Towards a generally covariant averaging process for metrics in general relativity

          @misc{ pirsa_PIRSA:08080029,
            doi = {10.48660/08080029},
            url = {https://pirsa.org/08080029},
            author = {Behrend, Juliane},
            keywords = {Quantum Gravity},
            language = {en},
            title = {Towards a generally covariant averaging process for metrics in general relativity},
            publisher = {Perimeter Institute},
            year = {2008},
            month = {aug},
            note = {PIRSA:08080029 see, \url{https://pirsa.org}}
          }
          

Abstract

The speculation that Dark Energy can be explained by the backreaction of present inhomogeneities on the evolution of the background cosmology has been increasingly debated in the recent literature. We demonstrate quantitively that the backreaction of linear perturbations on the Friedmann equations is small but is nevertheless non-vanishing. This indicates the need for an improved averaging procedure capable of averaging tensor quantities in a generally covariant way. We present an averaging process which decomposes the metric into Vielbeins selected employing a variational principle, and parallel-transports them to a single point at which they can be averaged. The functionality of the process is discussed in specific 2-d examples, and its application to 3-surfaces and metric recovery in cosmology is outlined.