= Quartic-inflation expansion from Planck density
{title2=$N\sim2\pi/\sqrt\lambda$}
With unreduced <Planck mass> $M_P$ and initial potential-dominated density $\lambda\phi_i^4/4\sim M_P^4$, one has $\phi_i^2\sim2M_P^2/\sqrt\lambda$. The <slow-roll e-fold count> is $N\simeq\pi(\phi_i^2-\phi_e^2)/M_P^2$. Thus small positive $\lambda$ produces a very large expansion factor $e^N$ in this classical quartic model. The order-one endpoint correction is negligible compared with $2\pi/\sqrt\lambda$; initial <kinetic energy>, spatial curvature and the model's validity at trans-Planckian field values are independent assumptions.
Back to article page
