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the assumption that the universe is homogeneous on large scales is a fundamental pillar of our current concordance cosmology . however , it is well known that very large - scale inhomogeneity exists in the form of sheets , voids , and filaments of matter . as structure formation proceeds , gravity acts to pile more matter onto the over - dense regions , and simultaneously evacuate the under - dense regions . models have shown that this phenomenon implies that cosmological observables measured by an observer will vary significantly depending on where that observer is located with respect to these large - scale structures . in two previous papers @xcite , we investigated large - scale inhomogeneity in the local universe . these studies were inspired , in part , by the fact that a number of recent cosmological modeling efforts have shown that the observational phenomena typically used to infer an accelerating expansion , namely the  dimming " of type ia supernovae , can be equally well fit by invoking a large local under - density instead of dark energy ( e.g. , @xcite ) . other models @xcite have shown that , even in the context of a universe dominated by dark energy , a large local under - density could explain the apparent discrepancy between local measurements of the hubble constant and those inferred by the planck team @xcite .    in the study presented here , we investigated the @xmath0band luminosity density ( as a proxy for stellar mass density ) as a function of distance from our position in the local universe . to accomplish this we combined photometry from the ukirt infrared deep sky large area survey ( ukidss - las , @xcite ) and the two micron all sky survey extended source catalog ( 2mass - xsc , @xcite ) with redshifts from the the sloan digital sky survey ( sdss , @xcite ) , the two - degree field galaxy redshift survey ( 2dfgrs , @xcite ) , the galaxy and mass assembly survey ( gama , @xcite ) the two micron redshift survey ( 2mrs , @xcite ) , and the six degree field galaxy redshift survey ( 6dfgs , @xcite ) . key results from our study @xcite are presented in the figures below . in figure 1a , we show our measurement of the @xmath0band luminosity function using our compiled sample in three separate redshift ranges ( with residuals showing the normalization offset between these ) . in figure 1b , we show the relative contribution to the total light as a function of absolute magnitude to demonstrate that we are resolving @xmath8 of the total light at @xmath9 . in figure 2a , we show a comparison of our estimate of the total luminosity density in different directions on the sky . in figure 2b , we show our results compared to other studies from the literature and models . we conclude that the local universe appears under - dense on a scale and amplitude sufficient to introduce significant biases into local measurements of the expansion rate , and , according to some models , to cause what looks like an accelerating expansion even when no dark energy is present . ( a ) the ukidss - las @xmath0band luminosity function split into three redshift ranges : @xmath10 ( red ) , @xmath11 ( green ) , and @xmath12 ( blue ) . we separate the redshift range @xmath11 to demonstrate that the excess at @xmath13 is not due to the sloan great wall or the other over - densities we observe at higher declination in this redshift range . here we fit @xmath14 in each redshift range with @xmath15 and @xmath16 fixed ( as described in @xcite ) . we list the @xmath17 values for each redshift range in the figure , and note that relatively good fits can be obtained using fixed lf shape parameters and letting the normalization ( @xmath14 ) vary as a function of redshift . residuals are shown relative to the low - redshift normalization . here we also include our own analysis of the 2m++ catalog ( all sky , @xmath18 galaxies ) . we have fit the normalization of the lf derived from the 2m++ catalog ( lf and residuals shown as light blue squares ) with the same shape parameters as for the ukidss sample . to extend the faint end of the @xmath19 lf , we use the gama redshift sample ( @xmath20 , shown as orange squares ) . ( b ) the relative contribution to the total luminosity density ( % per magnitude ) as a function of absolute magnitude . the blue shaded region shows the range of magnitudes covered by the ukidss sample at @xmath19 . in orange we show the extra fraction of light resolved by extending the faint end of the lf with the gama sample . this demonstrates that , at @xmath19 , we are making a robust measurement of the peak of the luminosity density distribution ( occurring at @xmath21 ) and resolving @xmath8 of the total light.,width=453 ]     @xmath0band luminosity density as a function of comoving distance . ( a ) our measured @xmath0band luminosity density for the full sample ( red circles ) versus different directions on the sky ( green , blue , and orange circles corresponding to different subregions in the ukidss sample ) . light blue squares indicate the @xmath0band luminosity density we measure in three different directions ( sdss , 6dfgrs , and 2mr regions ) using the 2m++ all sky catalog compiled by @xcite . ( b ) our measured @xmath0band luminosity density for the full sample ( red circles ) as a function of comoving distance compared with other studies from the literature . our estimate of the @xmath22 luminosity density from the 2m++ catalog ( sdss and 6dfgrs regions only ) is shown as a light blue circle . our estimates in three redshift bins for the gama survey only ( @xmath20 , same methods as for the ukidss sample ) are shown as black circles . the density contrast , @xmath23 , is displayed on the right - hand vertical axis . the scale of the right - hand axis was established by performing an error - weighted least - squares fit ( for the normalization only , not shape ) of the radial density profile of @xcite ( gray solid curve ) to all the luminosity density data in panel ( b ) . the dashed curve shows the radial density profile of @xcite . both @xcite and @xcite claimed these density profiles can provide for good fits to the snia data without dark energy . the dash - dot curve shows the scale and amplitude of the  hubble bubble " type perturbation that @xcite would require to explain the discrepancy between local measurements of the hubble constant and those inferred by planck.,width=453 ]
our recent estimates of galaxy counts and the luminosity density in the near - infrared @xcite indicated that the local universe may be under - dense on radial scales of several hundred megaparsecs . 
 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 @xcite , we measured the @xmath0band 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 @xmath1 ( radial distances @xmath2  @xmath3  mpc ) . 
 we found that the shape of the @xmath0band luminosity function is relatively constant as a function of distance and environment . 
 we derive a local ( @xmath4  @xmath3  mpc ) @xmath0band luminosity density that agrees well with previously published studies . at @xmath5 , 
 we measure an increasing luminosity density that by @xmath6 rises to a value of @xmath7 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 .