy automatically this constraint, the diffeomorphism invariance in the internal space is broken. In this case the constraint is dynamically implemented by the degrees of freedom that become physical due to the breaking of the internal diffeomorphism invariance. However, this constraint always dictates the vanishing of the cosmological constant term and the gravitational equations in the vacuum coincide with vacuum Einstein's equations with zero cosmological constant. The requirement that the internal diffeomorphisms be a symmetry of the theory points towards the unification of forces in nature like in the Kaluza-Klein scheme.