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Keq . The value of the small-scale suppression factor is plotted in Fig. 13 as a function of f and of the number N of degenerate massive neutrinos, still for ﬁxed ( m , ). The numerical result J. Lesgourgues, S. 2 0 10-4 10-3 10-2 1 10-1 k (h/Mpc) Fig. 13. 03, . . 10. neutrinos. 7 × 10−3 h Mpc−1 as shown on the top of the ﬁgure. 5 × 10−2 h Mpc−1 . 1 102 1000 0 2 200 400 600 800 1000 l 1200 1400 10-3 10-2 10-1 k (h/Mpc) Fig. 14. 6, a more realistic CDM model with three massless neutrinos (f 0), and ﬁnally a MDM model with three massive degenerate neutrinos , As , n, ) have been kept ﬁxed.
Lesgourgues, S. Pastor / Physics Reports 429 (2006) 307 – 379 Looking for solutions in p± = −1 ± √ cdm ∝ 2p , we ﬁnd two roots 1 + 24(1 − f ) 4 (131) and we conclude that the growing solution for the CDM density contrast reads cdm ∝ a p+ a 1−(3/5)f , (132) where in the last step we assumed f >1. As expected, the growth of cdm is reduced due to the fact that one of the component in the Universe contributes to the homogeneous expansion rate but not to the gravitational clustering. The Poisson equation gives −k 2 ∝ a p+ −1 a −(3/5)f , (133) showing that for the same reason the gravitational potential slowly decays during matter domination.
6. In all models, the values of ( b , m , , As , n, ) have been kept ﬁxed, with the increase in being compensated by a decrease in cdm . There is a clear difference between the neutrinoless and massless neutrino cases, caused by a large 346 J. Lesgourgues, S. Pastor / Physics Reports 429 (2006) 307 – 379 change in the time of equality and by the role of the neutrino energy–momentum ﬂuctuations in the perturbed Einstein equation . e. on the difference between the solid (red) and thick dashed (green) curves in Fig.
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