The idea of such a coupling has been addressed and developed by several authors within MaVaNs theories first [356, 714, 135, 12, 952, 280, 874, 856, 139, 178, 177] and more recently within growing neutrino cosmologies [36, 957, 668, 963, 962, 727, 179]. It has been shown that neutrinos can play a crucial role in cosmology, setting naturally the desired scale for dark energy. Interestingly, a coupling between neutrinos and dark energy may help solving the ‘why now’ problem, explaining why dark energy dominates only in recent epochs. The coupling follows the description illustrated in Section 1.4.4 for a general interacting dark-energy cosmology, where now .
Typically, in growing neutrino cosmologies, the function is such that the neutrino mass grows with time from low, nearly massless values (when neutrinos are non-relativistic) up to present masses in a range in agreement with current observations (see the previous section of this review for latest bounds on neutrino masses). The key feature of growing neutrino models is that the amount of dark energy today is triggered by a cosmological event, corresponding to the transition from relativistic to non-relativistic neutrinos at redshift . As long as neutrinos are relativistic, the coupling plays no role on the dynamics of the scalar field, which follows attractor solutions of the type described in Section 1.4.4. From there on, the evolution of dark energy resembles that of a cosmological constant, plus small oscillations of the coupled dark energy-neutrino fluid. As a consequence, when a coupling between dark energy and neutrinos is active, the amount of dark energy and its equation of state today are strictly connected to the present value of the neutrino mass.
The interaction between neutrinos and dark energy is a nice and concrete example of the significant imprint that dynamical coupled dark energy can leave on observables and in particular on structure formation and on the cosmic microwave background. This is due to the fact that the coupling, playing a role only after neutrinos become non-relativistic, can reach relatively high values as compared to gravitational attraction. Typical values of are order or even more such that even the small fraction of cosmic energy density in neutrinos can have a substantial influence on the time evolution of the quintessence field. During this time the fifth force can be of order times stronger than gravity. The neutrino contribution to the gravitational potential influences indirectly also dark matter and structure formation, as well as CMB, via the Integrated Sachs–Wolfe effect and the nonlinear Rees–Sciama effect, which is non-negligible at the scales where neutrinos form stable lumps. Furthermore, backreaction effects can substantially modify the growth of large scale neutrino lumps, with effects which are much larger than in the dark matter case. The presence of a fifth force due to an interaction between neutrinos and dark energy can lead to remarkably peculiar differences with respect to a cosmological constant scenario.
Here, we just recall some of the typical features that can arise when such an interaction is active:
Investigation of structure formation at very large scales (order ) as well as cross correlation with CMB are crucial in order to disentangle coupled neutrino-quintessence cosmologies from a cosmological constant scenario. Detection of a population of very large-scale structures could pose serious difficulties to the standard framework and open the way to the existence of a new cosmological interaction stronger than gravity.
Living Rev. Relativity 16, (2013), 6
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