What cosmological tools are clusters when calibrated for distance measurement?

Cosmological standard candles or standard rulers

Galaxy clusters are vital components in probing the universe's expansion history, particularly in constraining parameters related to dark energy. When astronomers select clusters that have reached a certain evolutionary stage, perhaps by ceasing star formation or exhibiting a specific mass-related X-ray signature, these clusters can be used as calibrated measuring sticks across cosmological distances. They function as either standard candles, relying on the predictable intrinsic brightness of their X-ray emission, or standard rulers, based on scaling relations derived from their total mass and galaxy population counts. By comparing these observed properties against theoretical predictions across cosmic time, scientists can effectively constrain models describing the accelerating expansion driven by dark energy.