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Our recent estimates of galaxy counts and the luminosity density in thenear-infrared (Keenan et al. 2010, 2012) indicated that the local universe maybe under-dense on radial scales of several hundred megaparsecs (Mpc). Such alarge-scale local under-density could introduce significant biases in themeasurement and interpretation of cosmological observables, such as theinferred effects of dark energy on the rate of expansion. In Keenan et al.(2013), we measured the K-band luminosity density as a function of distancefrom us to test for such a local under-density. We made this measurement overthe redshift range 0.01 < z < 0.2 (radial distances D ~ 50-800 Mpc). We foundthat the shape of the K-band luminosity function is relatively constant as afunction of distance and environment. We derive a local (z < 0.07, D < 300 Mpc)K-band luminosity density that agrees well with previously published studies.At z > 0.07, we measure an increasing luminosity density that by z~ 0.1 risesto a value of ~1.5 times higher than that measured locally. This implies thatthe stellar mass density follows a similar trend. Assuming that the underlyingdark matter distribution is traced by this luminous matter, this suggests thatthe local mass density may be lower than the global mass density of theuniverse at an amplitude and on a scale that is sufficient to introducesignificant biases into the measurement of basic cosmological observables. Atleast one study has shown that an under-density of roughly this amplitude andscale could resolve the apparent tension between direct local measurements ofthe Hubble constant and those inferred by Planck team. Other theoreticalstudies have concluded that such an under-density could account for what lookslike an accelerating expansion, even when no dark energy is present.

Local Large-Scale Structure and the Assumption of Homogeneity