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Michael Te Vrugt1, Sabine Hossenfelder2, Raphael Wittkowski1

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Area of Science:

  • Cosmology
  • General Relativity
  • Statistical Mechanics

Background:

  • Cosmology requires large-scale averaging (coarse-graining) of the universe.
  • The nonlinearity of general relativity complicates this averaging process.

Purpose of the Study:

  • To extend the Mori-Zwanzig projection operator formalism to general relativity.
  • To derive a new dynamic equation for the Hubble parameter.

Main Methods:

  • Applied the Mori-Zwanzig projection operator formalism.
  • Utilized the Buchert equations.
  • Derived a dynamic equation for the Hubble parameter incorporating a memory function.

Main Results:

  • Developed a novel coarse-graining method for general relativity.
  • Derived a new dynamic equation for the Hubble parameter.
  • Obtained an empirical prediction for the cosmic jerk.

Conclusions:

  • The Mori-Zwanzig formalism provides a viable approach for coarse-graining in general relativity.
  • The derived equation offers new insights into cosmic dynamics and predictions.
  • This work bridges statistical mechanics and cosmology.