  The process of phase separation in elastic solids and viscous fluids is of
fundamental importance to the stability and function of soft materials. We
explore the dynamics of phase separation and domain growth in a viscoelastic
material such as a polymer gel. Using analytical theory and Monte Carlo
simulations we report a new domain growth regime, in which the domain size
increases algebraically with a ripening exponent $\alpha$ that depends on the
viscoelastic properties of the material. For a prototypical Maxwell material,
we obtain $\alpha=1$, which is markedly different from the well-known Ostwald
ripening process with $\alpha=1/3$. We generalize our theory to systems with
arbitrary power-law relaxation behavior and discuss our findings in the context
of the long-term stability of materials as well as recent experimental results
on phase separation in cross-linked networks and cytoskeleton.
