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A cosmological equation of state is an equation of state (EoS) for dark energy, a means for describing its nature. The phrase is often short for the cosmological equation of state parameter (commonly symbolized by w), which is the universe's ratio of pressure to energy density:
w = p / ρ
Some kind of dark energy is considered necessary to explain observation, but various cosmological models have been developed, of which Lambda-CDM model is the current favorite, adopted for explaining a lot of observation data without excess complication. wCDM (one alternative to Lambda-CDM) is a cosmological model that presumes w is constant. Any other model presumes w varies with time.
Some research efforts aimed at measuring the effects of dark energy use this term in their title (rather than dark energy or lambda). An example is the SH0ES (for Supernova H0 for the Equation of State) supernova survey.