Local Large-Scale Structure and the Assumption of Homogeneity
  Our recent estimates of galaxy counts and the luminosity density in the near-infrared (Keenan et al. 2010, 2012) indicated that the local universe may be under-dense on radial scales of several hundred megaparsecs (Mpc). Such a large-scale local under-density could introduce significant biases in the measurement and interpretation of cosmological observables, such as the inferred 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 distance from us to test for such a local under-density. We made this measurement over the redshift range 0.01 < z < 0.2 (radial distances D ~ 50-800 Mpc). We found that the shape of the K-band luminosity function is relatively constant as a function 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 rises to a value of ~1.5 times higher than that measured locally. This implies that the stellar mass density follows a similar trend. Assuming that the underlying dark matter distribution is traced by this luminous matter, this suggests that the local mass density may be lower than the global mass density of the universe at an amplitude and on a scale that is sufficient to introduce significant biases into the measurement of basic cosmological observables. At least one study has shown that an under-density of roughly this amplitude and scale could resolve the apparent tension between direct local measurements of the Hubble constant and those inferred by Planck team. Other theoretical studies have concluded that such an under-density could account for what looks like an accelerating expansion, even when no dark energy is present. 
Ryan C. Keenan, Amy J. Barger, Lennox L. Cowie
astro-ph.CO