  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.
