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We show that charged-particles decaying in the early Universe can induce ascale-dependent or `running' spectral index in the small-scale linear andnonlinear matter power spectrum and discuss examples of this effect in minimalsupersymmetric models in which the lightest neutralino is a viablecold-dark-matter candidate. We find configurations in which the neutralinorelic density is set by coannihilations with a long-lived stau, and the latedecay of staus partially suppresses the linear matter power spectrum. Nonlinearevolution on small scales then causes the modified linear power spectrum toevolve to a nonlinear power spectrum similar (but different in detail) tomodels parametrized by a constant running $\alpha_{s}=d n_{s}/d{\rm ln} k$ byredshifts of 2 to 4. Thus, Lyman-$\alpha$ forest observations, which probe thematter power spectrum at these redshifts, might not discriminate between thetwo effects. However, a measurement of the angular power spectrum of primordial21-cm radiation from redshift $z \approx 30$--$200$ might distinguish betweenthis charged-decay model and a primordial running spectral index. The directproduction of a long-lived charged particle at future colliders is a dramaticprediction of this model.Comment: 15 pages, 12 figures, submitted to Phys. Rev.

A running spectral index in supersymmetric dark-matter models with quasistable charged particles