We present the idea that replacing the cosmological constant Λ in the Λ𝐶𝐷 𝑀 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 ∗ 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 𝑀𝑒𝑉) 3 .