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The cosmological constant is the energy density of space, or vacuum energy, that arises in Albert Einstein's field equations of general relativity. It is closely associated to the concept of dark energy, but, according to quantum field theory, it should also account for all the zero-point energies of quantum fields in space.
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About a hypothetical universe
Imagine a universe dominated by matter, but it is balanced with a cosmological constant $\Lambda=4\pi G\rho$ so the universe is static ($H=0$). However, what would happen if some of that matter turns …