Thawing quintessence from the inflationary epoch to today
  Using the latest observational data we obtain a lower bound on the initial
value of the quintessence field in thawing quintessence models of dark energy.
For potentials of the form V(\phi) \phi^{\pm2} we find that the initial value
|\phi_i|>7x10^{18}\gev. We then relate \phi_i to the duration of inflation by
assuming that the initial value of the quintessence field is determined by
quantum fluctuations of the quintessence field during inflation. From the lower
bound on $\phi_i$ we obtain a lower bound on the number of e-foldings of
inflation, namely, N>2x10^{11}. We obtain similar bounds for other power law
potentials for which too we obtain |\phi_{i}|>O(M_{P}.
