Why does the predicted mass of the quantum vacuum have a very little effect on the expansion of the universe?
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There are probably duplicates/variants of this question on this site.
Expressing the problem in mass terms seems a bit odd to me though, as it's been put in energy terms every other time I have seen it asked, unless I have misunderstood your question.
Here is an answer (to an identically worded question) based on the link: Predicted Mass of Quantum Vacuum
I think you are referring to dark energy and the cosmological constant problem. The expansion of the universe seems to be accelerating, and that can be explained by vacuum having non-zero energy density. Quantum field theories have generally non-zero vacuum energy, but the typical value is 10$^{120} $ times larger than the observed acceleration. Therefore we need to somehow explain why the universe is not accelerating much faster than it is in reality.
One answer, which makes sense but is still highly unsatisfactory, is that if the vacuum energy was even just 10 times higher than the observed value, the acceleration would have been enough to prevent the formation of galaxies in the early universe. Without galaxies, there would be no stars, and without stars we would not be here wondering about the value of the vacuum energy.
This argument does not give a physical reason for the smallness of the vacuum energy, and it even means that there may not be a good reason, because it could be that the small value is a result of some highly unlikely coincidence.
