An important development in our understanding of the `vacuum energy' was associated with the phenomenon of symmetry breaking in the electroweak Weinberg-Salam model. Consider the scalar field action
where is the Lagrangian density
and the scalar field potential has the form
This particular form of the potential (illustrated in Fig. 12) endows the system with some interesting properties. For instance since the symmetric state = 0 is unstable (V''() < 0) the system settles in the ground state = + or = -, where = [µ2 / ]1/2 thus breaking the reflection symmetry - present in the Lagrangian. The energy momentum tensor Tik of a scalar field with Lagrangian density is given by
Assuming to be homogeneous and time-independent one finds the ground state energy-momentum tensor to be
the vacuum state therefore has precisely the form of an effective cosmological constant Tik = gik eff where eff = V( = ) = V0 - µ4 / 4. Setting V0 = 0, results in a negative cosmological term eff = -µ4 / 4. Substituting parameters arising in the electroweak theory results in a lower limit on the value of the vacuum energy density  vac = |eff| / 8 G = 106 GeV4, which is almost 1053 times larger than current observational upper limits on the cosmological constant vac,0 = 0 / 8 G ~ 10-29 g/cm3 10-47 GeV4. Clearly in order not to violate observational bounds today, one must set V0 µ4 / 4 so that eff ~ 0. An interesting feature of this `regularization' of the cosmological constant is that, while drastically reducing the value of the cosmological constant today it simultaneously generates a large cosmological constant ~ V0 during an early epoch before symmetry breaking, thereby giving rise to the possibility of Inflation ! The cosmological constant problem therefore presents us with a dilemma: it is certainly good to have a large cosmological constant during an early epoch so as to resolve - via Inflation - the horizon and flatness problems and possibly generate seed fluctuations for galaxy formation. However one must simultaneously ensure that the value of today is small so as not to conflict with observations. As we have seen, in models with SSB this dual requirement of `large in the past + small at present' results in an enormous fine tuning of initial conditions.
Figure 12. The `Mexican top-hat' potential describing spontaneous symmetry breaking shown: before (dashed) and after (solid) the cosmological constant has been `renormalized'.