$F$-term inflation $Q$-balls

A general analysis of $Q$-ball solutions of the supersymmetric $F$-term hybrid inflation field equations is given. The solutions consist of a complex inflaton field and a real symmetry-breaking field, with a conserved global charge associated with the inflaton. It is shown that the $Q$-ball solutions for any value of the superpotential coupling, $\kappa$, may be obtained from those with $\kappa =1$ by rescaling the space coordinates. The complete range of $Q$-ball solutions for the case $\kappa =1$ is given, from which all possible $F$-term inflation $Q$-balls can be obtained. The possible role of $F$-term inflation $Q$-balls in cosmology is discussed.

Figure 1

$F$-term inflation $Q$-ball for the case $\kappa =1$, $\omega =1.1$.

Figure 2

$\frac{E}{Q_S{m}_S}$ versus $\omega$ for $\kappa =1$ $Q$-balls. The $Q$-ball stability condition, $\frac{E}{Q_S{m}_S}<1$, implies that $\omega \lesssim 1.26$.

Figure 3

Energy $E$ and charge $Q_S$ versus $\omega$ for $\kappa =1$ $Q$-balls. Both diverge as $\omega \to 0.57$.

Figure 4

${\varphi }_o$ versus $\omega$ for $\kappa =1$ $Q$-balls.

Figure 5

$s_o$ versus $\omega$ for $\kappa =1$ $Q$-balls.

Figure 6

Radius versus $\omega$ for $\kappa =1$ $Q$-balls.