Cosmology of Supersymmetric Models with Low-energy Gauge Mediation

Abstract

We study the cosmology of supersymmetric models in which the supersymmetry breaking effects are mediated by gauge interactions at about the 10^5 GeV scale. We first point out that the gravitino is likely to overclose the Universe in this class of models. This requires an entropy production, which prefers a baryogenesis mechanism at a relatively low temperature. The Affleck-Dine mechanism for baryogenesis is one of the possibilities to generate enough baryon asymmetry, but the analysis is non-trivial since the shape of the potential for the flat direction differs substantially from the conventional hidden sector case. To see this, we first perform a 2-loop calculation to determine the shape of the potential. By combining the potential with the supergravity contribution, we then find that the Affleck-Dine baryogenesis works efficiently to generate sufficient baryon asymmetry. On the other hand, we also point out that string moduli fields, if present, are stable and their coherent oscillations overclose the Universe by more than 15 orders of magnitude. One needs a very late inflationary period with an e-folding of N \gtrsim 5 and an energy density of \lesssim (10^7 GeV)^4. A thermal inflation is enough for this purpose. Fortunately, the Affleck-Dine baryogenesis is so efficient that enough baryon asymmetry can survive the late inflation.

Figures (8)

• Figure 1: The upper bound on $T_{\rm max}$ as a function of the gravitino mass from the requirement that the relic stable gravitinos do not overclose the Universe. We take the Hubble parameter to be $H_0 = 100~\hbox{Mpc}/\hbox{km}/\hbox{sec}$. There is no constraint below $m_{3/2} = 2$ keV, which is represented by the vertical line. For smaller $H_0$, the constraints become more stringent. The upper bound on $T_{\rm max}$ shifts towards smaller $T_{\rm max}$ as $(H_0)^2$. The vertical line moves towards smaller $m_{3/2}$ also as $(H_0)^2$. Note that the current data prefer $H_{0} \sim 70~\hbox{Mpc}/\hbox{km}/\hbox{sec}$.
• Figure 2: The initial motion of the flat direction with the potential given in Eq. (\ref{['V_tot']}). Here, we take $m_{3/2}=100$ keV, and $\phi_0=0.2M_*e^{i\pi/8}$.
• Figure 3: The resulting baryon-to-entropy ratio as a function of the initial amplitude $\phi_0$. The parameters are taken to be $V_0=(3\times 10^3{\rm GeV})^4$, $\theta_0=\pi/8$, $\phi_{\rm dec}=10^5$ GeV, and $m_{3/2}=1$ keV (dotted line), $m_{3/2}=100$ keV (solid line), and $m_{3/2}=10$ MeV (dashed line).
• Figure 4: Feynman diagrams which contribute to the vacuum energy in the background of the flat direction $\phi = \bar{\phi}$. The vertices are due to the $D$-term potential. The scalar field with mass $m=2g\langle \phi\rangle$ is the scalar component of the massive gauge multiplet in the presence of the background $\phi$. The scalar fields with masses $M_{+}$ and $M_{-}$ are the messenger scalars.
• Figure 5: A Feynman diagram with the gaugino of mass $m$, the messenger fermion of mass $M$, and the messenger scalars of mass $M_{\pm}$.