The KeV Majoron as Dark Matter Particle

We consider a very weakly interacting KeV majoron as dark matter particle (DMP), which provides both the critical density $\rho_{cr} = 1.88 \times 10^{-29} h^{2}$ $g/cm^{3}$ and the galactic scale $M_{gal}$ $\sim m^{3}_{Pl}/m^{2}_{J} \sim 10^{12} M_{\odot} (m_{J}/1 KeV)^{-2}$ for galaxy formation. The majoron couples to leptons only through some new "directly interacting particles", called DIPS, and this provides the required smallness of the coupling constants. If the masses of these DIPS are greater than the scale $V_s$ characterizing the spontaneous violation of the global lepton symmetry they are absent at the corresponding phase transition ($T \sim V_s$) and the majorons are produced during the phase transition, never being in thermal equilibrium during the history of the universe. In the alternative case $m_{DIP} < V_{s}$ the majorons can be for a short period in thermal equilibrium. This scenario is not forbidden by nucleosynthesis and gives a reasonable growth factor for the density fluctuations compatible with COBE. A possible signature is an X-ray line at $E_\gamma = \frac{m_J}{2}$, produced by the decay $J \to \gamma + \gamma$. A model is described which realizes the possibility of the KeV majoron as DMP and may also lead to observable rates for decays such as $\mu \ra e \gamma$ and $\mu \ra 3e$.