Structure formation in a string-inspired modification of the cold dark matter model

Motivated in part by string theory, we consider the idea that the standard $\Lambda \mathrm{C}\mathrm{D}\mathrm{M}$ cosmological model might be modified by the effect of a long-range scalar dark matter interaction. The variant of this widely-discussed notion considered here is suggested by the Brandenberger-Vafa [R. H. Brandenberger and C. Vafa, Nucl. Phys. B316, 391 (1989).] picture for why we perceive three spatial dimensions. In this picture there may be at least two species of dark matter particles, with scalar charges such that the scalar interaction attracts particles with like sign and repels unlike signs. The net charge vanishes. Under this condition the evolution of the mass distribution in linear perturbation theory is the same as in the $\Lambda \mathrm{C}\mathrm{D}\mathrm{M}$ cosmology, and both models therefore can equally well pass the available cosmological tests. The physics can be very different on small scales, however: if the scalar interaction has the strength suggested by simple versions of the string scenario, nonlinear mass concentrations are unstable against separation into charged halos with properties unlike the standard model prediction and possibly of observational interest.