A method for manufacturing polyethylene or an ethylene copolymer, including a step of free radical polymerization or copolymerization of the ethylene at an initiation temperature varying from 150° C. to 200° C., at a pressure varying from 500 to 3000 bar, in the presence of a peroxidic polymerization initiator selected from among the peroxide compounds of formula (I) in which R1 and R8 are, separately, a C2-C6 alkyl group; R2, R3, R6 and R7 are, separately, a C1-C5 alkyl group; and R4 and R5 are, separately, a C1-C6 alkyl group.