Is a massive tau neutrino just what cold dark matter needs?

The cold dark matter (CDM) scenario for structure formation in the Universe is very attractive and has many successes; however, when its spectrum of density perturbations is normalized to the COBE anisotropy measurement the level of inhomogeneity predicted on small scales is too large. This can be remedied by a tau neutrino of mass 1MeV − 10MeV and lifetime 0.1 sec − 100 sec whose decay products include electron neutrinos because it allows the total energy density in relativistic particles to be doubled without interfering with nucleosynthesis. The anisotropies predicted on the degree scale for “τCDM” are larger than standard CDM. Experiments at e colliders may be able to probe such a mass range. The cold dark matter (CDM) scenario for the formation of structure in the Universe (i.e., galaxies, clusters of galaxies, superclusters, and so on) is both well motivated and very successful [1]. The CDM model begins with a flat Universe with most of its mass in slowly moving (“cold”) particles such as axions or neutralinos and a baryon fraction compatible with primordial nucleosynthesis (∼ 5%). The density perturbations that seed structure formation are the nearly scale-invariant perturbations that arise from quantum fluctuations during inflation [2]. Standard CDM has one free parameter: the normalization of the spectrum. The recent COBE detection [3] of anisotropy in the temperature of the cosmic background radiation (CBR) now provides the normalization by fixing the amplitude of perturbations on very large scales (λ ∼ 10h Mpc). But, when the spectrum is so normalized, the level of inhomogeneity predicted on small scales (λ < ∼ 10h Mpc) is too large by a factor of two (the Hubble constant H0 = 100h km s −1 Mpc). Just how serious this problem is remains to be seen. A number of “fixes” have been proposed. They involve changing either the initial power spectrum or the energy content of the Universe. The simplest way of changing the power spectrum is “tilt” [4] (i.e., deviation from scale invariance) which reduces the power on small scales; in fact, several plausible models of inflation predict a tilted spectrum. However, this solution seems to lead to insufficient power on intermediate scales (λ ∼ 30h Mpc−100h−1 Mpc). Changing the energy content changes the transfer function, which relates the primeval power spectrum to that today [5]. For example, mixed dark matter (MDM) [6] (65% CDM + 30% hot dark matter in the form of 7 eV neutrinos + 5% baryons) or ΛCDM [7] (80% vacuum energy + 15% CDM + 5% baryons) both reduce the power on small scales. The fix advocated here involves increasing the energy density in relativistic particles, which also modifies the transfer function. In the standard scenario the radiation content at late times (t ≫ 1 sec) consists of photons and three massless neutrino species with slightly lower temperature Tν = (4/11) Tγ , accounting for a total radiation energy density ρrad = g∗π Tγ /30. Here g∗ = 2 + 2(7/8)(4/11) Nν counts the number of effectively massless degrees of freedom and is equal to 3.36 for Nν = 3. In our “τCDM” model g∗ will be about a factor of two larger. To see why this helps, consider the scale λEQ, which crossed the horizon at the time the energy density in matter was equal to that in radiation. On scales much greater than λEQ the transfer function is unity because pertur-