Is the dark matter a solid?

A smooth unclustered dark matter component with negative pressure could reconcile a flat universe with the many observations that find a density in ordinary, clustered matter well below the critical density and also explain the recent high red-shift supernova data suggesting that the expansion of the universe is now accelerating. For a perfect fluid negative pressure leads to instabilities that are most severe on the shortest scales. However, if instead the dark matter is a solid, with an elastic resistance to pure shear deformations, an equation of state with negative pressure can avoid these short wavelength instabilities. Such a solid may arise as the result of different kinds of microphysics. Two possible candidates for a solid dark matter component are a frustrated network of non-Abelian cosmic strings or a frustrated network of domain walls. If these networks settle down to an equilibrium configuration that gets carried along and stretched by the Hubble flow, equations of state result with $w=-1/3$ and $w=-2/3,$ respectively. One expects the sound speeds for the solid dark matter component to comprise an appreciable fraction of the speed of light. Therefore, the solid dark matter does not cluster, except on the very largest scales, accessible only through observing the large-angle CMB anisotropy. In this paper we develop a generally covariant, continuum description for the dynamics of a solid dark matter component. We derive the evolution equations for the cosmological perturbations in a flat universe with $\mathrm{C}\mathrm{D}\mathrm{M}+\left(\mathrm{solid}\right)\mathrm{}$ and compute the resulting large-angle CMB anisotropy. The formalism presented here applies to any generalized dark matter with negative pressure and a nondissipative resistance to shear.