Solution
= Solution
The acceleration equation requires $\rho+3P<0$, so $w=P/\rho<-1/3$. A canonical scalar field with nonnegative potential obeys $P\geq-\rho$. Hence inflation occurs for
$$
\boxed{-1\leq w<-\frac13}.
$$
= Solution
The acceleration equation requires $\rho+3P<0$, so $w=P/\rho<-1/3$. A canonical scalar field with nonnegative potential obeys $P\geq-\rho$. Hence inflation occurs for
$$
\boxed{-1\leq w<-\frac13}.
$$