Minimal Dark Matter is particle physics model proposed in 2005 
in order to solve the Dark Matter problem in a "minimalistic" way: while most particle physics Dark Matter candidates have their origins in elaborated Beyond the Standard Model theories (such as for instance the neutralino in SuperSymmetry), this approach proposes to add to the Standard Model just the ingredients that are necessary to explain Dark Matter. More precisely: just one multiplet of particles charged under the ElectroWeak forces (that is: a Weakly Interacting Massive Particle, WIMP, multiplet).
Within this general framework, one can then proceed to identify the assignments of ElectroWeak quantum numbers that yield a fully successful Dark Matter candidate particle. It turns out that the fermionic quintuplet with hypercharge
is such a fully successful candidate: it contains a neutral component which is automatically stable (thanks to the fact that no decay modes into Standard Model fields can exist for these assignments). For this reason, this fermionic quintuplet is referred to as the
Minimal Dark Matter candidate.
Because of its minimality, the model has no free parameters. The annihilation cross section in the Early Universe can be fully computed: imposing that such annihilations leave the observed amount of Dark Matter fixes the mass. For the quintuplet, it is 9.6 TeV. The other components of the multiplet are slightly heavier, due to a small splitting generated by electroweak loop corrections (166 MeV for the quintuplet). From the phenomenological point of view, the absence of free parameters also means that all signatures can be predicted in a univocal way. For the quintuplet, the elastic scattering cross section on nuclei for Direct Detection is
. The Dark Matter particle annihilates mainly into WW, giving rise to fluxes of galactic cosmic rays of positrons, antiprotons and gamma rays 
. The model attracted some attention in 2008 due to the fact that its predictions allow to explain very well 
the anomalous flux of positrons reported by the PAMELA satellite. Subsequent results on gamma rays from the galactic center and on the flux of electrons plus positrons from the HESS telescope are however not in agreement with the predictions.
In Minimal Dark Matter, the annihilation cross section is subject to the Sommerfeld enhancement (a velocity-dependent enhancement due to the exchange of force carriers) 
. In the case of the quintuplet, the enhancement reaches about three orders of magnitude.
More recently, the term of Minimal Dark Matter has also been used to refer generically to Dark Matter models that share the same philosophy of minimality.
- ^Minimal dark matter,
Marco Cirelli, Nicolao Fornengo, Alessandro Strumia.
DFTT40-2005, IFUP-TH-2005-34, Dec 2005. 16pp.
Published in Nucl. Phys. B 753: 178-194, 2006.
- Minimal Dark Matter: Model and results,
Marco Cirelli, Alessandro Strumia.
IFUP-TH-2009-04, SACLAY-T09-010, Mar 2009. 28pp.
e-Print: arXiv:0903.3381 [hep-ph]
- ^Cosmology and Astrophysics of Minimal Dark Matter,
Marco Cirelli, Alessandro Strumia, Matteo Tamburini.
IFUP-TH-2007-12, SACLAY-T07-052, Jun 2007. 24pp.
Published in Nucl. Phys. B 787: 152-175, 2007.
e-Print: arXiv:0706.4071 [hep-ph]
- ^Minimal Dark Matter predictions for galactic positrons, anti-protons, photons,
Marco Cirelli, Roberto Franceschini, Alessandro Strumia.
IFUP-TH-2008-05, SACLAY-T08-034, Feb 2008. 16pp.
Published in Nucl. Phys. B 800: 204-220, 2008.
e-Print: arXiv:0802.3378 [hep-ph]
- ^Minimal Dark Matter predictions and the PAMELA positron excess,
Marco Cirelli, Alessandro Strumia.
SACLAY-T08-127, Aug 2008.
e-Print: arXiv:0808.3867 [astro-ph]
-  A seminar on Minimal Dark Matter: http://www.marcocirelli.net/talks/MDM.pdf.
Another seminar: http://astrumia.home.cern.ch/astrumia/MDM.pdf.