Affleck-Dine baryogenesis just after inflation

We propose a new scenario of Affleck-Dine baryogenesis where a flat direction in the MSSM generates $B-L$ asymmetry just after the end of inflation. The resulting amount of baryon asymmetry is independent of low-energy supersymmetric models but is dependent on inflation models. We consider the hybrid and chaotic inflation models and find that reheating temperature is required to be higher than that in the conventional scenario of Affleck-Dine baryogenesis. In particular, nonthermal gravitino-overproduction problem is naturally avoided in the hybrid inflation model. Our results imply that Affleck-Dine baryogenesis can be realized in a broader range of supersymmetry and inflation models than expected in the literature.

Figure 1

Evolution of $B-L$ number density in a comoving volume (left panel) and the AD field (right panel) in the conventional scenario of ADBG. We set $n=6$, $c_H=-1$, $a{m}_{3/2}/m_{\varphi }=-1$, and ${\theta }_0=\pi /10$. The dimensionfull quantities are rescaled such as $t\to t/m_{\varphi }$ and $\varphi \to \varphi /{⟨|\varphi |⟩}_{t=H_{\mathrm{osc}}^{-1}}$.

Figure 2

Evolution of $B-L$ number density in a comoving volume (left panel) and the phase direction of the AD field (right panel) in the conventional scenario of ADBG. We set $c_H=-1$, $a_H{m}_{3/2}/H_{\mathrm{osc}}=-0.01$, and ${\theta }_0=\pi /10$. The dimensionfull parameters are rescaled as $t\to t/H_{\mathrm{osc}}$ and $\varphi \to \varphi /{⟨|\varphi |⟩}_{t=H_{\mathrm{osc}}^{-1}}$.

Figure 3

Evolution plot for $B-L$ number after hybrid inflation. The dashed curve is our prediction of Eq. (85) with a numerical factor of 0.2. We assume $\lambda =1$, $n=6$, $c_H=-1$, $c_2=0$, $\kappa =0.05$, $\mu =0.001$, and ${\theta }_{\varphi }^{\mathrm{ini}}=0.01$.

Figure 4

Dynamics of the field $I$ in the complex plane in the chaotic inflation model. We set $c_0=1$. The field $I$ slowly rolls along the line of $\mathrm{Re}[I]=-c_0/2$ during inflation. After it reaches the red point, inflation ends and it starts to oscillate and rotate around the origin.

Figure 5

Evolution plot for $B-L$ number density in our scenario of ADBG in the chaotic inflation model. The dashed curve is our prediction of Eq. (116) with a numerical factor of 0.01. We take $\lambda =1$, $n=6$, $c_0=0.5$, $c_1=2$, $|c_2|=1$, and $c_3=-1$.