arXiv2007
On the cosmological length scale, recent measurements by WMAP have validated $Λ$CDM to a precision not see before in cosmology. Such is not the case on galactic length scales, however, where the `cuspy-core' problem has demonstrated our lack of understanding of structure formation. Here, we propose a solution to the 'cuspy-core' problem based on the observation that with the discovery of Dark Energy, $Λ_{DE}$, there is now a universal length scale, $λ_{DE}=c/(Λ_{DE} G)^{1/2}$, associated with the universe. This length scale allows for an extension of the geodesic equations of motion that affects only the motion of massive test particles; the motion of massless test particles are not affected, and such phenomenon as gravitational lensing remain unchanged. An evolution equation for the density profile is derived, and an effective free energy density functional for it is constructed. We conjecture that the pseudoisothermal profile is preferred over the cusp-like profile because it has a lower effective free energy. A cosmological check of the theory is made using the observed rotational velocities and core sizes of 1393 spiral galaxies. We calculate $σ_8$ to be $0.68_{\pm0.11}$; this is within experimental error of the WMAP value $0.761_{-0.048}^{+0.049}$. We then calculate $R_{200}=270_{\pm 130}$ kpc, which is in agreement with observations. We estimate the fractional density of matter that cannot be determined through gravity to be $0.197_{\pm 0.017}$; this is nearly equal to the WMAP value for the fractional density of nonbaryonic matter $0.196^{+0.025}_{-0.026}$. The fractional density of matter that can be determined through gravity is then calculated to be $0.041_{-0.031}^{+0.030}$; this is nearly equal to $Ω_B=0.0416_{-0.0039}^{+0.0038}$.