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the cosmological principle ( cp ) is one the most fundamental hypothesis upon which the concordance model based . in this work , we discuss the validity of the cosmological isotropy with different compilations of type ia supernovae ( sne ) , namely the union2.1  @xcite ) and jla data sets  @xcite , using a hemispherical comparison method , hence determining whether the cosmological isotropy actually holds in large angular scales , and whether such hypothesis is not only a mathematical simplification , but a valid assumption . we test the isotropy of the universe expansion by mapping the @xmath0 and @xmath1 parameters through the celestial sphere , so that an opposite hemisphere comparison is performed following ref . ( see also ref .  ) . each pair of these hemispheres is well defined by the healpix pixelization scheme  @xcite , such that we fit @xmath0 and @xmath1 by minimising the following quantity    @xmath3    where the set @xmath4 contains the observational information of the sne data , i.e. , redshift , distance moduli and associated uncertainty of the _ i - th _ object , respectively , where @xmath5 is the distance modulus given by a specific cosmological model according to    @xmath6 } + 42.38 - 5\log_{10}(h ) \;,\ ] ]    where @xmath7 , @xmath8 , and @xmath9 is the adimensional luminosity distance , whose arguments are the redshift @xmath10 , in addition to the set of cosmological parameters @xmath11 which describe the underlying cosmological model  , @xmath9 is given by a cosmographic expansion up to second order , where @xmath12 . ] . furthermore , we quantify the angular non - uniformity of the data sets using the method named sigma - map , as performed in ref . ( see also ref .  ) , which is based upon the two - point angular correlation function of the cosmic objects distribution computed inside each assigned hemisphere . in other words , this estimator constructs a pixelised map in which its colour ranges from blue , when the actual distribution of sne is less correlated than the mean value expected in a random catalogue , to red , in the case when the correlation is larger . in addition , we analyse the anisotropies of the cosmological parameters and the angular sne distribution not only in the pixel space , but in the multipole space as well , so that @xmath13   represents the quantity scanned through the celestial sphere , such as the @xmath0 and @xmath1 parameters . ] , and @xmath14 is the angular power spectrum of the hubble- , q- and sigma - map . since we are interested in large scale angular correlations , we limit our analyses to @xmath15 . the statistical significance of the hubble and q - maps analyses is estimated with two different approaches . in the first approach , the galactic coordinates of each sne is fixed , yet the set @xmath16 is shuffled ( hereafter _ shuffle _ test ) . the second approach also keeps the original @xmath16 of each object yet the sne positions are isotropically redistributed on the celestial sphere ( hereafter the _ mc _ test ) . hence , we can test whether the directional dependence of these parameters are statistically significant in its amplitude as well as in its direction . the results of the sigma - map analyses are shown in fig . [ fig1 ] ( pixel space ) and fig . [ fig2 ] ( multipole space ) for both sne data sets . it is possible to note that they present a preferred direction on the celestial sphere , as discussed on the description of fig . [ fig1 ] , and that the both sne catalogues are highly inconsistent with a perfectly isotropic distribution , since the analyses performed in multipole space present much higher @xmath17 s than their average values obtained by the mcs . moreover , the hubble- and q - map results are featured in fig . [ fig3 ] ( [ fig4 ] ) for the union2.1(jla ) compilations , for the analyses performed in pixel space , whereas fig .  [ fig5 ] ( [ fig6 ] ) refer to the analyses carried out in multipole space for the union2.1 ( jla ) compilations as well . + we note that the direction @xmath18 obtained for the union2.1 hubble - map is consistent with the bulk flow motion direction estimated in ref .  , that is , @xmath19 km / s towards @xmath20 , as well as many works which probed the cosmological isotropy with a similar approach  @xcite . moreover , the anisotropy of the @xmath0 can possibly explain the tension between the @xmath0 determinations  @xcite ) from low-@xmath10 standard candles  @xcite and planck cmb temperature  @xcite . it was found that the maximal @xmath0 variance through the celestial sphere is consistent with their values , and that its direction is consistent with the bulk flow motion as well . this reinforces the idea that such anisotropy arises as a local effect , instead of an intrinsic cosmological anisotropy . we also evaluate the strength of the correlation between these maps , finding a negligible correlation between the hubble- and q - maps with the sigma - map of the union2.1 data set ( @xmath21 and @xmath22 , respectively ) , even though the correlation is moderate in the jla analyses : @xmath23 and @xmath24 , respectively . thus , we conclude that the anisotropy detected on the hubble and q - maps in the jla data is possibly explained by the incompleteness of the sample in terms of sky coverage , while the anisotropy pointed by the union2.1 sne is most likely of local origin . + the results of the statistical significance are depicted , in multipole space , in figs . [ fig5 ] and  [ fig6 ] for the union2.1 and jla case , respectively . it is possible to note that the union2.1 hubble - map present mild disagreement with the _ mc _ and _ shuffle _ tests specially in the lower @xmath25 ( @xmath26 ) , and that the q - map strongly disagrees with both realisations except for the dipole case , thus showing significant evidence for anisotropy in this analysis . nevertheless , this signal can be ascribed to the limited constraining power of the union2.1 data on this parameter , besides the degeneracy with the hubble parameter . for the jla catalogue , there is a better agreement between the real data and the _ shuffle _ realisations in both hubble- and q - maps , except for the dipole contributions , whereas the data presents stronger disagreement with the _ mc _ runs specially in the q - map analysis . this result shows , once again , the fact that the angular non - uniformity of the jla sample indeed biases the hubble and q - map analyses . we have shown that the anisotropy detected on the @xmath0 mapping with the sne sample can be attributed to the bulk flow motion due to its proximity of reported directions in the literature , and the @xmath1 significant anisotropy probably arises due to the limitation of this data set . on the other hand , the jla directional analyses show a significant dependence with its celestial coverage , then biasing the hubble and q - map results . therefore , we conclude that there is no significant violation of the cosmological isotropy with the latest sne data in the @xmath27 range , albeit next - generation surveys such as lsst and euclid may improve this test with the greater precision and much larger data sets that they shall provide . we thank roy maartens , ribamar reis and ivan soares ferreira for helpful discussions . we acknowledge the healpix package for the derivation of our analyses . this work is supported by cnpq , faperj and capes .
we investigate the validity of the cosmological principle by constraining the cosmological parameters @xmath0 and @xmath1 through the celestial sphere . 
 our analyses are performed in a low - redshift regime in order to follow a model independent approach , using both union2.1 and jla type ia supernovae ( sne ) compilations . 
 we find that the preferred direction of the @xmath0 parameter in the sky is consistent with the bulk flow motion of our local universe in the union2.1 case , while the @xmath1 directional analysis seem to be anti - correlated with the @xmath0 for both data sets . 
 furthermore , we test the consistency of these results with monte carlo ( mc ) realisations , finding that the anisotropy on both parameters are significant within @xmath2 confidence level , albeit we find a significant correlation between the @xmath0 and @xmath1 mapping with the angular distribution of sne from the jla compilation . 
 therefore , we conclude that the detected anisotropies are either of local origin , or induced by the non - uniform celestial coverage of the sne data set .