## 4.4.4 Results 

In this section, we combine the above constraints to find out the allowed parameter space (if any). 

## 4.4.4.1 The Case α = 1 

Even with α set to the value α = 1 , we still have six free parameters in the model. Therefore, the parameter space is very multi-dimensional and the number of allowed regions is potentially very vast. Given this, we show results only for one such allowed region of parameter space that we have ex- plored. Additionally, we also only show results for the case where Γ$_{ϕ}$ ≪ H$_{TI}$ , in that reheating from primordial inflation occurs at some time after the end of thermal inflation, as this scenario was found to yield more parameter space than the case where Γ$_{ϕ}$ ≳ H$_{TI}$ . 

From Eq. (4.107) we require g ≪ 1 . We also require the constraint given by Eq. (4.123) to be satisfied, where g is present as g − $^{16}$. Therefore, this latter constraint will start to become very strong very quickly as we decrease g . We find that a value of g =0 . 4 yields allowed parameter space, for reason- able values of $^{H}$∗ and Γ$_{ϕ}$ . The parameter space that we find here however, when all constraints are considered together and regardless of the $^{φ}$∗ case, is actually a sharp prediction of single values for all but one of the free param- eters and the other quantities in the model, to within an order of magnitude, rather than a range of parameter space. The values of the free parameters are displayed in Table 4.2. 

The allowed range of values for $^{ψ}$∗ , the contrast δψ$_{∗}$ ψ$_{∗}$ and H$_{T I}$ are dis- 

