  Cosmology and particle physics come across a tight connection in the attempt
to reproduce and understand quantitatively the results of experimental
findings. Indeed, the quark gluon plasma (QGP) found at colliders and the
baryon asymmetry provided by the WMAP collaboration are examples where to apply
field theoretical techniques in issues relevant for Cosmology. In the simplest
leptogenesis framework, heavy Majorana neutrinos are at the origin of the
baryon asymmetry. The non-relativistic regime appears to be relevant during the
lepton asymmetry generation where the interactions among particles occur in a
thermal medium. We discuss the development of an effective field theory (EFT)
for non-relativistic Majorana particles to address calculations at finite
temperature. We show an application of such a method to the case of a heavy
Majorana neutrino decaying in a hot and dense plasma of Standard Model (SM)
particles. These techniques are analogous to those widely used for the
investigation of heavy-ion collisions at colliders by exploiting hard probes.
Finally we sketch some commonalities between Majorana neutrinos and bound state
of heavy quarks in medium.
