The Near-Infrared Galaxy Counts Anomaly: Local Underdensity or Strong   Evolution?
  We analyze bright-end (K = 10 -17) galaxy counts from a number of near-infrared galaxy surveys. All studies available as of mid-1997, considered individually or collectively, show that the observed near-infrared galaxy number counts at low magnitudes are inconsistent with a simple no-evolution model. We examine evolutionary effects and a local underdensity model as possible causes of this effect. We find that the data are fit by either a factor of 1.7 - 2.4 deficiency of galaxies out to a redshift of z = 0.10 - 0.23, depending on the k corrections and evolution (e-) corrections used and the adopted values of the Schechter luminosity function parameters, or by unexpectedly strong low redshift evolution in the K-band, leading to (e+k)-corrections at z= 0.5 that are as much as 60% larger than accepted values. The former possibility would imply that the local expansion rate on scales of several hundred Mpc exceeds the global value of H_0 by up to 30% and that the amplitude of very large scale density fluctuations is far larger than expected in any current cosmogonic scenario. The latter possibility would mean that even the apparently most secure aspects of our understanding of galaxy evolution and spectral energy distributions are seriously flawed. 
L. A. Phillips and Edwin L. Turner (Princeton University Observatory)