As we saw in the last two sections,
the vacuum associated with both one-loop quantum effects and models with
spontaneous symmetry breaking, has properties identical to those of a
cosmological constant.
There is one problem however, in the case of zero-point fluctuations, the
vacuum density turns out to be
infinite leading to an infinitely large cosmological term and
resulting in a *cosmological constant problem* for cosmology
(see section 5). Assuming that the ultraviolet
divergences responsible for the cosmological constant problem can be
cured by (hitherto unknown) physics occurring near the Planck scale,
one gets a finite but very large value

where
_{Pl}
is the Planck density. On the other hand, as we saw earlier,
recent observations of the luminosities of high redshift
supernovae combined with CMB results give the
following value for the dimensionless density in

where _{cr}
= 3*H*^{2} /
8 *G* = 1.88 ×
10^{-29}h^{2} g/cm^{3} (see
sections 4.3 &
4.4), which leads to
_{}
_{Pl}
× 10^{-123}, *i.e.* the value of the cosmological
constant today is almost 123 orders of magnitude smaller than
the Planck density !

As we have shown in section 6,
a large (negative) value of the vacuum energy also arises in models with
spontaneous symmetry breaking. In this case, the fine tuning involved
in matching the present value of
to observations
depends upon
the symmetry breaking scale, and ranges from 1 part in 10^{123}
for the Planck scale, to 1 part in 10^{53} for the electroweak
scale.

Clearly the question begging an answer is: which physical processes can generate a small value for today without necessarily involving a delicate fine tuning of initial conditions? Although no clear cut answers are available at the time of writing (it may even be that a very small may demand completely new physics) some avenues which could lead us to interesting answers will be explored in this section.