Axion, $\mu$ term, and supersymmetric hybrid inflation

We show how successful supersymmetric hybrid inflation is realized in realistic models where the resolution of the minimal supersymmetric standard model $\mu$ problem is intimately linked with axion physics. The scalar fields that accompany the axion, such as the saxion, are closely monitored during and after inflation to ensure that the axion isocurvature perturbations lie below the observational limits. The scalar spectral index $n_{\mathrm{s}}\simeq 0.96–0.97$, while the tensor-to-scalar ratio $r$, a canonical measure of gravity waves, lies well below the observable range in our example. The axion domain walls are inflated away, and depending on the axion decay constant $f_{\mathrm{a}}$ and the magnitude of the $\mu$ parameter, the axions and/or the lightest supersymmetric particle compose the dark matter in the Universe. Nonthermal leptogenesis is naturally implemented in this class of models.

Figure 1

Postinflationary evolution of the field $\chi$ as a function of the number of $e$-foldings ${\mathbf{N}}_{\exp }$ for $m_{3/2}={10}^{-14}$ and $d_1=d_2=1$. The moving position in Eq. (38) of the minimum of the potential is also depicted.

Figure 2

Postinflationary evolution of the field $\chi$ as a function of the number of $e$-foldings ${\mathbf{N}}_{\exp }$ for $m_{3/2}={10}^{-13}$ and $d_1=d_2=1$. The moving position in Eq. (38) of the minimum of the potential is also depicted.

Figure 3

Postinflationary evolution of the field $\chi$ as a function of the number of $e$-foldings ${\mathbf{N}}_{\exp }$ for $m_{3/2}={10}^{-13}$ and $d_1=d_2=0.1$. The moving position in Eq. (38) of the minimum of the potential is also depicted.

Figure 4

Postinflationary evolution of the field $\chi$ as a function of the number of $e$-foldings ${\mathbf{N}}_{\exp }$ for $m_{3/2}={10}^{-13}$ and $d_1=d_2=10$. The moving position in Eq. (38) of the minimum of the potential is also depicted.

Figure 5

Postinflationary evolution of the field $\chi$ as a function of the number of $e$-foldings ${\mathbf{N}}_{\exp }$ for $m_{3/2}={10}^{-13}$ and $d_1=1$, 0.1, 10 and $d_2=0$.

Figure 6

Postinflationary evolution of the field $\chi$ as a function of the number of $e$-foldings ${\mathbf{N}}_{\exp }$ for $m_{3/2}={10}^{-13}$ and $d_1=2.2$, 2.5, 3, 5 and $d_2=-1$.