In the standard model of cosmic structure formation , dark matter haloes form by gravitational instability .
The process is hierarchical : smaller systems collapse earlier , and later merge to form larger haloes .
The galaxy clusters , hosted by the largest dark matter haloes , are at the top of this hierarchy representing the largest as well as the last structures formed in the universe , while the smaller and first haloes are those Earth-sized dark subhaloes which have been both predicted by theoretical considerations and found in numerical simulations , though it does not exist any observational hints of their existence .
The probability that a halo of mass m at redshift z will be part of a larger halo of mass M at the present time can be described in the frame of the extended Press & Schecter theory making use of the progenitor ( conditional ) mass function .
Using the progenitor mass function we calculate analytically , at redshift zero , the distribution of subhaloes in mass , formation epoch and rarity of the peak of the density field at the formation epoch .
That is done for a Milky Way-size system , assuming both a spherical and an ellipsoidal collapse model .
Our calculation assumes that small progenitors do not lose mass due to dynamical processes after entering the parent halo , and that they do not interact with other subhaloes .
For a \mathrm { \Lambda } CDM power spectrum we obtain a subhalo mass function \mathrm { d } n / \mathrm { d } m proportional to m ^ { - \alpha } with a model-independent \alpha \sim 2 .
Assuming the dark matter is a weakly interacting massive particle , the inferred distributions is used to test the feasibility of an indirect detection in the \gamma -rays energy band of such a population of subhaloes with a GLAST-like satellite .