Domain Walls and Hubble Constant Tension

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 $S= (8 {\rm MeV})^3$.