2013ApJ...775...62K

Galaxy counts and recent measurements of the luminosity density in the near-infrared have indicated the possibility that the local universe may be under-dense on scales of several hundred megaparsecs. The presence of a large-scale under-density in the local universe could introduce significant biases into the interpretation of cosmological observables, and, in particular, into the inferred effects of dark energy on the expansion rate. Here we measure the K-band luminosity density as a function of redshift to test for such a local under-density. For our primary sample in this study, we select galaxies from the UKIDSS Large Area Survey and use spectroscopy from the Sloan Digital Sky Survey (SDSS), the Two-degree Field Galaxy Redshift Survey, the Galaxy And Mass Assembly Survey (GAMA), and other redshift surveys to generate a K-selected catalog of ∼35, 000 galaxies that is ∼95% spectroscopically complete at K_AB< 16.3 (K_AB< 17 in the GAMA fields). To complement this sample at low redshifts, we also analyze a K-selected sample from the 2M++ catalog, which combines Two Micron All Sky Survey (2MASS) photometry with redshifts from the 2MASS redshift survey, the Six-degree Field Galaxy Redshift Survey, and the SDSS. The combination of these samples allows for a detailed measurement of the K-band luminosity density as a function of distance over the redshift range 0.01 < z < 0.2 (radial distances D ∼ 50-800 h₇₀^–1 Mpc). We find that the overall shape of the z = 0 rest-frame K-band luminosity function (M*-5log (h₇₀) = -22.15±0.04 and α = -1.02±0.03) appears to be relatively constant as a function of environment and distance from us. We find a local (z < 0.07, D < 300 h₇₀^–1 Mpc) luminosity density that is in good agreement with previous studies. Beyond z ∼ 0.07, we detect a rising luminosity density that reaches a value of roughly ∼1.5 times higher than that measured locally at z > 0.1. This suggests that the stellar mass density as a function of distance follows a similar trend. Assuming that luminous matter traces the underlying dark matter distribution, this implies that the local mass density of the universe may be lower than the global mass density on a scale and amplitude sufficient to introduce significant biases into the determination of basic cosmological observables. An under-density of roughly this scale and amplitude could resolve the apparent tension between direct measurements of the Hubble constant and those inferred by Planck.