The Dark Matter Problem matter : anything with equation of state w=0 more obvious contribution to matter: baryons (stars, planets, us!) and both Big Bang Nucleosynthesis and WMAP tell us that Ω baryons ~0.05 moreover, most baryons (not all) emit light and are visible, and visible matter (from counting stars and galaxies) provides only Ω visible 0.05 however, dynamical measurement of matter (through gravitational interactions) point to much higher values, an effect observed in very different systems and at very different distance scales WMAP implies Ω total =1, while the Hubble diagram of SN1a imply Ω dark energy ~0.7 so, what is the average density of matter in the Universe today?
Using movement to measure mass End Newtonian gravity: GM(r)=v rot 2 r
Rotation of spiral galaxies Vera Rubin in the 70 s was the first to show that observation of rotation of disks in their outer parts required a lot of invisible mass End http://burro.cwru.edu/javalab/rotcurveweb/main.html
(from http://burro.cwru.edu/javalab/rotcurveweb/main.html)
(from http://burro.cwru.edu/javalab/rotcurveweb/main.html)
Invisible mass near the Sun! (Oort, 1932)
Evidence from Galaxy Clusters at about the same time End <T>=-1/2 <V TOT >
COMA End Milky Way CfA redshift survey
clusters of galaxies are the largest structures we know we expect them to contain most of the matter of the Universe their size ranges from 1 to 10 Mpc they contain 50 to 1000 galaxies + hot X-ray emitting gas and large amounts of dark matter COMA cluster today Dark Matter in Clusters is deduced by the temperature of the X-ray emitting gas (assuming hydrostatic equilibrium) in fact, observed temperatures (kt~10 s kev) are much hotter than the ones deduced from the visible mass: moreover, they show an amount of DM about 4-5 times that of baryons this should be true also on Cosmological scales but since Ω baryons ~0.05 this implied Ω DM 0.25 <<1 before SN1a data
Gravitational lensing in Clusters
The Bullet Cluster (smoking gun of DM vs. MOND?) 1E 0657-56, 56, august 2006 DM weak lensing NB: in MOND lensing should follow baryons, i.e. the blue region should track the red one 3 components in each cluster: gas, stars (red=baryons) and lensing (blue=dark matter) stars pass through, gravitationally slowed gases interact electromagnetically, slowed further dark matter well separated in two regions near the visible galaxies see animation (MOND=Modified Gravity)
Evidence for Dark Matter Spiral galaxies rotation curves Clusters & Superclusters Weak gravitational lensing Strong gravitational lensing Galaxy velocities X rays Large scale structure Structure formation CMB anisotropy: WMAP Ω tot =1 Ω dark energy ~0.7 Ω matter ~ 0.27 Ω baryons ~0.05 Ω visible ~0.005 Ω dark matter ~ 0.22
The concordance model
Apart from being unable to drive galaxy formation (they decouple too late from photons, not enough time for gravitational instabilites to grow) baryons are too few in the Universe in order to explain the dark matter because of nucleosynthesis Observations give 0.6 < h < 0.8 Big Bang nucleosynthesis (deuterium abundance) and cosmic microwave background (WMAP) determine baryon contribution Ω B h 2 0.023, so Ω B 0.04 Ω lum (4 ± 2). 10-3 (stars, gas, dust) => baryonic dark matter has to exist (maybe as warm intergalactic gas?) But, now we know that Ω M > 0.2, so there has to exist non-baryonic dark matter Lithium underabundant? Fields & Sarkar, 2004
A lot of matter in the Universe is dark and non-baryonic P.S.:but also some baryonic DM needed
The properties of a good Dark Matter candidate: stable (protected by a conserved quantum number) no charge, no colour (weakly interacting) cold, non dissipative relic abundance compatible to observation* motivated by theory (vs. ad hoc ) subdominant candidates variety is common in Nature may be easier to detect
The first place to look for a DM candidate
The most trivial solution! We know that neutrinos have mass and that a lot of them should be around us in a neutrino background neutrinos are relativistic at decoupling (hot) so their density is easy to calculate. In fact, one simply has: i.e. the comoving density today is the same as at decoupling. The latter happens at T~MeV when: (particles in equilibrium are photons, neutrinos, electrons and positrons) so that:
while: ( ) with g=2. So today s energy density of massive light neutrinos is given by: with: and so: ( )
Combining everything together: Easy! as we will see when the particle is non relativistic at decoupling the final result will depend on the details of the decoupling process (microphysics) and is more involved, sometimes MUCH MORE
Neutrino Σm v <0.66 ev (WMAP+LSS+SN) LEP: N ν =2.994±0.012 m ν 45 GeV Ω ν h 2 10-3 DM searches exclude: 10 GeV m ν 4.7 TeV (similar constraints for sneutrinos and KK-neutrinos) does not work Ω 2 mν νh = 2 1 Ωνh < σannv> HOT 30 ev 91.5 ev Cowsik-McClelland COLD Lee-Weinberg 3 7 GeV mix with sterile component (both for neutrinos and sneutrinos)
2 early bounds on neutrino mass from cosmology (relic abundance): Cowsik-McClelland bound: m ν < few ev Lee-Weinberg limit: m ν >few GeV
Pioneering work on direct DM searches @ Homestake mine in late 80s: few GeV<M<few TeV excluded both for neutrinos ad sneutrinos* however, today the sneutrino is not completely dead (rescaling due to relic density not applied to the signal at the time, see later)
Neutrinos don t s work also because they are hot dark matter (=relativistic at decoupling, erase density perturbation through free-streaming): density fraction of light neutrinos (from Mark Tegmark home page)