A Running Spectral Index in Supersymmetric Dark-Matter Models with Quasi-Stable Charged Particles

We show that charged-particles decaying in the early Universe can induce a scale-dependent or `running' spectral index in the small-scale linear and nonlinear matter power spectrum and discuss examples of this effect in minimal supersymmetric models in which the lightest neutralino is a viable cold-dark-matter candidate. We find configurations in which the neutralino relic density is set by coannihilations with a long-lived stau, and the late decay of staus partially suppresses the linear matter power spectrum. Nonlinear evolution on small scales then causes the modified linear power spectrum to evolve to a nonlinear power spectrum similar (but different in detail) to models parametrized by a constant running $\alpha_{s}=d n_{s}/d{\rm ln} k$ by redshifts of 2 to 4. Thus, Lyman-$\alpha$ forest observations, which probe the matter power spectrum at these redshifts, might not discriminate between the two effects. However, a measurement of the angular power spectrum of primordial 21-cm radiation from redshift $z \approx 30$--$200$ might distinguish between this charged-decay model and a primordial running spectral index. The direct production of a long-lived charged particle at future colliders is a dramatic prediction of this model.