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Mori-Zwanzig Formalism for General Relativity: A New Approach to the Averaging Problem
Michael Te Vrugt1, Sabine Hossenfelder2, Raphael Wittkowski1
1Institut für Theoretische Physik, Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, D-48149 Münster, Germany.
Abstract:
Cosmology relies on a coarse-grained description of the universe, assumed to be valid on large length scales. However, the nonlinearity of general relativity makes coarse graining extremely difficult. We here address this problem by extending the Mori-Zwanzig projection operator formalism, a highly successful coarse-graining method from statistical mechanics, towards general relativity. Using the Buchert equations, we derive a new dynamic equation for the Hubble parameter which captures the effects of averaging through a memory function. This gives an empirical prediction for the cosmic jerk.
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