The origin of growth-tracking dark energy: a curvature response and the conditions it needs
Year: 2026
Type: preprint
Abstract: In the fD model an effective dark-energy component follows the growth rate fD of linear structure. For one combination of CMB, BAO and supernova data it improves the best fit over ΛCDM without additional parameters. Why dark energy should track cosmic growth is open. We show that the response of the local expansion rate to an initial curvature has the shape of the law, −∂ln Hloc/∂κi = fD/(5Ωm0). This holds exactly for linear growing perturbations on a flat background with conserved dust and no radiation. It further needs a dark component that is strictly smooth on slices of equal proper time. The relation is known separate-universe physics; we give its normalization, its conditions and its clock. Turning the response into a density needs three further choices. They are a closure of the dark component, the expansion rate as response variable and a linear coupling. A closure that fixes the dark pressure by age needs neither energy flux nor anisotropic stress. Its normalized response differs from the law by at most 0.0064 for 0.2 ≤ a ≤ 1. As a background law with the same perturbation treatment, it fits the data as well as fD. So does a purely geometric law in the Hubble radius, ρDE ∝ drH/d ln a, which uses no growth variable. Present data leave the choice among these laws open. A density that stays homogeneous on slices of equal age meets a conservation obstacle. Without radiation, a common adiabatic fluid of matter and dark energy is unstable at every nondegenerate maximum of the dark density. In the tested classes, uncoupled relaxation fails to supply the required stress and an elastic medium changes matter growth. The tested braiding models reproduce the early exponent of the law and leave calculable residuals. Without radiation, the large-scale equal-age curvature response of Cosmic Pace, the carrier of a companion paper, differs from that of the pressure closure by the factor 1 + (ρ + p)DE/ρm. If the law holds, cosmic expansion would encode the history of linear matter growth. We state the requirements that a physical reason for this would need to meet; other origins of the law remain possible. This record contains the paper (version 1). The reproduction package with the code and the results behind its numbers, tables and figures is a separate record (DOI 10.5281/zenodo.24068460). The companion paper that constructs the carrier Cosmic Pace is DOI 10.5281/zenodo.24068452. Preregistrations and result notes are in the time-stamped records, parts 1 to 5. All records are linked under related works. This work was done mainly in collaboration with the AI system Claude (Anthropic). Some computations were written and run with a second AI coding assistant and reviewed by Claude. Other AI models commented on drafts and suggested checks. The author is responsible for the content.
Author: Hug, Mike
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225782067