Inflation parameter value

Question

One of slow-roll Inflation condition is $$ \ddot{\phi} \ll H\dot{\phi}. $$

When i performed numeric calculation, I got a value: $$ \ddot{\phi} = -2, \\ H\dot{\phi} = -120. $$

I got confused because as I know that negative value which near to zero is bigger than negative value far from zero (e.g: -0.1 > -10). So, from my calculation above, the condition does not hold true?

But, if we absolute both value $$ \left|(\ddot{\phi} )\right| \ll \left|(H\dot{\phi} )\right| , $$ then slow-roll inflation condition is hold true.

Answer 1

Yes, absolute values should be considered. This condition is also written in the form $$ |\eta_H|=\left|\frac{\ddot{\phi}}{H\dot\phi}\right|\ll 1 $$ which is called the (second) Hubble slow-roll parameter (the first one being $\epsilon_H=\frac{\dot\phi^2}{2H^2}$).