The emptiness of voids: yet another overabundance problem for the Lambda cold dark matter model

We study the luminosity function, the peculiar velocities and the sizes of voids in the Local Volume (LV) in observational samples of galaxies which contain galaxies down to M-B = -10 and to M-B = -12 within the distance 4-8 Mpc. When we compare the results with the predictions of the standard cosmological lambda cold dark matter (Lambda CDM) model, we find that the theory faces a sever problem: it predicts a factor of 10 more dwarf haloes as compared with the observed number of dwarf galaxies. In the LV, we identify voids with sizes ranging from 1 to 4.5 Mpc and compare the observational distribution of void sizes with the voids in very high-resolution simulations of the Lambda CDM model with Wilkinson Microwave Anisotropy Probe 1(WMAP1) and WMAP3 parameters. The theoretical void function matches the observations remarkably well only if we use haloes with circular velocities V-c larger than 40-45 km s(-1) [M-vir = (1-2) x 10(10) M-circle dot] for models with sigma(8) = 0.9 and V-c > 35 km s(-1) [M-vir = (6-8) x 10(9) M-circle dot] for sigma(8) = 0.75. We exclude the possibility that in the Lambda CDM model haloeswith circular velocities < 35 km s(-1) can host galaxies as bright as MB = -12: there are too many small haloes in the Lambda CDM model resulting in voids being too small as compared with the observations. The problem is that many of the observed dwarf galaxies have HI rotational velocities below 25 km s(-1) that strictly contradicts the Lambda CDM predictions. Thus, the Lambda CDM model faces the same overabundance problem, which it had with the number of satellites in the Local Group (LG). We also estimate the rms deviations from the Hubble flow sigma(H) for galaxies at different distances from the LG and find that in most of our model LV candidates the rms peculiar velocities are consistent with observational values: sigma(H) = 50 km s-1 for distances less than 3Mpc and sigma(H) = 80 km s(-1) for distances less than 8Mpc. At distances 4 (8) Mpc, the observed overdensities of galaxies are 3.5-5.5 (1.3-1.6) - significantly larger than typically assumed.