Metric Expansion from Microscopic Dynamics in an Inhomogeneous Universe

TL;DR

This paper explores how microscopic dynamics and inhomogeneities in the universe influence the local expansion rate, suggesting that the Hubble constant varies with position and curvature, impacting cosmological models.

Contribution

It introduces a framework connecting local microscopic dynamics with the global expansion rate, incorporating inhomogeneities and curvature effects into cosmological expansion.

Findings

Hubble constant varies with position in inhomogeneous universe

Local expansion rate linked to Weyl curvature and vacuum polarization

Derived proportionality constant related to Kepler's third law

Abstract

Theories with ingredients like the Higgs mechanism, gravitons, and inflaton fields rejuvenate the idea that relativistic kinematics is dynamically emergent. Eternal inflation treats the Hubble constant H as depending on location. Microscopic dynamics implies that H is over much smaller lengths than pocket universes to be understood as a local space reproduction rate. We illustrate this via discussing that even exponential inflation in TeV-gravity is slow on the relevant time scale. In our on small scales inhomogeneous cosmos, a reproduction rate H depends on position. We therefore discuss Einstein-Straus vacuoles and a Lindquist-Wheeler like lattice to connect the local rate properly with the scaling of an expanding cosmos. Consistency allows H to locally depend on Weyl curvature similar to vacuum polarization. We derive a proportionality constant known from Kepler's third law and discuss the implications for the finiteness of the cosmological constant.