Majorons: A simultaneous solution to the large and small scale dark matter problems

Abstract

It is shown that the existence of majorons, which enable a heavy neutrino, 500 eV ≲ m νH ≲ 25 keV to decay into a light neutrino m νL ≲ 8 eV and a majoron, with lifetime 10 4 yr ≲ τ νH ≲ 10 8 yr can solve both the large and small scale dark matter problems. For a primordial “Zeldovich” spectrum of fluctuations the limits are m v H ≲ ̌ 550 eV and τ v H > 10 7 to 10 8 yr (the ranges m νH ≲ eV and τ νH ≳ 10 8 yr are allowed by the model but galaxy formation becomes problematic). The large scale dark matter problem is how to achieve the critical density as implied by inflation, the small scale problems deal with the halos of galaxies and galaxy formation and perturbation growth. The heavy neutrino could provide the solution to the small scale problem by initiating perturbation growth before decoupling. The decay products will be fast and thus not bound to the initial clumps, thus solving the large scale problem. The low mass relic neutrinos that were not decay products would remain bound in the gravitational potentials which grew from the initial perturbations. The resulting universe would be radiation dominated, which is consistent with present observations if H 0 ≲ 40 km/s/Mpc. An alternative solution can occur when m νH ≈ 10 eV: the universe can again become matter dominated in the present epoch. This solution still allows H 0 ∼ 50 km/s/Mpc. The majoron model parameters which best fit the dark matter considerations are presented.