$R$-invariant new inflation model versus supersymmetric standard model

We revisit the implications of the $R$-invariant new inflation model to the supersymmetric standard model in light of recent discussion of gravitino production processes by the decay of the inflaton and the supersymmetry breaking field. We show that the models with supergravity mediation do not work well together with the $R$-invariant new inflation model, where the gravitino abundance produced by the decay of the inflaton and the supersymmetry breaking field significantly exceeds the bounds from cosmological observations without fine-tuning. We also show that the models with gauge mediation can go together with the $R$-invariant new inflation model, where the dark matter abundance and the baryon asymmetry of the universe are consistently explained without severe fine-tuning.

Figure 1

(Left) The $g$ dependence of the gravitino mass for a given value of $n$. The shaded regions represent the typical gravitino mass regions for GMSB ($m_{3/2}\lesssim 30\mathrm{GeV}$), SUGRA [$m_{3/2}=O(100)\mathrm{GeV}–O(1)\mathrm{TeV}$], and AMSB [$m_{3/2}=O(10)–O(100)\mathrm{TeV}$]. (Right) The $g$ dependences of the mass and the VEV of the inflaton for $n=4$.

Figure 2

The yield of gravitinos for $m_{3/2}=1\mathrm{TeV}$ (left), 100 GeV (right). Solid (red) lines denote the yields of gravitinos produced by the inflaton decay in Eq. (16) and dashed (blue) lines denote the yields produced by the decay of SUSY breaking field in Eq. (23). Here, we have taken $C$ and $C_0$ to be 1 and $T_R$ to be ${10}^7\mathrm{GeV}$.

Figure 3

(Left) The size of the VEV of the SUSY breaking field, $⟨Z⟩=(m_{3/2}^4{m}_Z^{-3}{)}^{1/5}$, which we take as an example. (Right) The mass density parameter of the gravitino dark matter, ${\Omega }_{3/2}{h}^2$, produced by the decay of SUSY breaking field. The shaded region corresponds to the density parameter for $T_R={10}^{6–7}\mathrm{GeV}$. The solid (red) horizontal line shows the observed dark matter density $\Omega h^2={0.1050}_{-0.0040}^{+0.0041}(1\sigma )$ [28]. In both panels, we have taken $m_{3/2}=10\mathrm{GeV}$.

Figure 4

The mass density parameter of gravitino produced by the decay of the inflaton for $m_{3/2}=10\mathrm{GeV}$, $T_R={10}^{6–7}\mathrm{GeV}$, and $b=0$. For simplicity, we have assumed $⟨Z⟩=0$.