Energy density of the inflaton field

In the textbook introduction to cosmology by Barbara Ryden, the author say that the energy density of the inflaton field is:

$$\epsilon_{\phi} = \frac{\dot{\phi^2}}{2 \hbar c^3} + V(\phi)$$

However, she doesn't really explained how she get that expression. It is obvious? What am I missing?

Thanks

• There may be a detailed explanation in the books and articles of Andrei Linde (Stanford University), if I'm not mistaken.
– dtn
Mar 11 at 7:38

The first term is half a time derivative squared, so something analogous to $$\frac{1}{2} (\dot{x})^2 = \frac{1}{2} v^2$$. Hence, it's the kinetic energy, normalised by some universal constants to make the dimensions work. The second term is a generic potential, with no constraints apart from the usual restriction that it's a function of only the field. The total energy is thus just the sum of kinetic and potential energy, as it always is. Because the inflaton field is conjectured to be a scalar field, there's virtually nothing else the energy density could be.