Exact Solutions and Scalar Fields in Gravity - Instituto Avanzado de ...

108 EXACT SOLUTIONS AND SCALAR FIELDS IN GRAVITY
The value of the parameter is the same as in (24). The
cosmological function originated by the Higgs-potential is necessarily
positive and possesses the value:
It vanishes for the ground–state The first bracket on the right
hand side of (36) represents the effective energy–momentum tensor of
fermions and gauge bosons taking additionally into account the masses
of the gauge bosons and energy and momentum of the excited Higgs–
field.
In the same way it follows from (29) after insertion of (37) and (23)
with the square of the Higgs–mass:
Accordingly the value of (41) is smaller than the usual one (see (21)) by
the very small factor and of the same order of magnitude as see
(39). In consequence of the non-minimal coupling of the gravitational
and the Higgs field in (25), the trace T appears as an additional source
in (40, which results later in a total cancellation of the right hand side.
Finally we give the Dirac equation (30) and the Yang–Mills equation
(31) after symmetry breaking. One obtains with (19)
and with (20)
Now we are able to calculate the source of the excited Higgs-field
according to (40). From (33) and (42) we get for the trace of