Dark Energy and Extending the Geodesic Equations of Motion: Connecting the Galactic and Cosmological Length Scales

TL;DR

This paper extends the geodesic equations of motion using Dark Energy scale to analyze galactic dynamics, successfully matching observed galaxy rotation curves and cosmological parameters like $\sigma_8$ and $R_{200}$.

Contribution

It introduces a novel extension of geodesic equations incorporating Dark Energy, applied to galactic and cosmological scales, aligning theoretical predictions with observations.

Findings

Derived galaxy density profile consistent with observations.

Calculated $\sigma_8$ within experimental error of WMAP.

Estimated $R_{200}$ in agreement with observed galaxy sizes.

Abstract

Recently, an extension of the geodesic equations of motion using the Dark Energy length scale was proposed. Here, we apply this extension to the analyzing the motion of test particles at the galactic scale and longer. A cosmological check of the extension is made using the observed rotational velocity curves and core sizes of 1393 spiral galaxies. We derive the density profile of a model galaxy using this extension, and with it, we calculate $\sigma_8$ to be $0.73_{\pm 0.12}$; this is within experimental error of the WMAP value of $0.761_{-0.048}^{+0.049}$. We then calculate $R_{200}$ to be $206_{\pm 53}$ kpc, which is in reasonable agreement with observations.