Without the latter the curvaton can never lead to dominate the energy density of the universe while decaying. 2. The A -term curvaton and a false vacuum Let us consider an MSSM flat direction potential $^{107}$: where λ$_{n}$ ∼ O (1), n ≥ 4, and A ∼ m$_{0}$ ∼ O (100 GeV − 1 TeV), and depends on a phase. Note that we have not added the Hubble-induced corrections to the mass and the A-term. They can be avoided for a simple choice of no-scale type K¨ ahler potential, either motivated from R-symmetry [325, 326], shift symmetry or Heisenberg symmetry [416, 424]. The radial and angular direction of the potential remains flat during inflation, there- fore they obtain random fluctuations. There will be equally populated domains of Hubble patches, where the phase of the A -term is either positive or negative. In either case, during inflation, the flat direction VEV is given by: However there is a distinction between a positive and a negative phase of the A -terms. The difference in dynamics arises after the end of inflation. In the case of a positive A -term the flat direction starts rolling immediately, but in the case of a negative A -term, the flat direction remains in a false vacuum at a VEV which is given by Eq. (451). The mass of the flat direction around this false minimum is very small compared to the Hubble expansion rate during inflation, i.e. (3 n 2 − 9 n + 8) m 2 0 ≪ H 2 inf where n > 3. During inflation the flat direction obtains quantum fluctuations whose amplitude is given by Eq. (446). The flat direction can exit such a metastable minimum only if thermal corrections are taken into account. 107 Similar potential also arises in Refs. [863, 864], where the curvaton is a QCD axion in SUSY, and in [845] where the curvaton is treated as a SM gauge singlet. 214 V = m 2 0 | ϕ | 2 + λ 2 $_{n}$| ϕ | 2( n − 1) M 2( n − 3) P + ( Aλ$_{n}$ ϕ n M n − 3 P + h.c. ) , (450) ϕ$_{inf}$ ∼ ( m$_{0}$M n − 3 P ) 1 /n − 2 . (451)