Zoology of instanton solutions in flat potential barriers

Abstract

We perform a detailed study of the existence and the properties of O(4)-invariant instanton solutions in Einstein-scalar theory in the presence of flat potential barriers, i.e. barriers where the second derivative of the potential is small at the top of the barrier. We find a whole zoo of solutions: Hawking-Moss, Coleman-De Luccia (CdL), oscillating instantons, asymmetric CdL as well as other non-standard CdL-like solutions with additional negative modes in their spectrum of fluctuations. Our work shows how these different branches of solutions are connected to each other via "critical" instantons possessing an extra zero mode fluctuation. Overall, the space of finite action euclidean solutions to these theories with flat barriers is surprisingly rich and intricate

Fluctuations about the Fubini-Lipatov instanton for false vacuum decay in classically scale invariant models

“…(11), we indeed recover the negative eigenvalue (20). We therefore conclude that the negative eigenmode can be associated with dilatations in the thin-wall regime.…”

“…We note that, because the mode (26) has a single node and zero eigenvalue, there also is, as anticipated, a negative mode for j ¼ 0, which is associated with the metastability of the false vacuum state [20]. This negative eigenmode satisfies the eigenvalue equation 20 and, for simplicity, we label the pertaining lowest-lying mode with the index 0 rather than the pair fλ FL ; jg. Introducing the dimensionless variable z ¼ r=R and defining fðzÞ ≡ ð1 þ z 2 Þ 2 ϕ 0 ðrÞ, we are looking for the solution to…”

Oscillating Fubini instantons in curved space

“…For example, a 1L and a 1R solutions make a closed loop, which meets with the z 1 solution at a certain U o and Φ o . This point is known as a bifurcation point for Z 2 -asymmetric solutions [17,39]. The curves move to the left and downward as κ is increased.…”

“…From this numerical result, we can expect that all b j solutions behave like the b 1 solution. Figure 9 presents parametric phase diagrams in dS space [39]. The U o is from 10 −2 to 2.50 and Φ o is from 0 to −14.00.…”

“…We obtained the solutions with Z 2 symmetry in the dS background [37]. Recently, the oscillating bounce solutions under flat potential barriers was extensively studied in dS space [39], in which the authors analyzed the variety of solutions using an instanton diagram [40]. In the present paper, we investigate oscillating Fubini instantons in AdS and dS spaces constructing the parametric phase diagram.…”