Void analysis as a test for dark matter composition?

We use the void probability function (VPF) to compare the redshift–space galaxy distribution in the Perseus–Pisces redshift survey with artificial samples extracted from N –body simulations of standard cold dark matter (CDM) and broken scale invariance (BSI) models. Observational biases of the real data set are reproduced as well as possible in the simulated samples. Galaxies are identified as residing in peaks of the evolved density field and overmerged structures are fragmented into individual galaxies in such a way as to reproduce both the correct luminosity function and the two–point correlation function (assuming suitable M/L values). Using a similar approach, it was recently shown that the VPF can discriminate between CDM and a cold+hot dark matter (CHDM) model with Ω cold / Ω hot / Ω baryon = 0 . 6 / 0 . 3 / 0 . 1. Our main result is that both CDM (as expected from a previous analysis) and BSI fit observational data. The robustness of the result is checked against changing the observer’s position in the simulations and the galaxy identification in the evolved density field. Therefore, while the void statistics is sensitive to the passage from CDM to CHDM (different spectrum and different nature of dark matter), it is not to the passage from CDM to BSI (different spectrum but same dark matter). On such a basis, we conjecture that the distribution of voids could be directly sensitive to the nature of dark matter, but scarcely sensitive to the shape of the transfer function.