Although non-baryonic dark matter seems essential in the context of the currently favoured cosmological model, the standard dark matter scenario is facing problems: experimental searches have failed to find the relevant particles, closing the mass-corssection window of the ‘WIMP miracle’, and the model suffers from problems on (sub) galactic scales. The cold dark matter (CDM) invoked may turn out to be too cold and needs to be heated; so that its solution to the dearth of visible matter in the outer parts of galaxies is not accompanied by the problem of an excess of matter in their centres (along with other possibly related problems, such as the numerical excess of predicted satellites). After a heuristic introduction to some aspects of the rationales that lead to the CDM paradigm, I discuss the properties of self gravitating CDM structures (haloes) and the proposed reasons for their apparently ‘universal profiles’ (including new simulations attempting to explain aspects of their advent), the galactic-scale problems associated with them, and proposed solutions, focussing on baryonic solutions and the recently topical ultra-light axion particles as replacement for the standard weakly interacting massive particles (WIMPs). It is hoped that at least parts of this review would be helpful to a general physics audience interested in the problem of dark matter in an astrophysical context.
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