## TOPOLOGY OF A LARGE-SCALE STRUCTURE AS A TEST OF MODIFIED GRAVITY

The genus of the isodensity contours is a robust measure of the topology of a large-scale structure, and it is relatively insensitive to nonlinear gravitational evolution, galaxy bias, and redshift-space distortion. We show that the growth of density fluctuations is scale dependent even in the linear regime in some modified gravity theories, which opens a new possibility of testing the theories observationally. We propose to use the genus of the isodensity contours, an intrinsic measure of the topology of the large-scale structure, as a statistic to be used in such tests. In Einstein's general theory of relativity, density fluctuations growmore »