  We present a systematic investigation of the cosmological constant effects in
compact stars interiors in the framework of Einstein's gravity. Consideration
of a cosmological constant $\Lambda$ in compact stars is motivated by the
mechanism of acceleration of the observable universe, where $\Lambda$ is
usually related to the dark energy. In particular, we consider compact star
mass twins, hybrid neutron stars that populate both the second and third branch
of the mass-radius diagram. For those models, the need of consideration of
excluded volume effects in the equation of state, resulting from the finite
size volume of nucleons, leads to a stiffening of matter causing compact stars
to acquire higher mass and radius values. We demonstrate that certain values of
the cosmological constant can also modify the compact star properties but in an
opposite way. In addition, we find that the inclusion of $\Lambda$ can have a
similar effect to the existence of pasta phases at the hadron-quark interface.
