# Understanding the energy density of the the false vacuum

This note by Alan Guth says that

The false vacuum, however, cannot rapidly lower its energy density, so the energy density remains constant and the total energy increases. Since energy is conserved, the extra energy must be supplied by the agent that pulled on the piston.

1. Why is it that the false vacuum cannot lower its energy rapidly?

2. Do we know of a substance which behaves in this unusual fashion? In short, why is the energy density doesn't dilute with expansion?

• Minor comment to the post (v2): Please consider to mention explicitly author, title, etc. of link, so it is possible to reconstruct link in case of link rot. Jun 16, 2017 at 18:14

From continuity equation ($\varepsilon$ - energy density, $p$ - pressure, $H$ - Hubble parametre) \begin{equation} \dot{\varepsilon}=-3H(p+\varepsilon) \end{equation} you can see that for a substance with negative pressure $p=-\varepsilon$, above equation gives $\varepsilon=const$, with or without expansion. Such equation of state is exactly what we need from the inflaton field during the inflation. Since pressure and energy density are defined as $$\varepsilon=\frac{1}{2}\dot{\phi}^2+V(\phi)~,~~p=\frac{1}{2}\dot{\phi}^2-V(\phi)~,$$ when potential energy dominates, $V(\phi)\gg\frac{1}{2}\dot{\phi}^2$, we have $p\approx-\varepsilon$.