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 SDSS , 2DFGRS , GAMA , and other redshift surveys to generate a K - selected catalog of \sim 35 , 000 galaxies that is \sim 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 2MASS photometry with redshifts from the 2MASS redshift survey , the 6DFGRS , 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 \sim 50 - 800 h _ { 70 } ^ { -1 } Mpc ) .
We find that the overall shape of the z = 0 rest-frame K - band luminosity function ( M ^ { * } = -22.15 \pm 0.04 and \alpha = -1.02 \pm 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 h _ { 70 } ^ { -1 } Mpc ) luminosity density that is in good agreement with previous studies .
Beyond z \sim 0.07 , we detect a rising luminosity density that reaches a value of roughly \sim 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 .