  For precision cosmological studies it is important to know the local
properties of the reference point from which we observe the Universe.
Particularly for the determination of the Hubble constant with low-redshift
distance indicators, the values observed depend on the average matter density
within the distance range covered. Here we used the spatial distribution of
galaxy clusters to map the matter density distribution. The study is based on
our CLASSIX galaxy cluster survey, which is highly complete and well
characterised with galaxy clusters detected in X-rays. We find a local
underdensity in the cluster distribution of about 30 - 60% which extends ~85
Mpc to the north and ~170 Mpc to the south. For three regions for which the
galaxy density distribution has previously been studied, we find good agreement
between the density distribution of clusters and galaxies. Correcting for the
bias in the cluster distribution we infer an underdensity in the matter
distribution of about -0.3 +- 0.15 (-0.2 +- 0.1) in a region with a radius of
about 100 (~140) Mpc. Calculating the probability of finding such an
underdensity theoretically in a LambdaCDM universe with concordance
cosmological parameters, we find a probability characterised by sigma-values of
1.3-3.7. This indicates low probabilities, but with values of around 10% at the
lower uncertainty limit, the existence of an underdensity cannot be ruled out.
Inside this underdensity, the observed Hubble parameter will be larger by about
5.5 +2.1-2.8%, which explains part of the discrepancy between the locally
measured value of H_0 compared to the value of H_0 inferred from the Planck
observations of cosmic microwave background anisotropies. If distance
indicators outside the local underdensity are included, as in many modern
analyses, this effect is diluted.
