DARK MATTER AND DIRECT SEARCHES David G. Cerdeño (2) Freeze out of massive particles (WIMPs)
Contents • Freeze-out of massive species • The collisional operator • Argument for WIMPs • Important special cases • Coannihilation • Resonant annihilation • List of Dark Matter candidates 06-04-09 MPI
Freeze-out of massive species • The collisional operator • The WIMP “miracle” 06-04-09 MPI
How is Particle Dark Matter produced? time Today t~13.6 Gyr T~3K Temperature Due to the expansion of the Universe DM Thermal equilibrium particles fall out of equilibrium and cannot annihilate any more. A Relic Density of DM is obtained which remains constant. The number density, n, of DM decreases with T. time 06-04-09 MPI
How is Particle Dark Matter produced? time Today t~13.6 Gyr T~3K Temperature Due to the expansion of the Universe DM Thermal equilibrium particles fall out of equilibrium and cannot annihilate any more. A Relic Density of DM is obtained which remains constant. How much dark matter remains depends on its interaction rate The number density, n, of DM decreases with T. A particle with stronger interactions keeps in equilibrium for longer… … and is more diluted time 06-04-09 MPI
How is Particle Dark Matter produced? time Today t~13.6 Gyr T~3K Temperature Due to the expansion of the Universe DM Thermal equilibrium particles fall out of equilibrium and cannot annihilate any more. A Relic Density of DM is obtained which remains constant. How much dark matter remains depends on its interaction rate The number density, n, of DM decreases with T. Particles with very weak interactions decouple earlier, having a larger relic density time 06-04-09 MPI
How is Particle Dark Matter produced? • The resulting WIMP relic density is naturally of order 0.1 when the annihilation cross section is of “weak scale” σ ~ 10 -9 GeV Non-relativistic when they decoupled from the thermal plasma time 06-04-09 MPI
The WIMP “miracle” 06-04-09 MPI
The WIMP “miracle” • Very different scales conjure up to lead to the electroweak scale The relic abundance can be written as In terms of very different scales CMB Temperature Hubble parameter Planck scale Where the result turns out to be 06-04-09 MPI
The WIMP “miracle” • Very different scales conjure up to lead to the electroweak scale A typical electroweak scale cross section for a non-relativistic particle WIMP f M X _ WIMP f Notice that this implies (non-relativistic particle) Imposing (Griest, Kamionkowski '90) 06-04-09 MPI
Special cases • The low-temperature expansion for the annihilation cross section is not valid in some cases: Resonant annihilation Thresholds (Gondolo, Gelmini '91) Coannihilations with other particles close in mass (Griest, Seckel '91) 06-04-09 MPI
Special cases • Resonant annihilation: WIMP f (2 m WIMP ) 2 =(m X ) 2 M X _ WIMP f σ The resonant increase in the cross section implies a sharp decrease in the relic abundance. s = (2 m WIMP ) 2 General expression for thermal average of annihilation cross section (Gondolo, Gelmini '91) 06-04-09 MPI
Special cases • Coannihilations In principle, the evolution of all coupled species should be taken into account when determining the WIMP density, evolution and decoupling. In particular, particles which carry the same quantum number that protects the decay of DM (R-parity, KK-parity, T-parity) contribute to the abundance of the lightest one. In practice, the Boltzmann suppresssion of the equilibrium density implies that the abundance of all other exotic particles is suppressed and can be ignored. − E f eq = e T EXCEPTION: if there is a heavy exotic particle with approximately the same mass as the DM. (Griest, Seckel '91) 06-04-09 MPI
Special cases • Resonant annihilation The annihilation cross section is significantly increased in the pole of the propagator. As a consequence, the relic m A density decreases rapidly. m W = 2 Thermal motion allows resonant annihilation when m A − E m W 2 f eq = e T This is not possible for m A m W 2 (Griest, Seckel '91) 06-04-09 MPI
Dark matter candidates • Conditions • A brief list of “usual suspects” 06-04-09 MPI
Conditions for Dark Matter candidates 1) Correct relic abundance Remember that the different production mechanisms rely on a given “thermal history”of our Universe. WIMPs are successful candidates if thermally produced and if there was no subsequent reheating or entropy injection. From unitarity of the S matrix we know that Which leads to an upper bound on the WIMP mass 06-04-09 MPI
However.... • Not applicable to non-thermal candidates (for which the relic abundance is calculated differently, such as decays of heavier particles) (e.g., gravitinos and axinos) • Non-standard Cosmology, e.g., The presence of scalar fields in the Early Universes may induce a period of a much higher expansion rate. WIMPs decouple earlier and have a much larger relic abundance (by several orders of magnitude). (Catena, Fornengo, Masiero, Pietroni, Rosati, '04) Changes in the cosmology also affect the calculation of relic abundance for non-thermal dark matter. E.g., quintessence-motivated kination models. (Gómez, Lola, Pallis, Rodríguez-Quintero '08) Late entropy production which dilutes the DM density See, e.g., (Giudice, Kolb, Riotto '01) E.g., decay of heavy sterile neutrinos (Abazajian,Koushiappas '06) (Asaka, Shaposnikov, Kusenko '06) 06-04-09 MPI
However.... Late (out of equilibrim) decay of semistable particles induce an injection of entropy. The only constraint to be considered is not to spoil BBN predictions T R 5 MeV There are various possibilities depending on whether T R is smaller or larger than the DM freeze out temperature and on whether the decay produces more DM particles. (Kolb, Turner Chapt.5) T R T f No change in the predicted dark matter thermal relic abundance. Chemical equilibrium is restored. 06-04-09 MPI
T R T f • Thermal production without chemical equilibrium GeV − 2 m X g x 7 3 / 2 ~ 〈 v 〉 5 X T R 100 GeV 10 Production of DM is − 16 GeV suppressed cdm 10 • Thermal production with chemical equilibrium The particle freezes out before 3 T f T f − 4 cdm X ∝ T R new the reheating with a too large relic density and is then diluted. • Non-thermal production without chemical equilibrium m X MeV 6 b X T R m The particle freezes out before ~ 2 × 10 the reheating with a too large cdm relic density and is then diluted. • Non-thermal production with chemical equilibrium T f The particle freezes out before X ~ cdm the reheating with a too large T R relic density and is then diluted. 06-04-09 MPI
Conditions for Dark Matter candidates 2) Non-relativistic at the epoch of structure formation (a.k.a. cold) Relativistic (hot) dark matter (with a large free-streaming length) damp the power spectrum of density fluctuations at large scales (for neutrinos this corresponds to the scale of superclusters) Also, hot dark matter predict a top-down hierarchy in structure formation (small structures forming by fragmentation of larger ones). Observation show that galaxies are older than superclusters. For cold dark matter only fluctuations smaller than the Earth scale are suppressed. N-body simulations also support this kind of DM for structure formation. However, N-body simulations usually predict many more satellites of galaxies than are observed... Solutions include strongly interacting DM or warm dark matter with masses around 1 keV. 06-04-09 MPI
Numerical simulations with warm dark matter show the reduction in the number of subhaloes. Structure of a DM distribution in a simulated halo comparable to the Milky Way. Left) Halo formed assuming that DM is made of cold, massive particles. Right) The same halo simulated from same initial cosmological parameters and resolution, but assuming that DM is made of warm, light particles with rest mass = 3 keV 06-04-09 MPI
Conditions for Dark Matter candidates 3) Neutral (.... or not) Charged stable (DM) particles could bind to nuclei, forming exotic isotopes that would have shown in searches for this kind of atoms. However, this need not be the case if the DM is very heavy. Charged Massive Particles (CHAMPS), could be viable with masses of 1- 1000 TeV. (de Rújula, Glashow, Sarid '90) 4) Consistency with BBN constraints Crucial in the case of particles with non-thermal production due to late decays of massive particles. E.g., the gravitino or the axino. (MORE ON THIS LATER...) 5) Stellar evolution Important to particles with very small masses that could be produced in the interior of stars and excape, leading to energy losses, modifying stellar evolution. 06-04-09 MPI
Neutrinos • Light neutrinos are “hot” dark matter, known to contribute very little but also excluded from structure formation. However: what about massive sterile neutrinos? (i.e., cold) COLD HOT HOT COLD A heavy neutrino can have the correct relic abundance! 06-04-09 MPI
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