A device for cooling the slots in a turbomachine rotor disk, the device comprising: a rotor disk comprising: at its periphery, a plurality of substantially axial slots that are regularly distributed around the axis of rotation of the disk; and an annular flange extending upstream from an upstream radial face of the disk; a retaining annulus mounted against the upstream radial face of the disk and including an annular flange that extends upstream and that is placed around the flange of the disk, co-operating therewith to leave an annular space forming a cooling air diffusion cavity, this diffusion cavity opening out at its downstream end into the bottom of each of the disk slots, at the upstream ends thereof; and a plurality of air admission orifices regularly distributed around the axis of the rotation of the disk and opening out into the diffusion cavity at the upstream end thereof; the outer face of the flange of the disk, and/or the inner face of the flange of the retaining annulus presenting, at its downstream end and at the level of each slot of the disk that is situated radially in register with an air admission orifice, a projection projecting into the air diffusion cavity, each projection presenting a maximum height facing the slots of the disk that are situated radially in register with the corresponding air admission orifice such that the flow section for air thereat is at a minimum, and presenting minimum heights halfway between the corresponding air admission orifice and the two orifices that are directly adjacent thereto, such that the flow sections for air thereat are at a maximum. a rotor disk comprising: at its periphery, a plurality of substantially axial slots that are regularly distributed around the axis of rotation of the disk; and an annular flange extending upstream from an upstream radial face of the disk; at its periphery, a plurality of substantially axial slots that are regularly distributed around the axis of rotation of the disk; and an annular flange extending upstream from an upstream radial face of the disk; a retaining annulus mounted against the upstream radial face of the disk and including an annular flange that extends upstream and that is placed around the flange of the disk, co-operating therewith to leave an annular space forming a cooling air diffusion cavity, this diffusion cavity opening out at its downstream end into the bottom of each of the disk slots, at the upstream ends thereof; and a plurality of air admission orifices regularly distributed around the axis of the rotation of the disk and opening out into the diffusion cavity at the upstream end thereof; the outer face of the flange of the disk, and/or the inner face of the flange of the retaining annulus presenting, at its downstream end and at the level of each slot of the disk that is situated radially in register with an air admission orifice, a projection projecting into the air diffusion cavity, each projection presenting a maximum height facing the slots of the disk that are situated radially in register with the corresponding air admission orifice such that the flow section for air thereat is at a minimum, and presenting minimum heights halfway between the corresponding air admission orifice and the two orifices that are directly adjacent thereto, such that the flow sections for air thereat are at a maximum.