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.