Kurtosis consistency relation in large-scale structure as a probe of gravity theories

Various gravity theories beyond general relativity have been rigorously investigated in the literature such as Horndeski and degenerate higher-order scalar-tensor (DHOST) theories. In general, numerous model parameters are involved in such theories, which should be constrained to test the theories with experiments and observations. We construct the kurtosis consistency relations, calculated based on matter density fluctuations, in which the information of gravity theories is encoded. We derive two independent consistency relations that should hold in the framework of the DHOST theories and argue that such consistency relations would be useful for testing gravity theories.