I'm currently writing a review paper on the accelerated expansion of the universe (focussing on scalar field models like quintessence) and was wondering if there is a specific name for the approximation used in obtaining the condition for cosmic acceleration, given by

$\dot{\phi}^2 < V(\phi)$.

When this is substituted into

$w = \frac{P}{\rho} = \frac{\frac{1}{2}\dot{\phi}^2 - V(\phi)}{\frac{1}{2}\dot{\phi}^2 + V(\phi)}$,

we get

$w < -\frac{1}{3}$,

  which is the condition for cosmic acceleration. It is very similar to the slow-roll approximation used for inflation

 $\dot{\phi}^2 \ll V(\phi)$.

Is there a name for this approximation?

I'm currently writing a review paper on the accelerated expansion of the universe (focussing on scalar field models like quintessence) and was wondering if there is a specific name for the approximation used in obtaining the condition for cosmic acceleration, given by

$$\dot{\phi}^2 < V(\phi).$$

When this is substituted into

$$w = \frac{P}{\rho} = \frac{\frac{1}{2}\dot{\phi}^2 - V(\phi)}{\frac{1}{2}\dot{\phi}^2 + V(\phi)},$$

we get $w < -1/3$, which is the condition for cosmic acceleration. It is very similar to the slow-roll approximation used for inflation: $\dot{\phi}^2 \ll V(\phi)$.

Is there a name for this approximation?