I watched a video lecture from Alan Guth on inflation (undergrad level), and there is something in it I don't understand. He first presents the inflation scalar field, Φ, which has an energy density associated with it, V(Φ). V(Φ) is stuck at a local minimum, at Φ = 0 (what is called a "false vaccum") : He then invoke an equation, derived earlier in the course, which relates the derivative with respect to time of the mass density of the Universe, ρ, to its pressure p : Then, at around 9:43 prof. Guth says that the left-hand side of the equation, d(ρ)/dt, is 0, because the scalar field is stuck at the false vaccum value. Leading to : Where u is the energy density of the Universe. Here is what bugs me : ρ represents the mass density of the Universe, not the energy density of the false vaccum, V(Φ). I get that V(Φ) is constant, but why does that implies that the mass density ρ is also constant ?