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 ?Mpc). We find that the overall shape of the z = 0 rest-frame K-band luminosity function (M*-5log (h 70) = –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 ?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.
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机译：星系计数和近红外光度密度的最新测量表明，局部宇宙可能在数百兆帕的尺度上密度不足。局部宇宙中大规模低密度的存在可能会给宇宙学可观测物的解释带来明显的偏差，尤其是暗能量对膨胀率的推断影响。在这里，我们将K波段的光度密度作为红移的函数进行测量，以测试这种局部密度不足。对于本研究的主要样本，我们从UKIDSS大面积调查中选择星系，并使用Sloan数字天空调查（SDSS），两度视野星系红移调查，星系和质量装配调查（GAMA）以及其他的红移调查生成了一个由K选择的〜35，000个星系的目录，在K AB <16.3（GAMA字段中的K AB <17）下，在光谱上约95％是完整的。为了在低红移下补充该样本，我们还分析了2M ++目录中的K选择样本，该样本将两个微米全天候测量（2MASS）光度与2MASS红移测量，六度视野银河红移测量以及SDSS。这些样本的组合可以详细测量K波段发光度密度，它是红移范围0.01 0.1时局部测量的值的约1.5倍。这表明恒星质量密度作为距离的函数遵循相似的趋势。假设发光物质追踪了潜在的暗物质分布，这意味着宇宙的局部质量密度可能低于整体质量密度，其规模和幅度足以在确定基本宇宙学观测值时引入明显的偏差。大约如此规模和幅度的欠密度可以解决哈勃常数的直接测量值与普朗克推断的测量值之间的表观张力。
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