4.1 Thermal Inflation 45 Fig. 4.1: Blue: T > m$_{0}$ √$_{2}$$_{g}$ Cyan: T < m$_{0}$ √$_{2}$$_{g}$ Purple: T =0 in string theory. They are flaton fields, which are flat directions in SUSY. These have no tree-level terms in the potential from SUSY and they get a mass term from SUSY breaking (they do not have a quartic (self-interaction) term). Flaton fields have nearly flat potentials (with √$_{V}$ ′′ being the relevant quantity, with a prime indicating the (partial) derivative of V with respect to the flaton field) and large VEVs, ∼ M$_{P}$ . The problem is that when inflation ends and a modulus starts to oscillate around its large VEV, the oscillations will also be very large and the energy density of the moduli will start to dominate the energy density of the Universe. This has the affect of creating an abundance of moduli particles that are long-lived and do not decay prior to BBN, thus creating unwanted relics. Thermal Inflation alleviates this problem by diluting away the moduli during the period of inflation. They -< > 0 < > V