A solution to the baryon and dark-matter coincidence puzzle in a $\tilde{N}$ dominated early universe

If a bosonic partner of a right-handed neutrino dominates the early universe sufficiently before its decay, important ingredients in the present universe are related to physics of the right-handed neutrino sector. In particular, we find that the ratio of the baryon to the dark-matter densities is given only by low-energy parameters such as a neutrino mass and a gravitino mass if the reheating temperature of inflation is much higher than $10^{12}$ GeV. Here, the gravitino is assumed to be the lightest supersymmetric particle and the dominant component of the dark matter. The observed ratio, $\Omega_{B}/\Omega_{DM} \simeq 0.21\pm 0.04$, suggests the mass of the gravitino to be in the range of $\cal O$(10) MeV provided the CP violating phase is of the order 1.