content_image/320019.jpg content_image/320025.jpg content_image/320024.jpg
the time-independent result 

<img src='content_image/320019.jpg'>

which is the Hawking Temperature for de Sitter spacetime. See [45] for the original derivation of this result. 

Now let us consider a time well after horizon exit. The solution for ϕ$_{k}$ ( η ) , Eq. (3.50), tends to 

i.e. a purely imaginary solution. Eq. (3.46) now becomes 

<img src='content_image/320025.jpg'>

<img src='content_image/320024.jpg'>

Therefore, we can see that, before horizon exit, the perturbation ϕ k of the scalar field φ is a quantum object. However, well after horizon exit, the per- turbation has become an almost scale-invariant classical perturbation. The classical perturbation is conserved whilst outside the horizon [46]. 

After the end of inflation, there must exist a mechanism for transferring the energy density of φ into the components that will initiate the Hot Big Bang. This mechanism is called Reheating . At around the time of horizon entry, the classical perturbation starts to oscillate and thus we have a particle interpretation for φ within the context of QFT. Reheating can be sudden or take some cosmic time to complete and is complete when we have a cosmic fluid whose components are radiation (i.e. relativistic), which are all in ther- mal equilibrium with each other and that this fluid is the initiation of the 

