content_image/310106.jpg content_image/310107.jpg content_image/310108.jpg content_image/310110.jpg
V = 0 at the VEV. 4 V$_{0}$ is obtained by inserting the VEV into the zero temperature potential and then looking along the ψ =0 direction. We obtain 

We use the Friedmann equation 

<img src='content_image/310106.jpg'>

<img src='content_image/310107.jpg'>

giving the energy density of the Universe during thermal inflation to obtain the Hubble parameter during thermal inflation as 

<img src='content_image/310108.jpg'>

Within this model, we will consider two cases regarding the decay rate of the inflaton, Γ$_{ϕ}$ , with ϕ , the inflaton, being the field driving the period of primordial inflation prior to thermal inflation. Firstly, the case that Γ$_{ϕ}$ ≳ H$_{TI}$ , i.e. that reheating from primordial inflation occurs before or around the time of the start of thermal inflation. Secondly, we will consider the case that Γ$_{ϕ}$ ≪ H$_{TI}$ , i.e. that reheating from primordial inflation occurs at some time after the end of thermal inflation. In the case of Γ$_{ϕ}$ ≳ H$_{TI}$ , thermal inflation will begin at a temperature 

<img src='content_image/310110.jpg'>

