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

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.