Emergent universe by tunneling

In this work we propose an alternative scheme for an emergent universe scenario where the universe is initially in a static state supported by a scalar field located in a false vacuum. The universe begins to evolve when, by quantum tunneling, the scalar field decays into a state of true vacuum. The emergent universe models are interesting since they provide specific examples of nonsingular inflationary universes.

Figure 1

Schematic representation of a potential for a standard emergent universe scenario.

Figure 2

A double-well inflationary potential $V(\varphi )$. In the graph, some relevant values are indicated. They are the false vacuum $V_F=V({\varphi }_F)$ from which the tunneling begins, $V_W=V({\varphi }_W)$ where the tunneling stops and where the inflationary era begins, while $V_T=V({\varphi }_T)$ denote the true vacuum energy.

Figure 3

Potential with a false and true vacuum.

Figure 4

Time evolution of the bubble in the outside coordinates $x(t)$, and time evolution of the surface energy density $\sigma (t)$. The left panel is for a static universe dominated by dust and the bubble wall containing dust. The right panel is the same situation but with radiations instead of dust. In all these graphics we have considered dashed line for $R=1000$, dotted line for $R=500$, and continuous line for $R=100$.

Figure 5

Time evolution of the bubble in the outside coordinates $x(t)$, and time evolution of the surface energy density $\sigma (t)$, for a background with $R=500$. Dashed line corresponds to a static universe dominated by dust and bubble wall containing radiation. Continuous line corresponds to a static universe dominated by radiation and a bubble wall containing dust.