Skewness consistency relation in large-scale structure and test of gravity theory

We investigate the skewness of galaxy number density fluctuations as a possible probe to test gravity theories. We find that the specific linear combination of the skewness parameters corresponds to the coefficients of the second-order kernels of the density contrast, which can be regarded as the consistency relation and used as a test of general relativity and modified gravity theories. We also extend the analysis of the skewness parameters from real space to redshift space and derive the redshift-space skewness consistency relation.