Bounding the Cosmological Constant using Galactic Rotation Curves from the SPARC Dataset

TL;DR

This paper uses galactic rotation curves from the SPARC dataset to establish an upper limit on the cosmological constant, finding it to be only two orders of magnitude higher than the value measured by Planck, with implications for future observations.

Contribution

It introduces a method to constrain the cosmological constant using galactic rotation data, providing a new upper limit based on galaxy models and dynamics.

Findings

Upper limit on Λ is about 10^{-25} kg/m^3.

Galaxies with detectable velocities far from the core yield lower Λ limits.

Larger orbital periods correspond to lower upper limits on Λ.

Abstract

Dark energy (and its simplest model, the Cosmological Constant or $\Lambda$) acts as a repulsive force that opposes gravitational attraction. Assuming galaxies maintain a steady state over extended periods, the estimated upper limit on $\Lambda$ studies its pushback to the attractive gravitational force of dark matter. From the SPARC dataset, we select galaxies that are best fitted by the Navarro-Frenk-White (NFW) and Hernquist density models. Introducing the presence of $\Lambda$ in these galaxies helps to establish the upper limit on its repulsive force. This upper limit on $\Lambda$ is around $\rho_{\left(<\Lambda\right)} \sim 10^{-25}$~kg/m$^3$, only two orders of magnitude higher than the one measured by Planck. {We show that for galaxies with detectable velocities far from the galaxy core, the upper limit on $\Lambda$ is lower. Furthermore, we show that galaxies and other systems follow the same principle: for larger orbital periods the upper limit on $\Lambda$ is lower. Consequently, we address the implications for future measurements on the upper limit and the condition for detecting the impact of $\Lambda$ on galactic scales.