Is it possible to create a universe out of a monopole in the laboratory?

To explore the possibility that an inflationary universe can be created out of a stable particle in the laboratory, we consider the classical and quantum dynamics of a magnetic monopole in the thin-shell approximation. Classically there are three types of solutions: stable, collapsing, and inflating monopoles. We argue that the transition from a stable monopole to an inflating one could occur either by collision with a domain wall or by quantum tunneling.

Figure 1

Conformal diagrams for (a) de Sitter spacetime, (b) Reissner-Nordström spacetime with $m<q$, and (c) Reissner-Nordström spacetime with $m>q$. ${\mathcal{I}}^{+}$ and ${\mathcal{I}}^{-}$ represent future and past null infinity, $i^{+}$ and $i^{-}$ represent future and past timelike infinity, and $i^0$ represents spacelike infinity. A double line denotes timelike singularity. In Figs. 2, 3, 4, 5 monopole solutions are described by joining a left part of de Sitter spacetime to a “right” part of Reissner-Nordström. The left $r=0$ line in the diagram (a) corresponds to the monopole center. Accordingly, the normal vector $n^{\mu }$ of $\Sigma$ points to the right in all diagrams. $r_D$ and $r_{(+)}(r_{(-)})$ denote de Sitter horizons and the black-hole outer (inner) horizons, respectively. In the region $r_{-}<r_D$ [$r_{+}>r_{(+)}$] the sign of ${\beta }^{-}={\partial }_n{r}_{-}$ (${\beta }^{+}={\partial }_n{r}_{+}$) is definite regardless of the shell motion. Brick-pattern domains denote spacetime regions of positive-definite $\beta$, while stripe-pattern domains denote those of negative-definite $\beta$.

Figure 2

Solutions with $m=0.58$, $q=0.6$, $s_0=0.6$, and $s_1=0.1$. (a) represents the effective potential $U(\tilde{R})$. There is a classically stable solution (type $\mathrm{A}$) and a expanding solution (type ${\mathrm{A}}^{\prime }$). No black-hole horizon. Circles at the top denote the region of ${\beta }^{-}>0$, while squares at the bottom denote the region of ${\beta }^{+}>0$. (b) and (c) show the conformal diagrams of type $\mathrm{A}$ and ${\mathrm{A}}^{\prime }$ solutions, respectively. The upper figures show how the trajectory of the shell is embedded in Reissner-Nordström full spacetime, where gray domains indicate nonexistent regions. The lower figures show complete spacetimes.

Figure 3

A solution with $m=0.64$, $q=0.6$, $s_0=0.6$, and $s_1=0.1$. (a) represents the effective potential $U(\tilde{R})$. There is an inflationary solution (type $\mathrm{B}$). A cross denotes a black-hole horizon. (b) shows the conformal diagram of the solution.

Figure 4

Conformal diagram of the model that a spherical domain wall surrounds the type $\mathrm{A}$ monopole and collides with it. A ball denotes an event of the collision. The stable monopole evolves into the type $\mathrm{B}$ inflating monopole by the collision. The shaded domain denotes a set of antitrapped surfaces in the de Sitter side, that is, the created inflationary universe. The past directed outgoing radial null geodesics emanating from this region necessarily hit the timelike singularity.

Figure 5

Solutions with $m=0.61$, $q=0.6$, $s_0=0.6$, and $s_1=0.1$. (a) represents the effective potential $U(\tilde{R})$. There are a classically stable solution (type $\mathrm{C}$) and an expanding solution (type ${\mathrm{C}}^{\prime }$). (b) shows the conformal diagram of the two solutions. $\mathrm{C}$ dashed line denotes a possible tunneling path.

Figure 6

Plot of $G{H}^{2}B$ vs $q/m$ for several values of $m$, $s_0$ and $s_1$. (a) $m=0.6$, $s_0=0.6$, and $s_1=0.1$; (b) $m=0.4$, $s_0=0.6$, and $s_1=0.1$; (c) $m=0.6$, $s_0=0.3$, and $s_1=0.1$; (d) $m=0.6$, $s_0=0.6$, and $s_1=0.2$.