Identification of Cosmic Voids as the Cluster Counterpart

We present a new void definition that connects voids with clusters, the high-density counterpart. According to the standard scenario of structure formation, clusters are expected to form at peaks of the initial density field, whereas cosmic voids form at troughs. Then, a cluster would be a void if the sign of the initial density fluctuation of the universe were inverted. To study the relevance of anti-structures of clusters to cosmic voids, we use a pair of simulations whose initial density fields are sign inverted versions to each other. By examining the spatial distribution and environment of the particles in inverted simulation, which are the member particles of clusters in the other simulation, we discuss the characteristics of the antipode structures of clusters including their size, density, internal structure, and redshift evolution.