Mori-Zwanzig formalism for general relativity: a new approach to the averaging problem

TL;DR

This paper extends the Mori-Zwanzig formalism from statistical mechanics to general relativity, providing a new dynamic equation for the Hubble parameter that incorporates averaging effects via a memory function, predicting cosmic jerk.

Contribution

It introduces a novel application of the Mori-Zwanzig formalism to general relativity, deriving an equation that accounts for averaging effects in cosmology.

Findings

Derivation of a new dynamic equation for the Hubble parameter.

Prediction of the cosmic jerk from the model.

Demonstration of the formalism's applicability to cosmological averaging.

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.