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GR: Fachverband Gravitation und Relativitätstheorie

GR 9: Cosmology

GR 9.3: Talk

Thursday, September 2, 2021, 17:00–17:15, H9

Mori-Zwanzig formalism for general relativity: a new approach to the averaging problem* — •Michael te Vrugt¹, Sabine Hossenfelder², and Raphael Wittkowski¹ — ¹Institut für Theoretische Physik, Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, D-48149 Münster, Germany — ²Frankfurt Institute for Advanced Studies, D-60438 Frankfurt am Main, Germany

Cosmology provides a coarse-grained description of the universe that is valid on very large length scales. However, the Einstein field equations are not valid for coarse-grained quantities since, due to their nonlinearity, they do not commute with an averaging procedure. Thus, it is unclear in which way small-scale inhomogeneities affect large-scale cosmology (backreaction). In this work, we address this problem by extending the Mori-Zwanzig projection operator formalism, a highly successful coarse-graining method from statistical mechanics, towards general relativity. This allows to derive a dynamic equation for the Hubble parameter in which backreaction is taken into account through memory and noise terms. Our results are linked to cosmological observations.

*Funded by the Deutsche Forschungsgemeinschaft (DFG) – WI 4170/3-1