We present here a realistic model to produce a very large lepton asymmetry
L similar or equal to 10(-2)-1, without producing a large baryon asymmetry.
The model is based on the Affleck and Dine scenario, in which the field ac
quiring a large vacuum expectation value during inflation is an s-neutrino
right. We require L to be large enough for the electroweak symmetry to be s
pontaneously broken at all temperatures after inflation, with the consequen
t suppression of sphaleron transitions. (C) 1999 Published by Elsevier Scie
nce B.V.