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