Cosmological consequences of MSSM flat directions

Abstract

We review the cosmological implications of the flat directions of the Minimally Supersymmetric Standard Model (MSSM). We describe how field condensates are created along the flat directions because of inflationary fluctuations. The post-inflationary dynamical evolution of the field condensate can charge up the condensate with B or L in a process known as Affleck-Dine baryogenesis. Condensate fluctuations can give rise to both adiabatic and isocurvature density perturbations and could be observable in future cosmic microwave experiments. In many cases the condensate is however not the state of lowest energy but fragments, with many interesting cosmological consequences. Fragmentation is triggered by inflation-induced perturbations and the condensate lumps will eventually form non-topological solitons, known as Q-balls. Their properties depend on how supersymmetry breaking is transmitted to the MSSM; if by gravity, then the Q-balls are semi-stable but long-lived and can be the source of all the baryons and LSP dark matter; if by gauge interactions, the Q-balls can be absolutely stable and form dark matter that can be searched for directly. We also discuss some cosmological applications of generic flat directions and Q-balls in the context of self-interacting dark matter, inflatonic solitons and extra dimensions.

Figures (14)

• Figure 1: Contours of K for two d=4 flat directions in the $(A, \xi\equiv m_g/m(t=0))$-plane: (a) $K=0$ (b) $K=-0.01$; (c) $K=-0.05$; (d) $K=-0.1$. The directions are (i) $Q_3Q_3QL$; (ii) $QQQL$, no stop; (iii) $\bar{u}_3\bar{u}\bar{d}\bar{e}$; (iv) $\bar{u}\bar{u}\bar{d}\bar{e}$ with equal weight for all $\bar{u}$-squarks, from enqvist00483.
• Figure 2: Affleck-Dine condensate formation with $x=\phi_{1}$ and $y=\phi_{2}$, for (a) gravity mediated case with $d=4$ (solid) and $d=6$ (dashed), and (b) gauge mediated case with $d=4$, $m_{\phi}=1{\rm\ TeV}$ (solid) and $m_{\phi}=10{\rm\ TeV}$ (dashed) with the initial condition $\theta_i=-\pi/10$, from jokinen02.
• Figure 3: Pressure-to-energy density ratio, $p/\rho\equiv w=\gamma-1$, in the gravity mediated case vs. (a) time in logarithmic units for $d=4$, (b) different initial conditions for $d=4,\,6$; (c) ellipticity $\varepsilon=B/A$ vs. initial conditions for $d=4$ (thin lines), $d=6$ (thick lines), D-term (solid), F-term (dashed) with $K=-0.01$ and $t=100m_{3/2}^{-1}$. In (b) $w$ is shown at $t=300m_{3/2}^{-1}$ with dotted lines for the $d=4$ D-term case, from jokinen02.
• Figure 4: Pressure-to-energy density ratio, $w$, in the gauge mediated D-term case (without Hubble induced $A$-term) vs. time in logarithmic units for (a) $d=4$ and (b) $d=6$; (c) ellipticity of the orbit where $d=4$ (thin lines) and $d=6$ (thick lines). The scalar masses $m_{\phi}=1,\,10,\,100{\rm\ TeV}$ are denoted respectively with solid, dotted and dashed lines, from jokinen02.
• Figure 5: Energy-to-charge ratio, $x$, in the gravity mediated case vs. (a) time in logarithmic units for $d=4,\,6$; (b) the D-term case; (c) the F-term (with Hubble induced $A$-term) case with $d=4,5,6,7$ (solid, dash-dot, dashed and dotted lines), $K=-0.01$ and $t=100m_{3/2}^{-1}$, from jokinen02.