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}.
The low reheat temperature at the end of inflation from the gravitino bound constrains the creation of heavy Majorana neutrinos associated with models of leptogenesis. However, a detailed view of the reheating of the Universe at the end of inflation
implies that the maximum temperature during reheating, $Tmax$, can be orders of magnitude higher than the final reheat temperature. This then allows for the production of the heavy Majorana neutrinos needed for leptogenesis. We carry out the complementary calculation of the gravitino production during reheating and its dependence on $Tmax$. We find that the gravitino abundance generated during reheating for a quartic potential is comparable to the standard estimate of the abundance generated after reheating and study its consequences for leptogenesis.
An epoch of accelerated expansion, or inflation, in the early universe solves several cosmological problems. While there are many models of inflation only recently has it become possible to discriminate between some of the models using observations o
f the cosmic microwave background radiation and large-scale structure. In this talk, we discuss inflation and its observational consequences, and then the status of current cosmological observations and their implications for different models of inflation.
