= Solution
Separate <stress-energy conservation> and the constant <equation-of-state parameter> $w$ give the <constant-equation-of-state density scaling>
$$
\rho_{\rm ph}=\rho_{{\rm ph},0}a^{-3(1+w)}.
$$
Because $w<-1$, the <phantom energy> density grows with the <scale factor>, whereas the <pressureless matter> density decays as $a^{-3}$. Phantom energy therefore dominates at late times. With $\Lambda=0$, the <Friedmann equation> becomes
$$
\frac{\dot a}{a}=C a^{-3(1+w)/2},
\qquad C=\sqrt{\frac{8\pi\rho_{{\rm ph},0}}3}.
$$
Integrating and absorbing the integration constant into the finite time $t^*$ gives
$$
\boxed{a(t)\sim
\left[-\frac32(1+w)C(t^*-t)\right]^{2/[3(1+w)]}}.
$$
The exponent is negative, so $a(t)\to\infty$ as $t\to t^{*-}$. This is a <Big Rip>.
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