Nonlinear matter spectra in growing neutrino quintessence

We investigate the nonlinear power spectra of density perturbations and acoustic oscillations in growing neutrino quintessence. In this scenario, the neutrino mass has a strong dependence on the quintessence field. The induced coupling stops the evolution of the field when the neutrinos become nonrelativistic, and triggers the transition to the accelerating phase of the cosmological expansion. For the calculation of the nonlinear spectra we employ the time renormalization group, which resums subsets of diagrams of arbitrarily high order in cosmological perturbation theory. At redshifts around five, the neutrino fluctuations are still linear and acoustic oscillations are present in the neutrino power spectrum, induced by the acoustic oscillations in the baryonic and dark-matter sectors. The neutrino perturbations become nonlinear at redshifts around three. The mode coupling generated by the nonlinearities erases the oscillations in the neutrino spectrum at some redshift above two. There is a potential danger that at later times the influence of the gravitational potentials induced by the neutrino inhomogeneities could erase the oscillations from the baryonic and dark-matter spectra, making the scenario incompatible with observations. For the scenario to be viable, the neutrino-induced gravitational potentials in the range of baryon acoustic oscillations should not grow to average values much larger than 10^-4. The magnitude of the expected potentials is still not known reliably, as the process of structure formation is poorly understood in growing neutrino quintessence. The time renormalization group cannot describe the effects of nonlinear clustering. Alternative methods, such as hydrodynamic simulations, must be empoloyed for the calculation of the spectra at low redshifts.