content_image/342662.jpg content_image/342661.jpg
This mode is kinematically allowed at all times, but the rate is suppressed by a factor of ∼ ( m$_{φ}$/y | ϕ | ) $^{2}$Γ$_{d}$ . It becomes efficient at: 

<img src='content_image/342662.jpg'>

Therefore, if the decay products are coupled to a flat direction with a non-zero VEV, the inflaton will actually decay at a time when the expansion rate of the universe is given by [122] 

<img src='content_image/342661.jpg'>

In general it is possible to have, H$_{d}$ ≪ Γ$_{d}$, particularly for large values of ϕ$_{0}$ . Flat directions can therefore significantly delay inflaton decay on purely kinematical grounds. 

## 3. Decay of a flat direction 

There is a crucial difference between a rotating and an oscillating flat direction when it comes to decay. It is well known that an oscillating condensate can decay non-perturbatively via preheating, as we discussed in the earlier subsections. 

In the case of a rotating condensate, there is the conservation of global charges asso- ciated with the net particle number density in fields [324–326] $^{94}$. This ensures that the total number density of quanta will not decrease and, consequently, the average energy of quanta will not increase. The actual decay of a rotating flat direction into other fields hap- pens perturbatively, through the F -term couplings, as originally envisaged by Affleck and Dine [324–326], see also [817, 818]. 

It was argued that there could be possible non-perturbative effects [819–821], stemming from the D -terms of the potential for a rotating flat direction condensate. However it was shown in [410, 411] that such non-perturbative effects have no bearing for the decay of energy density in rotating flat direction(s). In the case of a rotating condensate all that can happen is a mere redistribution of the energy among the fields on the D -flat subspace. 

There is a no-go theorem for a rotating condensate [410, 411], which states; for MSSM flat direction(s), which are represented by gauge-invariant combinations of fields Φ$_{i}$ = e $^{iα$_{i}$}$Φ$_{i}$ , possible non-perturbative particle production from time-variation in the mass eigenstates 

