Neutrino lumps and the cosmic microwave background

The interaction between the cosmon and neutrinos may solve the why now problem for dark energy cosmologies. Within growing neutrino quintessence it leads to the formation of nonlinear neutrino lumps. For a test of such models by the integrated Sachs-Wolfe effect for the cosmic microwave background (CMB) we estimate the size and time evolution of the gravitational potential induced by these lumps. A population of lumps with size of 100 Mpc or more could lead to observable effects on the CMB anisotropies for low angular momenta. The linear approximation is found to be invalid for the relevant length scales. Quantitative estimates depend strongly on the details of the transition between the linear and nonlinear regimes. In particular, important backreaction effects arise from the nonlinearities of the cosmon interactions. At the present stage the uncertainties of the estimate make it difficult to constrain the parameter space of growing neutrino models. We explicitly discuss scenarios and models that are compatible with the CMB observations.