  We investigate the properties of high density compact objects in a vector
type theory, inspired by Einstein's 1919 theory of elementary particles, in
which Einstein assumed that elementary particles are held together by
gravitational as well as electromagnetic type forces. From a modern
perspective, Einstein's theory can be interpreted as a vector type model, with
the gravitational action constructed as a linear combination of the Ricci
scalar, of the trace of the matter energy-momentum tensor, and of a massive
self-interacting vector type field. To obtain the properties of stellar models
we consider the field equations for a static, spherically symmetric system, and
we investigate numerically their solutions for different equations of state of
quark and neutron matter, by assuming that the self-interaction potential of
the vector field either vanishes or is quadratic in the vector field potential.
We consider quark stars described by the MIT bag model equation of state and in
the Color Flavor Locked phase, as well as compact stars consisting of a
Bose-Einstein Condensate of neutron matter, with neutrons forming Cooper pairs.
Constant density stars, representing a generalization of the Interior
Schwarzschild solution of general relativity, are also analyzed. Also, we
consider the Douchin-Haensel (SLy) equation of state. The numerical solutions
are explicitly obtained in both standard general relativity, and the Einstein
dark energy model and an in depth comparison between the astrophysical
predictions of these two theories are performed. As a general conclusion of our
study, we find that for all the considered equations of state a much larger
variety of stellar structures can be obtained in the Einstein dark energy
model, including classes of stars that are more massive than their general
relativistic counterparts.
