Fate of false vacuum in non-perturbative regimes: Gravity effects

Abstract

A recent analysis of the false-vacuum decay in non-perturbative regimes is here extended in the presence of Einstein gravity, computing the corresponding effective potential and decay rate. We consider a $λφ^4$ scalar field theory and we observe that, in comparison to the usual perturbative decay rate, the higher the coupling $λ$, the greater the decay probability. We evaluate the running of the self-interaction coupling and obtain a weakly coupled theory at lower energies, proving that Einstein gravity grants an even more reliable weak coupling approximation with the universe cooling down. We also provide an extended study of a non-minimal coupling $ξ$ of the scalar field with gravity showing how this term makes the false-vacuum decay more difficult. Minima can also disappear at large coupling $ξ$. We discuss possible applications of these results to cosmological phase transitions, gravitational-wave astronomy, and condensed matter systems.

Figures (7)

• Figure 1: Plot of $U(\phi)$ obtained from Eq. (\ref{['eq:FullU']}) at constant $\phi_0$. The effect of non-perturbative regimes is noted by the way the decay is eased at increasing $\lambda$.
• Figure 2: Same as in Fig. \ref{['fig3']} but with varying $\theta$ and keeping $\lambda$ fixed.
• Figure 3: Limit on $\operatorname{sn}^2(\theta,\kappa^2(y))$ to obtain minima in the effective potential.
• Figure 4: Effective potential for different values of $\lambda$ within the existence threshold of eq.(\ref{['eq:snth']}).
• Figure 5: Effective potential for $\lambda=5$ at $\theta$ varying between the limits of existence of the minima.