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For instance, could massive neutrinos constitute the dark matter halos of galaxies? For neutrinos to be gravitationally bound to galaxies it is necessary that their velocity be less that the escape velocity ❀❂❁❄❃❆❅ , and thus their maximum momentum is ❇❉❈ ➽❋❊❍● ✹ ✻ ❀❂❁❄❃❆❅ . How many neutrinos can be packed in the halo of a galaxy? e. ❑ ❑ ❈ ➽▲❊ ● ● ❈ ➽▲❊ ✹✼✻ ● ❇❏▼❈ ➽▲❊❖◆❏€❘◗❚❙ . Therefore, the maximum local density in dark matter neutrinos is ❯ ❈ ➽▲❊ Ø ✹✼❱✻ ❀ ❁❄ ➽✜➾❳❲ ● ✾❏❨ € GeV cm ❩ ▼ . For a typical ▼ ❃❆❅ ◆❏€❘◗ ❙ , which must be greater than the typical halo density ❯ 142 spiral galaxy, this constraint, known as the Tremaine-Gunn limit, gives ✹❬✻❪❭✺✲❫✾ eV, see Ref.

However, if most of the energy of the universe resists gravitational collapse, it is impossible for structure in the universe to grow. This dilemma can be resolved if the hypothetical dark energy was negligible in the past and only recently became the dominant component. According to general relativity, this requires that the dark energy have ❰ ❣❆à negative pressure, since the ratio of dark energy to matter density goes like ß ♥ ❩ ▼ ➀▲á . This argument [67] would rule out almost all of the usual suspects, such as cold dark matter, neutrinos, radiation, and kinetic energy, since they all have zero or positive pressure.

6 Weak gravitational lensing Since the mid 1980s, deep surveys with powerful telescopes have observed huge arc-like features in galaxy clusters, see for instance Fig. 19. The spectroscopic analysis showed that the cluster and the giant arcs were at very different redshifts. The usual interpretation is that the arc is the image of a distant background galaxy which is in the same line of sight as the cluster so that it appears distorted and magnified by the gravitational lens effect: the giant arcs are essentially partial Einstein rings.

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