  We show that, by using recently developed exact resummation techniques based
on the extension of the methods of Yennie, Frautschi and Suura to Feynman's
formulation of Einstein's theory, we get quantum field theoretic descriptions
for the UV fixed-point behaviors of the dimensionless gravitational and
cosmological constants postulated by Weinberg. Connecting our work to the
attendant phenomenological asymptotic safety analysis of Planck scale cosmology
by Bonanno and Reuter, we estimate the value of the cosmological constant
\Lambda. We find the encouraging estimate \rho_\Lambda\equiv
\frac{\Lambda}{8\pi G_N} \simeq (2.4\times 10^{-3}eV)^4. While this numerical
value is close to recent experimental observations, we caution the reader that
the estimate involves a number of model parameters that still possess
significant levels of uncertainty, such as the value of the transition time
between the Planck scale cosmology era and the Friedmann-Robertson-Walker
radiation dominated era, where our current understanding allows for at least
two orders of magnitude in its uncertainty and this would change our estimate
of \rho_\Lambda by at least four orders of magnitude. We discuss such
theoretical uncertainties as well. We show why GUT and EW scale vacuum energies
from spontaneous symmetry breaking are suppressed in our approach to the
estimation of \rho_\Lambda. As a bonus, we show how our estimate constrains
susy GUTS.
