Relic neutrinos and mixed dark matter

The active neutrinos decoupled just prior to big bang nucleosynthesis, when the age of the universe was around 1s and the temperature around 1 MeV. Their momentum distribution subsequently redshifted to an effective temperature $T_\nu \sim 1.9$ K, and they have an average density of around 300$/{\rm cm}^3$. The direct detection of such low-energy neutrinos remains an ultimate challenge.

Massive neutrinos in the eV range will contribute a significant hot dark matter (HDM) component to the total matter of the universe. Constraints on the total energy density imply

$$\sum m_{\nu_i} \mathrel{\mathpalette\lower2.pt\vbox{\baseline... ...=0pt ;\hfil ...$$ (17)

where the sum extends over the light, stable, active neutrinos, and also includes light sterile neutrinos for some ranges of masses and mixings. However, pure HDM models have long been excluded by observations of structure, since neutrinos free-stream and produce large structures first, and there has not been enough time for the observed smaller structures to form. Until recently, mixed dark matter (MDM) models were very popular. In these, neutrinos with

$$\sum m_{\nu_i} \mathrel{\mathpalette\lower2.pt\vbox{\baseline... ...pt ;\hfil ...$$ (18)

contribute a hot component and account for large scales such as superclusters, while a larger component of cold dark matter (CDM) explains structure on smaller scales. These MDM models were a primary motivation for the degenerate 3 neutrino models and an attractive aspect of 4 $\nu$ models. Most assumed $\Omega_{\rm matter} = \Omega_\nu + \Omega_{\rm CDM} = 1$, as expected in inflation models.

Recently things have changed dramatically, because:

• Most determinations now yield $\Omega_{\rm matter} \sim 0.3$.
• Studies using Type IA supernovae as standard candles suggest an accelerating universe, with a cosmological constant (or other form of dark energy, such as quintessence), with $\Omega_\Lambda \sim 0.7$.
• Consistent and independent information comes from recent observations of the location of the first Doppler peak in the cosmic microwave background radiation (CMB) asymmetry spectrum, which implies $\Omega_{\rm matter} + \Omega_\Lambda \sim 1$.

There is therefore emerging a fairly compelling picture involving a low $\Omega_{\rm matter}$ and larger $\Omega_\Lambda$. This is consistent with the expectations of inflation ( $\Omega_{\rm matter} + \Omega_\Lambda = 1$), but the evidence is purely observational. In this scenario, there is no need for a significant component of HDM, although it is not excluded.

Nevertheless, the observation of neutrino mass implies a small contribution to $\Omega_{\rm matter}$. In particular, $m_3 \sim (\Delta m^2_{\rm atm})^{1/2}$ (hierarchical neutrinos) implies $\Omega_\nu \sim 0.001-0.003$, while in the degenerate schemes $\Omega_\nu$ could be as large as $\sim 0.1$. Masses less than $m_\nu \sim 1$ eV are not important for the observed structure, but may be noticeable in the CMB spectrum for $m_\nu > 0.1$ eV.