Quantification of LSS using the persistent homology in the SDSS fields

Using galaxy samples from the Sloan Digital Sky Survey (SDSS) Data Release 12 (DR12), we first estimate the topology of cosmic large-scale structure (LSS) by means of a new method of persistent homology which captures the size and robustness of the void structure in a compact and meaningful manner. To avoid cosmic variance, we create three volume-limited subsamples, which contain more than 2000 galaxies in different redshift slices (Δz = 0.01). The result shows the clearer differences from the topology of uniform distribution as the redshift decreases, and supports the scenario of modern cosmology that the LSS has been formed through the growth in time of an initial density perturbation. Future work will include an analysis for different types of galaxies and a comparison with N-body simulation to constrain cosmological models.