Neutrino mass bounds from cosmology

Neutrinos are the among the most abundant particles in the universe. This means that they have a profound impact on many different aspects of cosmology, from the question of leptogenesis in the very early universe, over big bang nucleosynthesis, to late time structure formation. At late times (T ∼<TEW) neutrinos mainly influence cosmology because of their energy density and, even later, their mass. The absolute value of neutrino masses are very difficult to measure experimentally. On the other hand, mass differences between neutrino mass eigenstates, (m1,m2,m3), can be measured in neutrino oscillation experiments. The combination of all currently available data suggests two important mass differences in the neutrino mass hierarchy. The solar mass difference of δm12 ≃ 8×10 −5 eV and the atmospheric mass difference δm23 ≃ 2.6× 10 −3 eV [1,2,3,4]. In the simplest case where neutrino masses are hierarchical these results suggest that m1 ∼ 0, m2 ∼ δmsolar, and m3 ∼ δmatmospheric [5]. If the hierarchy is inverted one instead finds m3 ∼ 0, m2 ∼ δmatmospheric, and m1 ∼ δmatmospheric. However, it is also possible that neutrino masses are degenerate, m1 ∼ m2 ∼ m3 ≫ δmatmospheric, in which case oscillation experiments are not useful for determining the absolute mass scale [5]. Experiments which rely on kinematical effects of the neutrino mass offer the strongest probe of this overall mass scale. Tritium decay measurements have been able to put an upper limit on the electron neutrino mass of 2.3 eV (95% conf.) [6] (see also contribution by G. Drexlin to the present volume). However, cosmology at present yields a much stronger limit which is also based on the kinematics of neutrino mass. Very interestingly there is also a claim of direct detection of neutrinoless double beta decay in the Heidelberg-Moscow experiment [7], corresponding to an effective neutrino mass in the 0.1− 0.9 eV range. If this result is confirmed then it shows that neutrino masses are almost degenerate and well within reach of cosmological detection in the near future. Neutrinos are not the only possibility for stable eV-mass particles in the universe. There are numerous other candidates, such as axions and majorons, which might be present. As will be discussed later, the same cosmological mass bounds can be applied to any generic light particle which was once in thermal equilibrium. Here I focus mainly on the issue of cosmological mass bounds. Much more detailed reviews of neutrino cosmology can for instance be found in [8,9].