Is the Dark Matter a Solid?

TL;DR

Is the Dark Matter a Solid? investigates whether a dark matter component with substantial negative pressure can exist as a solid-like medium, thereby avoiding the small-scale instabilities of a negative-pressure fluid. The authors develop a generally covariant elasticity theory for a relativistic solid, derive scalar/vector/tensor cosmological perturbation equations, and analyze the resulting large-angle CMB signatures in a flat FRW universe with CDM plus solid dark matter. They argue that two microphysical realizations—frustrated networks of non-Abelian strings ($w=-1/3$) and frustrated networks of domain walls ($w=-2/3$)—predict an essentially non-clustering dark matter on observable scales and yield distinctive ISW effects that could distinguish SDM from $ ext{Lambda}$ or quintessence. The framework provides testable predictions for the CMB and gravitational waves and motivates future Boltzmann-code calculations to constrain SDM parameters.

Abstract

A smooth unclustered dark matter component with negative presure 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 redshift supernova data suggesting that the expansion of the universe is now accelerating. For a perfect fluid negative presure 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 presure 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, expect 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 CDM+(solid) and compute the resulting large-angle CMB anisotropy. The formalism presented here applies to any generalized dark matter with negative pressure and a non-dissipative resistance to shear.