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For example, choose $w=-5/3$. A schematic solution can join the pressureless matter law $a\propto t^{2/3}$ to the phantom-dominated law $a\propto (t^{\ast }-t{)}^{-1}$. It begins at the Big Bang, bends down during matter domination, changes to accelerated expansion when phantom energy takes over, and has a vertical asymptote at the finite Big Rip time $t^{\ast }$.

Separate stress-energy conservation and the constant equation-of-state parameter $w$ give the constant-equation-of-state density scalingBecause $w<-1$, 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 becomesIntegrating and absorbing the integration constant into the finite time $t^{\ast }$ givesThe exponent is negative, so $a(t)\to \infty$ as $t\to t^{\ast -}$. This is a Big Rip.

A fluid with $w<-1$ grows in density during expansion and can produce a finite-time Big Rip singularity.