Mori-Zwanzig formalism for general relativity: a new approach to the averaging problem
arXiv:2107.11497 · doi:10.1103/PhysRevLett.127.231101
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.
7 pages, 1 figure
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