Vacuum Decay Constraints on a Cosmological Scalar Field

If the potential of a scalar field $\phi$ which currently provides the “dark energy” of the Universe has a minimum at $\phi {=-M}_0^4<0\mathrm{}$, then quantum-mechanical fluctuations could nucleate a bubble of $\phi$ at a negative value of the potential. This bubble would then expand at the speed of light. Given that no such bubble enveloped us in the past, we find that any minimum in $V\left(\phi \right)$ must be separated from the current $\phi$ value by more than $\min \{{1.5M}_0{,0.21M}_{\mathrm{Pl}}\}$, where $M_{\mathrm{Pl}}$ is the Planck mass. We also show that vacuum decay renders a cyclic or ekpyrotic universe with $M_0^4\gtrsim {10}^{-10\mathrm{}}{M}_{\mathrm{Pl}}^4$ untenable.