  We present the idea that replacing the cosmological constant $\Lambda$ in the
$\Lambda$CDM model by a distribution of walls, with very low tension compared
to what one would expect from new physics, could help explaining the tension in
the Hubble constant fits in the Standard Cosmological Model. Using parameters
from our model for dark matter as macroscopic pearls, we can get a promising
order of magnitude for the correction to the Hubble constant estimated from
observations of the cosmic microwave background. Our model is on the borderline
of failing by predicting too large extra fluctuations as a function of
direction in the cosmological microwave background radiation. However,
imagining the bubbles in the voids to have come from more somewhat smaller big
bubbles also occurring outside the big voids may help. We estimate that, in
order to have big volumes of the new vacuum in intergalactic space, a very high
temperature is needed and that such regions would be likely to get cooled,
freeze and shrink down to the degenerate form of dark matter if hitting some
ordinary matter, as is likely in the denser parts of the Universe. We also
review our model for dark matter, and develop the understanding of the stopping
of the dark matter particles in the shielding of say the DAMA-LIBRA underground
experiment and the counting rate this experiment observes. We manage to obtain
a consistent fit with a mass $M = 2 \cdot 10^{-18}$kg = $10^9$GeV and radius $R
= 10^{-10}$m for the dark matter pearls, corresponding to a tension in the
domain wall of $S= (8 {\rm MeV})^3$.
