Higgsino-like Dark Matter From Sneutrino Late Decays

We consider Higgsino-like dark matter (DM) in the Minimal Supersymmetric Standard Model (MSSM) with additional right-handed neutrino chiral superfields, and propose a new non-thermal way of generating the right amount of relic DM via sneutrino late decays. Due to the large DM annihilation cross-section, decays must occur at lower temperatures than the freeze-out temperature $T_d\ll T_{F,\tilde{\chi}^0_1}\sim \mu/25$, implying a mostly right-handed lightest sneutrino with very small Yukawa interactions. In that context, the right amount of Higgsino-like DM relic density can be accounted for if sneutrinos are produced via thermal freeze-in in the early Universe.Comment: 10 pages, 2 figures. Final version PL

The proof of three power-exponential inequalities

In this paper we prove three power-exponential inequalities for positive real numbers. In particular, we conclude that this proofs give affirmatively answers to three, until now, open problems (conjectures~4.4, 2.1 and 2.2) posed by C{\^i}rtoaje in the following two works: "{\it J. Inequal. Pure Appl. Math.} 10, Article 21, 2009" and "{\it J. Nonlinear Sci. Appl.} 4:2:130-137, 2011". Moreover, we present a new proof of the inequality $a^{ra}+b^{rb}\ge a^{rb}+b^{ra}$ for all positive real numbers $a$ and $b$ and $r\in [0,e]$. In addition, three new conjectures are presented.Comment: 9 page