Cosmological zoom-in perturbation theory as a consistent beyond point-particle approximation framework

TL;DR

This paper introduces a covariant multi-scale framework for cosmological structure formation that addresses the limitations of point-particle models by decomposing spacetime into hierarchical regions, leading to insights like explaining galaxy rotation curves without dark matter.

Contribution

It develops a first-principles covariant approach to multi-scale cosmological modeling, incorporating geometric backreaction effects into structure formation simulations.

Findings

Backreaction naturally explains flat galaxy rotation curves.

Hierarchical geodesic domains resolve long dynamical range.

Consistent boundary matching leads to a covariant effective energy-momentum tensor.

Abstract

Modelling structure formation across the full dynamical range of the Universe remains a major challenge in cosmology. This difficulty originates from a fundamental limitation of geodesics in general relativity: a one-parameter family of geodesics can cease to be geodesic at a finite time. This implies that the conventional point-particle approximation is not the primary issue; rather, the breakdown of geodesic flow restricts a consistent description across scales. We develop a covariant multi-scale framework that resolves this problem by decomposing spacetime into hierarchical regions separated by matter horizons. We show how to match shared boundary consistently at the level of the action, leading to a covariant backreaction contribution. The resulting construction provides a first-principles theoretical foundation for cosmological zoom-in simulations and yields an effective energy-momentum tensor capturing the impact of the geometric backreaction effect. As an application, we demonstrate that this backreaction naturally produces flat galaxy rotation curves without invoking an additional dark matter component. Our results establish a new perspective on nonlinear structure formation, in which long dynamical range is resolved through a hierarchy of discrete geodesic domains.