On the Trace-Free Einstein Equations as a Viable Alternative to General Relativity

TL;DR

The paper reviews the Trace-Free Einstein Equations as an alternative to general relativity, addressing the cosmological constant problem by removing vacuum energy contributions while maintaining standard cosmological and astrophysical predictions.

Contribution

It demonstrates that Trace-Free Einstein Equations are a viable alternative to Einstein's equations, resolving the cosmological constant discrepancy without disrupting existing models.

Findings

Trace-Free Einstein Equations resolve the vacuum energy discrepancy

Standard cosmological equations are preserved

No issues with stellar model junction conditions

Abstract

The quantum field theoretic prediction for the vacuum energy density leads to a value for the effective cosmological constant that is incorrect by between 60 to 120 orders of magnitude. We review an old proposal of replacing Einstein's Field Equations by their trace-free part (the Trace-Free Einstein Equations), together with an independent assumption of energy--momentum conservation by matter fields. While this does not solve the fundamental issue of why the cosmological constant has the value that is observed cosmologically, it is indeed a viable theory that resolves the problem of the discrepancy between the vacuum energy density and the observed value of the cosmological constant. However, one has to check that, as well as preserving the standard cosmological equations, this does not destroy other predictions, such as the junction conditions that underlie the use of standard stellar models. We confirm that no problems arise here: hence, the Trace-Free Einstein Equations are indeed viable for cosmological and astrophysical applications.