Assessing the potential of cluster edges as a standard ruler on constraining dark energy models

We assess comprehensively the potential of galaxy cluster edges as a standard ruler in measuring cosmological distances and probing exotic physics. Confronting five alternative models with from near future Dark Energy Spectroscopic Instrument survey, we conclude that can serve promising probe to constrain beyond $\Lambda$CDM. Especially, constraining precision equation state dark energy is just about two times larger than Pantheon Type Ia supernovae sample. find power be exhibited better by combining it other probes. Combining cosmic microwave background, baryon acoustic oscillations, supernovae, chronometers simulated gravitational-wave events space-based Einstein Telescope, respectively, $\Lambda$CDM data combination background gives best constraint on Hubble constant $H_0$ $0.5\%$ matter density ratio $\Omega_m$ $1.6\%$ among these pair datasets, gravitational waves almost shares same edges. also give most stringent available data. With help probes, new insights physics at scales.