General cosmological constraints on the masses of stable neutrinos and other “inos”

Abstract

The arguments favoring non-baryonic dark matter are summarized. In particular, if the cosmological density parameter Ω≳ 0.15, the universe must be dominated by non-baryonic matter. General cosmological constraints, independent of detailed galaxy formation scenarios, are presented on the masses of stable neutrinos and other “inos,” where ino represents any candidate particle for the dark matter in the universe: (i) The requirement that the total mass density not exceed Ω ≲ 4 restricts neutrinos to two mass ranges, ∑ m v ≲ 400 eV and m v ≳ 1 GeV. (ii) From age of the universe arguments, tighter constraints on the lower of the two mass ranges become ∑ m v ≲ 25 eV (∑ m ino ≲ 400 eV) or ∑ m v ≲ 100 eV (∑ m ino ≲ 2 keV) depending on age technique used. An actual determination of a neutrino mass puts an upper limit on the age of the universe, and in a neutrino-dominated universe Ω = 1 is only possible for ∑ m v ≳ 25 eV. (iii) From phase-space density arguments, a necessary (but not sufficient) condition for the clustering of neutrinos on large scales is that m v ≳ 3 eV. (iv) For the formation of large-scale structure, the maximum neutrino Jeans mass should not exceed supercluster scales and therefore m v ≳ 10 eV. Three neutrinos of equal mass can be excluded if one uses globular cluster determinations of the age in (ii) above. (v) If the formation of large-scale structure requires damping of small scales and hence a minimum value of the maximum neutrino Jeans mass, m ino ≲ 200 eV for dominant particles. In a universe with Ω ⋍ 1 and photon temperature T γ0 = 2.7 K, this also leads to the constraint that decoupling temperature if T D of the dominant ino is T D ≲ 100 MeV. (vi) Big-bang nucleosynthesis restricts the number of neutrino species to at most four, probably only three. These arguments are then synthesized to show that all of the independent constraints can only be simultaneously met in a “best-fit” model with 10 eV ≲ m v ≲ 25 eV for the most massive neutrino eigenstate. Independently of galaxy formation arguments and with only the extremely conservative age limit, it can still be said that 3 eV ≲ m v ≲ 100 eV. Note also that if constraint (v) is valid then the dominant ino acts in every way like a massive neutrino and thus if (vi) also holds, it probably is a massive neutrino. Differences in adiabatic and isothermal fluctuation models are discussed; in particular the GUTs preferred adiabatic mode is only consistent with limits on 3 K anisotropies if non-baryonic matter dominates. Problems on small-scales with galaxy correlation studies and equilibrium time scales in a neutrino-dominated universe with adiabatic fluctuations are discussed. For Ω ∼ 0.2–0.6 cold matter such as axions or GeV mass inos could be dominant matter, but in an Ω ⋍ 1 universe these as well as keV mass “inos” are not optimal for the dominant matter and the best fit is a neutrino of mass m v ⋍ 25 eV .