Inflaton as the Affleck-Dine baryogenesis field in hilltop supernatural inflation

In this paper, we investigate the parameter space in the framework of hilltop supernatural inflation in which the inflaton field can play the role of Affleck-Dine field to produce successful baryogenesis. The suitable value of reheating temperature could coincide with the reheating temperature required to produce lightest supersymmetric particle dark matter. The baryon isocurvature perturbation is shown to be negligible. We consider $p=3$, $p=4$, and $p=6$ type III hilltop inflation and discuss how to connect the models to supersymmetric theories.

Figure 1

$\lambda$ as a function of ${\eta }_0$ for $V_0^{1/2}={10}^{-12}$ for $p=3$.

Figure 2

$\lambda$ as a function of ${\eta }_0$ for $p=4$. Note that here $\lambda$ is independent of $V_0$.

Figure 3

$\lambda$ as a function of ${\eta }_0$ for $V_0^{1/2}={10}^{-12}$ for $p=6$.

Figure 4

$\psi /M_P$ as a function of ${\eta }_0$ for $V_0^{1/2}={10}^{-12}$ and $p=3$. The field value at the end of supernatural inflation is plotted for comparison.

Figure 5

$T_R$ as a function of $m_{\psi }$ for ${\eta }_0=0.03$ and ${\eta }_0=0.021$ in the case of $p=3$. Here it is assumed that $m_{\psi }=m_{3/2}$. If $m_{\psi }<m_{3/2}$, the gravitino bound shifts to the left and becomes weaker or even negligible. We also include a bound of LSP production from Eq. (48).

Figure 6

$\psi /M_P$ as a function of ${\eta }_0$ for $V_0^{1/2}={10}^{-12}$ and $p=4$. The field value at the end of supernatural inflation is plotted for comparison.

Figure 7

$T_R$ as a function of $m_{\psi }$ for ${\eta }_0=0.02$ and ${\eta }_0=0.011$ in the case of $p=4$. Here it is assumed that $m_{\psi }=m_{3/2}$. If $m_{\psi }<m_{3/2}$, the gravitino bound shifts to the left and becomes weaker or even negligible. We also include a bound of LSP production from Eq. (48).

Figure 8

$\psi /M_P$ as a function of ${\eta }_0$ for $V_0^{1/2}={10}^{-12}$ and $p=6$. The field value at the end of supernatural inflation is plotted for comparison.

Figure 9

$T_R$ as a function of $m_{\psi }$ for ${\eta }_0=0.01$ and ${\eta }_0=0.0051$ in the case of $p=6$. Here it is assumed that $m_{\psi }=m_{3/2}$. If $m_{\psi }<m_{3/2}$, the gravitino bound shifts to the left and becomes weaker or even negligible. We also include a bound of LSP production from Eq. (48).