# Physical explanation of Dirac-Born-Infeld (DBI) inflation

I am studying the Dirac-Born-Infeld (DBI) inflation model and came across this question in a past exam paper from Cambridge that considered the following Lagrangian:

$$\mathcal{L}=\sqrt{-g}A(X,\phi)$$ where $$X=\frac{1}{2}\partial^\mu\phi\partial_\mu\phi$$ and $$A$$ is given by:

$$A=\frac{1}{f(\phi)}\Big(1-\sqrt{1-2Xf(\phi)}\Big)-V(\phi)$$

where $$f(\phi)$$ is the warp factor of the throat.

I calculated the slow roll parameter which is given by:

$$\epsilon=3\frac{\frac{\gamma}{2}\dot{\phi}^2}{\frac{\gamma^2}{\gamma+1}\dot{\phi}^2+V}$$ where $$\gamma=\frac{1}{\sqrt{1-2Xf(\phi)}}$$

The problem then asks to provide a physical explanation on why inflation can be achieved even if $$\epsilon_V>1$$ which is different from the more conventional models seen. I can see from the $$\epsilon$$ that the kinetic energy times $$\gamma$$ must be smaller than $$V$$ but can't see any physical explanation for why inflation can work for $$\epsilon_V>1$$.