**7.3. Late-time Inflation and
**

Conceivably, one might appeal to inflationary mechanisms which are so
successful at generating a large cosmological constant during an early epoch
to generate a small cosmological constant today.
As pointed out in section 6, effective
potentials giving rise to symmetry breaking generically predict a large
negative value for a cosmological constant
which has to be `regularized' to give the small positive
observed
today. The problem with these methods is that they usually
prescribe an unevolving cosmological term
whose present value is fixed at the time of symmetry breaking.
This necessarily implies some fine tuning of
parameters which can be as large as one part in
10^{123} (for symmetry breaking at the
Planck scale) to one part in 10^{53} for the electroweak scale.

A different possibility is suggested by
the family of potentials which lead to `chaotic Inflation'
*V*
^{q},
*q* 2. For instance
*V* = 1/2 *m*^{2}
^{2} will lead to
the inflationary equation of state
*P* -
associated
with a cosmological constant
provided the scalar field rolls down its potential `slowly'
so that
0 or
(*m*/*H*_{0})^{2}
1.
In other words, the Compton wavelength of the inflaton should be larger
than the present Hubble radius
=
/*mc*
*cH*_{0}^{-1}
suggesting an extremely small mass for the inflaton
*m*
10^{-33} eV.
One may be tempted to associate *m* with the small
mass difference associated with solar neutrino oscillations
*m* =
*m*_{}^{2}
/ *M*_{P}
10^{-33} eV where
*m*_{}^{2}
10^{-5}
eV^{2}, an idea which is speculative but not implausible
[69,
90].