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We study the evolution of non‐linear structure as a function of scale in samples from the 2dF Galaxy Redshift Survey, constituting over 221 000 galaxies at a median redshift of   z = 0.11 . The two flux‐limited galaxy samples, located near the Southern Galactic Pole and the Galactic equator, are smoothed with Gaussian filters of width ranging from 5 to  8  h  −1  Mpc  to produce a continuous galaxy density field. The topological genus statistic is used to measure the relative abundance of overdense clusters to void regions at each scale; these results are compared with the predictions of the analytic theory, in the form of the genus statistic for (i) the linear regime case of a Gaussian random field and (ii) a first‐order perturbative expansion of the weakly non‐linear evolved field. The measurements demonstrate a statistically significant detection of an asymmetry in the genus statistic between regions corresponding to low‐ and high‐density volumes of the Universe. We attribute the asymmetry to the non‐linear effects of the gravitational evolution and biased galaxy formation, and demonstrate that these effects evolve as a function of scale. We find that neither analytic prescription satisfactorily reproduces the measurements, though the weakly non‐linear theory yields substantially better results at some scales, and we discuss the potential explanations for this result.

Topology of non‐linear structure in the 2dF Galaxy Redshift Survey