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Effects of neutrino mass and asymmetry on cosmological structure formation

Light but massive cosmological neutrinos do not cluster significantly on small scales, due to their high thermal velocities. With finite masses, cosmological neutrinos become part of the total matter field and contribute to its smoothing. Structure formation in the presence of massive neutrinos is therefore impeded compared to that in the standard ΛCDM cosmology with massless neutrinos. Neutrinos' masses also distort the anisotropy power spectrum of cosmic microwave background (CMB). Furthermore, a finite chemical potential μ for cosmological neutrinos, still allowed by current data, would have a non-negligible impact on CMB and structure formation. We consistently evaluate effects of neutrino masses and chemical potentials on the matter power spectrum by use of a neutrino-involved N-body simulation, with cosmological parameters obtained from a Markov-Chain Monte-Carlo (MCMC) refitting of CMB data. Our results show that while a finite averaged neutrino mass mν tends to suppress the matter power spectrum in a range of wave numbers, the neutrino degeneracy parameters ξi ≡ μi /T (i= 1, 2, 3) enhance the latter, leading to a large parameter degeneracy between mν and ξi. We provide an empirical formula for the effects on the matter power spectrum in a selected range of wave numbers induced by mν and η ≡ √∑i ξ2i. Observing a strong correlation between mν and η, we propose a single redshift-independent parameter mν − 4/3 η2 to characterize the neutrino effects on the matter power spectrum.