Gauge-Invariant Average of Einstein Equations for finite Volumes
  For the study of cosmological backreacktion an avaragng procedure is
required. In this work a covariant and gauge invariant averaging formalism for
finite volumes will be developed. This averaging will be applied to the scalar
parts of Einstein's equations. For this purpose dust as a physical laboratory
will be coupled to the gravitating system. The goal is to study the deviation
from the homogeneous universe and the impact of this deviation on the dynamics
of our universe. Fields of physical observers are included in the studied
system and used to construct a reference frame to perform the averaging without
a formal gauge fixing. The derived equations resolve the question whether
backreaction is gauge dependent.
