Abstract
The accelerating expansion of the Universe points to a small positive vacuum energy density and negative vacuum pressure. A strong candidate is the cosmological constant in Einstein's equations of general relativity. Possible contributions are zero-point energies and the condensates associated with spontaneous symmetry breaking. The vacuum energy density extracted from astrophysics is 10 56 times smaller than the value expected from quantum fields and standard model particle physics. Is the vacuum energy density time dependent? We give an introduction to the cosmological constant puzzle and ideas how to solve it.
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