Bounding the cosmological constant using galactic rotation curves from SPARC dataset

Dark energy (and its simplest model, the cosmological constant or $\mathrm{\ensuremath{\Lambda}}$) acts as a repulsive force that opposes gravitational attraction. Assuming galaxies maintain a steady state over extended periods, the estimated upper limit on $\mathrm{\ensuremath{\Lambda}}$ 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 $\mathrm{\ensuremath{\Lambda}}$ in these galaxies helps to establish the upper limit on its repulsive force. This upper limit on $\mathrm{\ensuremath{\Lambda}}$ is around ${\ensuremath{\rho}}_{(<\mathrm{\ensuremath{\Lambda}})}\ensuremath{\sim}{10}^{\ensuremath{-}25}\text{ }\text{ }\mathrm{kg}/{\mathrm{m}}^{3}$, 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 $\mathrm{\ensuremath{\Lambda}}$ is lower. Furthermore, we show that galaxies and other systems follow the same principle: for larger orbital periods the upper limit on $\mathrm{\ensuremath{\Lambda}}$ is lower. Consequently, we address the implications for future measurements on the upper limit and the condition for detecting the impact of $\mathrm{\ensuremath{\Lambda}}$ on galactic scales.