Preheating in an inflationary model with disformal coupling

In this work, we investigate the preheating mechanism in a disformally coupled inflationary model where the scalar field $\varphi$ (which is the inflaton field) naturally coupled to another matter field $\chi$ induced by the disformal transformation. In the present scenario, novel derivative interactions mixing the kinetic terms of the two fields emerge inherently. We start by deriving the evolution of the background system when the backreaction on the background field is neglected. We examine the particle production due to parametric resonances in the models and find in Minkowski space that the stage of parametric resonances can be described by the Mathieu equation. Interestingly, we discover that broad resonances in our models can be typically achieved. Finally, we compare our results with the previously studied model with derivative couplings.

Figure 1

The upper panels show the evolution of $A_{*}\equiv \log (D{\dot{\varphi }}^2/C)$ after inflation for the cases where $\alpha =\beta =0$ (left panel) and $\alpha =\beta =1$ (right panel). The lower left panel shows the evolution of $A_{*}$ for the case where $(\alpha ,\beta )=(0,-2)$. The lower right panel shows the evolution of $\gamma$. In this panel, the lines “1” and “2” represent the cases where $\alpha =\beta =0$ and $(\alpha ,\beta )=(0,-2)$, respectively. In the plots for the case $\alpha =\beta$, we set $C_0=1$ and $D_0=0.9(3/2)10^{14}$, while we set $C_0=1$ and $D_0=0.9(3/2)e^{0.06{\varphi }_i}10^{14}$ for the case $\alpha \ne \beta$.

Figure 2

We plot the approximate solution of the field $\varphi (t)$ as given in Eq. (30). The value of the scalar field here is measured in units of $M_{\mathrm{P}}$ and time is measured in units of $m_{\varphi }^{-1}$.