Cosmological Symmetry Breaking, Pseudo-scale invariance, Dark Energy and the Standard Model

The energy density of the universe today may be dominated by the vacuum energy of a slowly rolling scalar field. Making a quantum expansion around such a time dependent solution is found to break fundamental symmetries of quantum field theory. We call this mechanism cosmological symmetry breaking and argue that it is different from the standard phenomenon of spontaneous symmetry breaking. We illustrate this with a toy scalar field theory, whose action displays a U(1) symmetry. We identify a symmetry, called pseudo-scale invariance, which sets the cosmological constant exactly equal to zero, both in classical and quantum theory. This symmetry is also broken cosmologically and leads to a nonzero vacuum or dark energy. The slow roll condition along with the observed value of dark energy leads to a value of the background scalar field of the order of Planck mass. We also consider a U(1) gauge symmetry model. Cosmological symmetry breaking, in this case, leads to a non zero mass for the vector field. We also show that a cosmologically broken pseudo-scale invariance can generate a wide range of masses.