Bounding the cosmological constant using galactic rotation curves from SPARC dataset

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 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 ${\rho }_{(<\Lambda )}\sim {10}^{-25}\mathrm{kg}/m^3$, 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.