Non-Baryonic Dark Matter in Cosmology

Non-Baryonic Dark Matter in Cosmology
Antonino Del Popolo Department of Physics and Astronomy University of Catania, Italy IX Mexican School on Gravitation and Mathematical Physics "Cosmology for the XXI Century: Inflation, Dark Matter and Dark Energy" Puerto Vallarta, Jalisco, Mexico, December 3-7, 2012 1 1

LECTURE 3 The nature of dark Matter
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So what is DM? Baryons: too few to explain all the dark matter
Big Bang nucleosynthesis (deuterium abundance) and cosmic microwave background (WMAP) determine baryon contribution ΩB=0.0456±0.0016, ΩM =0.227±0.014 (WMAP+BAO+Ho) Baryons: too few to explain all the dark matter because of nucleosynthesis. Moreover unable to drive galaxy formation (decouple too late from photons, not enough time for gravitational instabilites to grow) Ωlum  (stars, gas, dust) (Persic & Salucci (1992); 0.02 (Fukugita, Hogan & Peebles (1998) (including plasmas in groups and clusters) =>ΩB>Ωlum baryonic dark matter has to exist We already discussed the MACHO, EROS1, etc limits Rees (1977) : DM could be of a “more exotic character”-> e.g., small rest mass neutrinos So what is DM? Aλ =1-10 scale dependent growth factor Tm<0.14 eV T0 =2.35x10-4 (CMB tempertaure now) Basic facts Fields & Sarkar, 2004

The properties of a good Dark Matter candidate:
Non-baryonic (two reasons: BBN, structure formation) Stable (protected by a conserved quantum number) No charge, No colour (weakly interacting) -if DM non electrically neutral could scatter light -> non DARK cold, non dissipative (structure formation) relic abundance compatible to observation

First place to look for candidates: SM
Desired DM properties Gravitationally interacting Not hot Not baryonic Not short-lived Unambiguous evidence for new particles 5

DARK MATTER candidates
gauge hierarchy problem especially motivates Terascale masses DM Candidates AXION MSSM LSP UED LKP Hierarchy problem (bino, wino, two neutral higgsinos)->Neutralinos; 3 sneutrinos; gravitino Momentum Conserv. (KK-parity): KK photon excitation, Z, Neutrinos, Higgs bosons or graviton Strong CP-problem (PQ Symmetry) “Ad-Hoc” DM Candidates Super-heavy DM MeV DM keV sterile n’s Neutrino masses and mixing Warm Dark Matter 511 keV line Ultra-GZK Cosmic Rays CR with Energy> Greisen- Zatsepin-Kuzmin cut-off Sterile neutrinos[nb 1] are a hypothetical type of neutrino that do not interact via any of the fundamental interactions of the Standard Model except gravity. It is a light right-handed neutrino or left-handed anti-neutrino which may be added to the Standard Model and may take part in phenomena, such as neutrino mixing. The search for these particles is an active area of particle physics. FDM: (Fuzzy): ultra-light scalar particles whose Compton wavelength (effective size) is the size of galaxy core. DM cannot be concentrated on smaller scales, resulting is softer cores and reduce small-scale structure.

Neutralinos favorite because they have at least three virtues…
1) Required by supersymmetry, and so motivated by electroweak symmetry breaking force unification 2) Stable: the neutralino is typically the LSP, and so stable (in R-parity conserving supergravity) 3) Correct relic density, detection promising

DM FORMATION,FREEZE OUT: QUALITATIVE
Assume a new heavy particle X is initially in thermal equilibrium interacting with the SM particles q: (or if X is its own antiparticle ) (1) (2) (3) Increasing annihilation strength ↓ Feng, ARAA (2010) 1) In the very early universe when TUniv>>mx the processes of creation and annihilation were equally efficient -> X present in large quantities 2) Universe cools: T<mx the process of creation exponentially suppressed, annihilation process continues. In thermal equilibrium XX  qq If particles remain in thermal eq. Indefinitely -> number density suppressed → ← / gx Degree of freedom of X 3) Self-annihilation contained by the competing Hubble expansion:Universe expands: XX  qq → ← / Expansion-> dilution of WIMPs-> increasingly dominates over the annihilation Rate-> number density of X sufficiently small that they cease to interact with each other, and thus survive to the present day. Zeldovich et al. (1960s)

FREEZE OUT: MORE QUANTITATIVE
The Boltzmann equation: L [f]=C [f] Dilution from expansion cc → f f ‾ f f → cc ‾ Thermally averaged anihilation cross section T>>mx (Г>H) n ≈ neq until interaction rate drops below expansion rate T<<mx (Г<H) : T<<mx (Г<H) equilibrium density small: 3Hnx and deplete number density For sufficiently small nx annihilation insignificant with respect dilution due to expansion -> Freez-out Might expect freeze out at T ~ m, but the universe expands slowly! First guess: m/T ~ ln (MPl/mW) ~ 40

In case of presence of other species
Resulting (relic) density today: ~ xFo / <v> Non-relativistic expansion for heavy states =65, 1 GeV =120, 1 TeV in SM In case of presence of other species i,j=1 -> WIMP For a particle with a GeV-TeV mass, to obtain a thermal abundance equal to the observed dark matter density, we need an annihilation cross section of <v> ~ pb Generic weak interaction yields: <v> ~ 2 (100 GeV)-2 ~ pb Numerical coincidence? Or an indication that dark matter originates from EW physics? WIMP MIRACLE

Neutrinos Light neutrinos: mν≤ 30 eV HDM (relativistic at decoupling, erase density perturbation through free-streaming. MJeans =1012 Mʘ ->Top-Down In SM absence right handed neutrino state-> no neutrino mass (*) BUT adding a right hand state -> Dirac mass for the neutrino (Dirac mass term Adding the term to > Majorana mass Particles decouple when An example: neutrino decoupling. By dimensional analysis the decoupling T-> Neutrinos more massive than 1 MeV annihilate before decoupling, and while in equilibrium their number is suppressed. Lighter neutrinos <1 MeV do not experience suppression due to annihilation-> calculation of number density of neutrinos different for m<1 MeV, m>1 MeV (*) Unless adding non-renormalizable lepton number violating interactions, HHLL

mv≥ 1 MeV, Boltzman Equation ->
HST key project data SIa, BBN From the condition t>12Gyr-> (*) and > Majorana. For Dirac depends from right state interaction ~ Combining with (*) gives: Dirac or Majorana LEP-> excludes 45 GeV< <100 TeV with In 10 GeV < < 4.7 TeV Dirac excluded by Lab constraints and for >45 GeV Majorana has >cosmologically uninteresting Finally: Neutino mixing, LEP limit on neutrino species -> > light weakly interacting neutrinos

Excluded by LEP SM Beyond SM Excluded by direct DM experiments

Axions The theta-term of QCD poses the so-called strong CP-problem
dn-QCD ~10-15 e cm dn-data ~10-26 e cm Experiments: no CP violation in the QCD sector but natural terms in QCD Lagrangian able to break CP simm. The theta-term of QCD poses the so-called strong CP-problem Promoting Q to a dynamical variable, and postulating a spontaneously broken (at a scale fA) global U(1)PQ symmetry, the theta-term is effectively driven to zero The associated pseudo-NG boson, the axion, features Ωa/ Ωc = (fa/1012GeV)7/6 Stellar cooling (globular clusters) SN 1987A data (neutron star cooling) Microwave cavity Ex. (resonant conversion of A’s in monoch. M.w. radiation) Optical & Radio Tlscp. (monoch. emission from A decay in clusters) Photon Regeneration (Parallel E -laser- and B fields; after optical barrier the E|| component can be regenerated) fA ≤1012 cosmological density limit fA ≥1010 emission from red giants ………. QCD, possess a non-trivial vacuum structure permitting CP violation-> large electric dipole moment for the neutron much larger than exerimental limits Peccei-Quinn solution: the effective strong CP violating term, Θ, is promoted to a field (particle) by adding a new global symmetry (called a Peccei–Quinn symmetry) to the standard model that becomes spontaneously broken -> creation of a new particle (Nambu-Goldstone boson) this particle fills the role of Θ—naturally relaxing the CP violation parameter to zero Anomalous Signal reported by the PVLAS collaboration was interpreted as a possible hint(*) (Zavattini et al., Phys.Rev.Lett.96:110406,2006; (**) Rabaden et al., Phys.Rev.Lett.96:110407,2006); Rizzo 2007 problem in the experiment

Have Axions been detected?!
Other Axion detection technique: Polarization Experiments The E|| component is depleted by the production of real Axions, resulting in a rotation of the polarization vector and vacuum birifrangence Polarized Light propagating through a transverse magnetic field is affected by Axions C. Rizzo 2007 showed the experiment result was wrong Higher order QED effects (“light-by-light”) also contribute and constitute a Background An Anomalous Signal reported by the PVLAS collaboration was interpreted as a possible hint(*) The claimed signal can be readily tested with a Regeneration setup(**) The proposed experiment will actually be carried out soon at DESY (*) Zavattini et al., Phys.Rev.Lett.96:110406,2006; (**) Rabaden et al., Phys.Rev.Lett.96:110407,2006

SUSY DM Tracing back the early motivations for low energy Supersymmetry... Item 1. (~1979) FINE-TUNING PROBLEM GAUGE-COUPLING UNIFICATION Item 2. (~1981) DARK MATTER CANDIDATE Item 3. (~1982) Dm2H~ L2UV Lightest Neutralino is a suitable WIMP DM candidate SM SUSY Dm2H~ log(LUV / m) + *See: L.Maiani (1979); S.Dimopoulos,S.Raby,F.Wilczek (1981); H.Pagels, J.R.Primack (1982)

Hierarchy problem, Supersimmetry
SM predict very precisely the results of experiments This high precision requires calculations of higher orders (HO) Example MW : first order HO (%) Higgs mass, as MW, gets correction from HO Dependence on cut-off Λ(energy/distance up to which the SM is valid; we know that at distance at which gravity gets important, Planck scale, SM non valid) All particles get radiative correction to their mass but while for fermions mass increase logarithmically, for scalars quadratically with corrections at 1-loop The radiative corrections to the Higgs mass (which is expected to be of the order of the electroweak scale MW ∼ 100 GeV) will destroy the stability of the electroweak scale if is higher than ∼ TeV, e.g. if Λ is near the Planck mass -> “HIERARCHY PROBLEM OF THE SM” hierarchy between electroweak scale (~100 GeV) and the Planck scale SOLUTION: introduce a “supersymmetry” Since the contribution of fermion loops to δm2s have opposite sign to the corresponding bosonic loops, at the 1-loop level provided quadratic divergenge to Higg mass cancelled δM2Hα ln Λ Supersymmetry is an extension that creates 'superpartners' for all Standard Model particles: squarks, gluinos, charginos, neutralinos, and sleptons . The Minimal Supersymmetric Standard Model (MSSM): minimal extension to the Standard Model containing the fewest number of new particles and interactions necessary to make a consistent theory

R-PARITY, PROTON DECAY AND STABLE LSPS
Abesence interactions responsible responsible for extremely rapid proton decay-> assume the conservation of R-parity: R = (-1) 3B+L+2S (B, L and S= baryon number, lepton number and spin) R = +1 for all SM particles; R = -1 for all superpartners R-parity conservation requires superpartners to be created or destroyed in pairs, leading at least one supersymmetric particle (the lightest supersymmetric particle (LSP)) to be stable, even over cosmological timescales. Minimal model (MSSM) contains the fewest number of new particles and interactions necessary to make a consistent theory (in any case a lot) Identity of the Lightest Stable Particle (LSP) depends on the hierarchy of the supersymmetric spectrum -> depends from the details of how supersymmetry is broken. The only electrically neutral and colorless superparnters in (MSSM) are the four neutralinos (superpartners of the neutral gauge and Higgs bosons), three sneutrinos, and the gravitino. The lightest neutralino, in particular, is a very attractive and throughly studied candidate for dark matter (*) Minimal Supersymmetric Standard Model (MSSM) is the minimal extension to the Standard Model that realizes N=1 supersymmetry.The MSSM was originally proposed in 1981 to stabilize the weak scale, solving the hierarchy problem NEUTRALINO SNEUTRINO GRAVITINO AXINO Mass eigenstate of the SUSY partners of the U(1)Y and SU(2) gauge bosons and of the two neutral Higgses The Neutralino properties depend critically upon its composition = N11B 0 + N12W 0 + N13Hd0 + N14Hu0 BINO WINO HIGGSINO Ruled out by Direct Detection within the MSSM; viable if mixed with sterile sneutrino Super-WIMPs (not directly detectable) Wide mass range (down to the keV, up to the TeV) Require the extension of the MSSM to include gravitons/axions MSSM ext-MSSM

PARAMETERS AND SIMPLIFIED MODELS
MSSM, despite its minimality in particles and interactions contains over a hundred (124) new parameters related to supersymmetry breaking. Often assumed that at some unification scale, all of the gaugino masses receive a common mass, m1/2. Gaugino massses at EW scale obtained running a set of RGEs. Similarly, one often assumes that all scalars receive a common scalar mass, m0, at the GUT scale. Higgs mixing mass parameter, μ. In MSSM two Higgs doublets -> two vacuum expectation values. One combination of these is related to the Z mass, and therefore is not a free parameter, while the other combination, the ratio of the two vevs, tan β, is free. If the supersymmetry breaking Higgs soft masses also unified at the GUT scale (and take the common value m0) -> μ and the physical Higgs masses at the weak scale are determined by electroweak vacuum conditions (μ is determined up to a sign). This scenario is often referred to as the constrained MSSM or CMSSM. CSSM parameters: m1/2 gaugino mass •m0 scalar masses •A0: soft breaking trilinear coupling constant (higgs-sfermionsfermion) •tanβ = v1/v2 ratio of the VEVs of the two Higgs •sign(μ) sign of the Higgsino mass parameter (bilinear higgsino coupling constant)

Particle physics alone  neutral, stable, cold dark matter
Running of the mass parameters in the CMSSM. Here: m1/2 = 250 GeV, m0 = 100 GeV, tan β =3, A0 = 0, and μ < 0. Knowing few input parameters, all of the masses of the supersymmetric particles can be determined. Characteristic features: colored sparticles are typically the heaviest in the spectrum. This is due to the large positive correction to the masses due to α3 in the RGE’s. B (the partner of the U(1)Y) gauge boson), is typically the lightest sparticle. One of the Higgs mass, goes negative triggering electroweak symmetry breaking. (The negative sign in the figure refers to the sign of the mass, even though it is the mass of the sparticles which are depicted.) WHAT’S THE LSP? ~ High-scale  weak scale through RGEs. Gauge couplings increase masses; Yukawa couplings decrease masses “typical” LSPs: c , t̃R Olive (2003) RG evolution of the mass parameters Particle physics alone  neutral, stable, cold dark matter

NEUTRALINOS ~ Four neutralinos, each of which is a linear combination of the R =-1 neutral fermions: the wino W3 (partner of the 3rd component of the SU(2)L gauge boson); the bino, B superpartner of the U(1)Y gauge field corresponding to weak hypercharge and the two neutral Higgsinos, H1, and H2 Neutralinos: linear combination of bino, wino, and higgsinos Lightest of the four states referred to as: Neutralino, given by gaugino and higgsino components: Neutralino mass matrix M1 and M2 are the bino and wino masses, μ is the higgsino mass parameter, θW is the Weinberg angle and tanβ=v2/v1 the ratio of the vacuum expectation values of Higgs doublets Mass and composition of the lightest neutralino= f(M1, M2, μ,β) ~ ~ ~ ~ ~ ~ ~ χ0 =N11B+N12W3+N13H1+N14H2 neutral, colourless, only weak-type interactions stable if R-parity is conserved, thermal relic non relativistic at decoupling  Cold Dark Matter relic density can be compatible with cosmological observations The Weinberg angle or weak mixing angle is a parameter in the Weinberg–Salam theory of the electroweak interaction, and is usually denoted as θW. It is the angle by which spontaneous symmetry breaking rotates the original W0 and B0 vector boson plane, producing as a result the Z0 boson, and the photon. Relic abundance in excess of the observed dark matter density over much or most of the supersymmetric parameter space-> consider the regions of parameter space which lead to especially efficient neutralino annihilation

Relic Abundance Relic abundance of LSP’s -> solving the Boltzmann equation for the LSP number density in an expanding Universe, after neutralinos general annihilation cross-section is known Bino, LSP In much of the parameter space of interest (annihilation proceeds mainly through sfermion exchange) Final neutralino relic Relic abundance in excess of the observed dark matter density over much or most of the supersymmetric parameter space To avoid this, we are forced to consider the regions of parameter space which lead to especially efficient neutralino annihilation in the early universe. Scenarios which can lead to a phenomenologically viable density of neutralino DM --lightest neutralino has a significant higgsino or wino fraction -> can have large couplings-> annihilate efficiently --mass of the lightest neutralino near a resonance, such as the CP-odd Higgs pole -> annihilate efficiently -- lightest neutralino is only slightly lighter than another superpartner (e.g., stau) -> coannihilation-> depletion f=freez-out

Figure. Representative regions of the CMSSM parameter space.
All scalar masses set to a common value mo at GUT; the 3 gaugino masses set to m1/2 a GUT (CMSSM) A0 = 0 and µ > 0 Blue region: parameter space in which neutralino DM abundance consistent with DM abundance The shaded regions to the upper left and lower right are disfavored by the LEP chargino bound and as a result of containing a stau LSP, respectively (focus point region) The LEP bound on the light Higgs mass is shown as a solid line (mh = 114 GeV). RECENT MEASURES ->125 GeV for Higgs Boson mass The region favored by measurements of the muon’s magnetic moment are shown as a light shaded region (at the 3 σ confidence level) Region where lightest stau (˜τ ) is the LSP -> not provide a viable dark matter candidate. Just outside of this region, stau slightly heavier than the lightest neutralino,leading to a neutralino LSP which effciently coannihilates with the nearly degenerate stau. In the lower right frame, a viable region also appears along the CP-odd Higgs resonance (m χ0 ~ mA/2). This is often called the A-funnel region.

R-parity conservation, radiative electroweak symmetry breaking
mSUGRA or CMSSM: simplest (and most constrained) model for supersymmetric dark matter R-parity conservation, radiative electroweak symmetry breaking Free parameters (set at GUT scale): m0, m1/2, tan b, A0, sign(m) 4 main regions where neutralino fulfills WMAP relic density: bulk region (low m0 and m1/2) stau coannihilation region m  mstau hyperbolic branch/focus point (m0 >> m1/2) funnel region (mA,H  2m) (5th region? h pole region, large mt ?) H. Baer, A. Belyaev, T. Krupovnickas, J. O’Farrill, JCAP 0408:005,2004

… UED AND KK DARK MATTER mass
Models with extra dimensions: one or more additional dimensions beyond the usual (3+1): (3+1) dimensions (brane) embedded in a (3+δ+1) spacetime (bulk). SM fields confined in the brane; gravity propagates in the extra dimensions. Hierarchy problem addressed as: extra dimensions compactified on circles (or other topology) of some size, R, (e.g., ADD (Arkani-Hamed, Dimopoulos and Dvali) scenario -> lowers Planck scale energy near the EW. Otherwise: introduce ED with large curvature (e.g., RS (Randall and Sundrum)). ED Motived also by string theory and M-theory (6, 7 ED needed). General feature of ED theories: upon compactification of ED all of the fields propagating in the bulk have their momentum quantized in units of p2 ~ 1/R2 -> for each bulk field, a set of Fourier expanded modes, called Kaluza–Klein (KK) states, appears. Particles moving in extra dimensions appear as heavy particles (a set of copies of normal particles) (KK states). In the 4-d world, KK states appear as a series (called a tower) of states with masses mn = n/R, (nlabels the mode number). Each of these new states contains the same quantum numbers, such as charge, color, etc Universal extra dimensions (UED): All fields of SM propagate universally in the FLAT extra dimensions << than those in the ADD Universal extra dimensions compactified with radii >> Planck length although smaller than in the ADD model, ~10−18 m Extra dimensions R~1/TeV … Generation of tower of KK states for each SM field with tree-level masses mass 1/R 2/R 3/R 4/R X (n) n-th KK excitation of the SM field, X X (0) =zero mode (ordinary SM particle

If extra dimensions are compactified (wrapped) around a circle or torus, the extradimensional momentum conservation implies conservation of KK number n-> lightest 1-st level KK state stable. HOWEVER, Realistic models require an orbifold to be introduced, which leads to the violation of KK number conservation-> introduce KK parity In order to obtain chiral fermions at zeroth KK level, the extra dimension is compactified on an S1/Z2 orbifold (orbit-fold) Compactification on an orbifold, S1/Z2, a circle S1 with the extra identification of y with −y.This corresponds to the segment y ∈ [0, πR], a manifold with boundaries at y = 0 and y = πR A consequence: KK-parity (-1)KK conserved: interactions require an even number of odd KK modes

Universal extra dimensions
Idea: All SM particles propagate compact spatial extra dimensions For definiteness, we concentrate on one-extra dimensional case Dispersion relation: Mass spectrum for Momentum along the extra dimension  Mass in four-dimensional viewpoint For compactification with radius , is quantized Momentum conservation in the extra dimension Conservation of KK number in each vertex If extra dimensions are compactified (wrapped) around a circle or torus, the extra dimensional momentum conservation -> conservation of KK number n-> lightest 1-st level KK state stable. Realistic models, however, require an orbifold to be introduced, which leads to the violation of KK number conservation-> introduce KK parity

Parameters in UED models
Theories with compact extra dimensions can be written as theories in ordinary four dimensions by performing a Kaluza Klein (KK) reduction. Let us now consider that the fifth dimension is compact with the topology of a circle S1 of radius R, which corresponds to the identiﬁcation of y with y + 2πR. In such a case, the 5D complex scalar field can be expanded in a Fourier series: Kaluza-Klein expansion (Fourier expansion): Zero modes are identified with SM fields 4D theory Parameters in UED models are completely specified in terms of the SM parameters Only three free parameters in minimal UED model: : Cutoff scale : Higgs boson mass : Size of extra dimension c.f. minimal SUGRA: and

Minimal UED In order to obtain chiral fermions at zeroth KK level, the extra dimension is compactified on an S1/Z2 orbifold (orbit-fold) Compactification on an orbifold, S1/Z2, a circle S1 with the extra identification of y with −y.This corresponds to the segment y ∈ [0, πR], a manifold with boundaries at y = 0 and y = πR Dirac Chiral In 5D spacetime, spinor representation has 4 complex components Reflection sym. under  Chiral fermions in 4D e.g. Conservation of KK parity [+ (--) for even (odd) ] { The lightest KK particle (LKP) is stable Dark matter Single KK particle cannot be produced c.f. R-parity and the LSP in SUSY models Experimental limit on is weaker than other extra-dimensional models: Electroweak precision tests

Particle contents in minimal UED
KK level New particles: Massless Massive (Mass ) Dirac Gauge boson Fermion (SU(2)L) Real scalar Scalar (SU(2)L) SM particles: (Mass ) Chiral Complex scalar Electroweak symmetry breaking effects are suppressed for higher KK modes There appear infinite towers of KK modes with quantum numbers identical to SM particles LPK: KK excitation of photon; Z; neutrinos; Higgs boson; graviton Relatively large zero-mode mass of the Higgs make its first level KK excitation an unlikely candidate. KK sneutrinos excluded by direct detection (as sneutrinos and 4° generation Dirac neutrinos. -> KK photon; KK Z whose mass eigenstates are nearly identical to their gauge eigenstates, B (n) , W 3(n) KK state B(1) annihilates largely to SM (zero-mode) fermions through the t-channel exchange of KK fermions

Study at linear colliders is mandatory
UED is similar to SUSY SUSY UED 1st KK mode mass Superparticle mass  SUSY breaking mass KK parity stabilizes the LKP R parity stabilizes the LSP SM Same spin SUSY Different spin SM Kinematics of 1st KK modes resembles that of superparticles with degenerate mass Attention to spins of new particles and second KK modes Study at linear colliders is mandatory

KK DARK MATTER RELIC DENSITY
KK leptons lead to a larger relic abundance, due to the fact that they freeze-out quasi-independently from the LKP and then increase the number of LKPsthrough their decays.

Beyond WIMPS (a.k.a. Weird Animals)
PASCOS 2006 AXIONS Strong CP problem Sterile n’s Warm Dark Matter MeV DM 511 keV line SuperHeavy GeV Ultra-GZK CR’s SuperWIMPs gravitino,axino WIMPs Particle Mass meV eV MeV GeV keV TeV First suggested as explanation for the observationof cosmic rays with energy above the so-called GreisenZatsepin-Kuzmin (GZK) cut-off Spin-1/2 SU(2)-singlet particles interacting with the “active” ν via ordinary mass terms

DIRECT DETECTION c DIRECT DETECTION WIMP properties
Observe scattering of c’s off nuclei in low bckg. environments Experiments which attempt to detect dark matter particles through their elastic scattering with nuclei (normal matter recoiling from DM collisions), including CDMS, XENON , ZEPLIN, EDELWEISS, CRESST, CoGeNT, DAMA/LIBRA, COUPP, WARP, and KIMS . WIMP properties m ~ 100 GeV velocity ~ 10-3 c Recoil energy ~ keV Typically focus on ultra-sensitive detectors placed deep underground c Direct detection 35

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SPIN-INDEPENDENT THEORY
WIMP nucleus recoil energy The spin-independent WIMP-nucleus elastic scattering cross section is where fp and fn are the WIMP’s couplings to protons and neutrons, given by where aq are the WIMP-quark couplings and are quantities measured in nuclear physics Is the fraction of the nucleon’s mass carried by quark q, where and the terms with TG corresponds to Interactions with the gluons in the target through a colored loop diagram. = Using Spin-dependent couplings, 3000 larger than spin-independent couplings

SPIN-INDEPENDENT EXPERIMENT
The rate observed in a detector is , where Results are typically reported assuming fp=fn, so sA ~ A2 , and scaled to a single nucleon A detector made up of Germanium targets (CDMS or Edelweiss) would expect a WIMP with a nucleon-level cross section of 10-6 pb (10-42 cm2) to yield approximately 1 elastic scattering event per kilogram-day of exposure. fp and fn are the WIMP’s couplings to protons and neutrons Experiment: number of target nuclei Astrophysics: local DM density recoil energy DM velocity distribution Nuclear physics: form factor

Neutralino-Nucleon cross sections
Neutralinos can elastically scatter with quarks through either t-channel CP-even Higgs exchange, or s-channel squark exchange: Scattering dominated by heavy Higgs (H) exchange through its couplings to strange and bottom quarks : ∼100 GeV neutralino, 200 GeV heavy Higgs mass-> cross section with nucleons: 10-5 to 10-7 pb for |μ| ∼ 200 GeV, or 10-7 to 10-9 pb for |μ| ∼ 1 TeV. 2. Cross section is dominated by light Higgs boson (h) exchange through its couplings to up-type quarks. μ in the range of 200 GeV to 1 TeV, Higgs (H) is heavier than about ∼500 GeV, exchange of the light Higgs generally dominates -> 10-8 – pb KK-Nucleon cross sections Very small cross section-> ton-scale detectors before this model will be tested by direct detection experiments

DIRECT DETECTION IMPLICATIONS
Spin-independent elastic WIMP-nucleon cross-section as function of WIMP mass. Thick blue line XENON100 limit at 90% CL. Expected sensitivity (yellow/green band). The limits from XENON100 (2010), EDELWEISS (2011), CDMS (2009) , CDMS (2011) and XENON10 (2011) are also shown. Expectations from CMSSM are indicated at 68% and 95% CL (shaded gray , gray contour), as well as the 90% CL areas favored by CoGeNT and DAMA WIMPs are assumed to be distributed in an isothermal halo with v0 = 220 km/s, Galactic escape velocity vesc =544 (+64, -46) km/s, and a density of 0.3 GeV/cm3 (0.008 Mʘ/ pc3 ) σ ~ 1-10 zb Aprile et al. (2011) 40

DIRECT DETECTION: DAMA
Collision rate should change as Earth’s velocity adds constructively/destructively with the Sun’s  annual modulation Drukier, Freese, Spergel (1986) DAMA: 8.9s signal with T ~ 1 year, max ~ June 2 DAMA Collaboration (2008) 41

Indirect Detection of Dark Matter
Another major class of dark matter searches are those which attempt to detect the products of WIMP annihilations, including gamma rays, neutrinos, positrons, electrons, and antiprotons. Also gamma rays production directly, also production of final stateaγγ, γZ or γh through loop diagrams. -> monoenergetic spectral signatures Eγ = mdm and Eγ = mdm(1-m2Z/4m2dm)  W+ WIMP Annihilation Typical final states include heavy fermions, gauge or Higgs bosons W- Places where the dark matter is strongly concentrated, Galactic centre Bengtsson et al.‘90, Berezinsky et al. ’94, … near black holes　Gondolo&Silk ’99, Bertone et al. ’05, … Dwarf satellite galaxies, e.g. DRACO Bergstrom ‘06, Profumo ‘06 Nearby galaxies, e.g. M31 Extragalactic Ullio et al. ’02, … Microhalos Narumoto&Totani ’06; Diemand et al. ‘07

 WIMP Annihilation Typical final states include heavy fermions, gauge or Higgs bosons 2) Fragmentation/Decay Annihilation products decay and/or fragment into some combination of electrons, protons, deuterium, neutrinos and gamma rays  W- q W+ q  e+ 0 p  

 WIMP Annihilation Typical final states include heavy fermions, gauge or Higgs bosons 2) Fragmentation/Decay Annihilation products decay and/or fragment into some combination of electrons, protons, deuterium, neutrinos and gamma rays 3) Synchrotron and Inverse Compton Relativistic electrons up-scatter starlight to MeV-GeV energies, and emit synchrotron photons via interactions with magnetic fields  W- q W+ q  e+ 0 p    e+

Gamma Rays from WIMPs annihilation
Gamma ray flux from annihilation WIMP’s annihilation cross section. ψangle relative to galactic center ρ(r) , DM density spectrum gamma Solid angle observed Depends only on DM distribution and is the average over the observed solid angle of the quantity

Galactic Centre γ Ave J 1.5 3×104 1.0 103 0.7 30
GC flux predictions can vary considerably Inner (<1pc) profile uncertain: N-body simulations generally predict a cusp observations show no clear evidence of a cusp/core This causes a large difference. Also, Difficult to predict the distribution of DM in the inner parsecs (100 pcs N-body sim.) effects of baryons [Prada ‘04] background [Zaharijas ‘06] : emission observed from HESS from GC, spectrum 160 GeV-20 TeV Profile γ Ave J Moore 1.5 3×104 NFW 1.0 103 Kra 0.7 30

FERMI Mazziotta et al. 2012 Feng 2012 - Fermi Launched in 2008
Upper limits at 95% CL, same annihilation channels as MW. The continuous lines indicate the upper limits obtained neglecting the systematic uncertainties, while the dotted lines indicate the upper limits obtained including the uncertainties on the J-factors (J(∆Ω)). Dashed Line: as in the MW case. Upper limits at 95% CL on <σv> as a function of the WIMP mass for the annihilation channels µ+µ−, τ+τ−, bb and W+W−. The dashed line is the annihilation cross section of 3 × 10−26 cm3/s in the canonical thermal relic WIMP scenario. - Fermi Fermi Launched in 2008 The analysis of dwarf spheroidal galaxies yields upper limits on the product of the dark matter pair annihilation cross section and the relative velocity of annihilating particles that are well below those predicted by the canonical thermal relic scenario in a mass range from a few GeV to a few tens of GeV for some annihilation channels.

Gamma-Ray sourc in GC (FERMI)
Analysis of 3.8 years of data from the Fermi-LAT in the inner 7oX 7o toward the MW GC using the current second year Fermi-LAT point source catalog (2FGL), the second- year Fermi-LAT diffuse Galactic map, isotropic Emission model Abazajian & Kaplinghat (20012) TS= point source test statistic signicance= = log-likelihood with and without the source Detections extended source with gamma-ray spectrum consistent with DM particle masses ~10 GeV to 1 TeV annihilating to quarks, and masses approximately 10 GeV to 30 GeV annihilating to leptons. A part of the allowed region in this interpretation is in conflict with constraints from Fermi observations of the Milky Way satellites. The gamma-ray intensity and spectrum also well fit with emission from a millisecond pulsar (MSP) population following a density profile like that of lowm ass X-ray binaries observed in M31.

Cosmological signal of DM
DM forms structures in gravitational collapse, and in those over-dense regions, DM selfannihilation signal is greatly enhanced. IGRB (Isotropic Gamma Ray Background) Measurements of the IGRB by Fermi-LAT and EGRET, together with three types of gamma-ray spectra induced by DM. Cross sections chosen for visulaization The solid lines are with the Gilmore et al. absorption model applied, and the dotted lines with the Stecker et al. [69] absorption. Also shown the line spectra convoluted with the energy resolution of the Fermi-LAT experiment (dashed line). The dotted line passing through the Fermi data points is a power law with the spectral index of

Extended gamma-ray emission from galaxy clusters
From 3-year Fermi-LAT data PT (point source) model Han et al. (2012) Extended profiles µ+µ. channel. Upper limit for the DM annihilation cross-section in the bb channel. - Joint analysis of the Milky Way dwarf galaxies Canonical thermal cross-section of ion of 3 x cm3/s

Charged Cosmic Rays from WIMPs annihilation
WIMP annihilations throughout the galactic halo-> charged cosmic rays, including electrons, positrons, protons and antiprotons. From spectrum of the particles-> signatures of DM annihilations. PAMELA experiment (began June of 2006): anomalous rise in the cosmic ray positron fraction (the positron to positron-plus-electron ratio) above 10 GeV, confirming earlier indications from HEAT and AMS-01. ATIC balloon experiment: data revealing a feature in the cosmic ray electron (plus positron) spectrum between approximately 300 and 800 GeV, peaking at around 600 GeV WMAP experiment: excess of microwave emission from the central region of the MW: interpreted as synchrotron emission from a population of electrons/positrons with a hard spectral index FERMI…. PAMELA ATIC

Electron-Positron Diffusion
When electrons/positrons are produced in dark matter annihilations, they travel through the galaxy’s tangled magnetic fields, losing energy via synchtrotron and inverse Compton Resulting spectrum can be calculated by solving the diffusion-loss equation: For GeV e+/- in the inner galaxy, leads to ~0.1-1 kpc diffusion (~1-10) Source Term Diffusion Constant Energy Loss Rate

PAMELA results of antiparticles in cosmic rays
Positron fraction Spectrum from GALPROP (Moskalenko & Strong) pure secondary production of positrons during the propagation of cosmic-rays in the galaxy Nature 458, 607 (2009) The total electron+positron spectrum Fermi LAT CR electron spectrum (red ﬁlled circles; gray band systematic errors). ATIC bump Fermi excess PAMELA released data on the positron/electron ratio up to about 100 GeV, which show clear excess above ~10 GeV. The low energy data is affected by the solar environment and we do not need care it too much. FERMI Fermi LAT CR electron spectrum (red ﬁlled circles; gray band systematic errors). Two-headed arrow: size and direction of the rigid shift of the spectrum implied by a shift of +5% −10% of the absolute energy As can be clearly seen from the blue dashed line in figure 3, this model produces too steep a spectrum after propagation to be compatible with the Fermi measurement reported here. The observation that the spectrum is much harder than the conventional one may be explained by assuming a harder electron spectrum at the source, which is not excluded by other measurements. However, the significant flattening of the LAT data above the model predictions for E > 70 GeV may also suggest the presence of one or more local sources of high energy CR electrons. We found that the LAT spectrum can be nicely fit by adding an additional component of primary electrons and positrons, with injection spectrum Jextra(E) / E− e exp{−E/Ecut}, Ecut being the cutoff energy of the source spectrum. The main purpose of adding such a component is to reconcile theoretical predictions with both the Fermi electron data and the Pamela data [7] showing an increase in the e+/(e-+e+) fraction above 10 GeV. The latter cannot be produced by secondary positrons coming from interaction of the Galactic CR with the ISM. Such an additional component also provides a natural explanation of the steepening of the spectrum above 1 TeV indicated by H.E.S.S. data [9]. As discussed in [12] and references therein, pulsars are the most natural candidates for such sources. Other astrophysical interpretations (e.g. [22]), or dark matter scenarios, can not be excluded at the present stage. Excess of galactic cosmic-ray electrons at energies of ~ GeV Chang et al. Nature456, PRL102: ,2009

Compilation of recent and less recent data in charged cosmic rays, superimposed on plausible but uncertain astrophysical backgrounds from secondary production. Left: positron fraction. Center: antiproton flux. Right: sum of electrons and positrons. Charged cosmic ray data interpreted in terms of Dark Matter annihilations: the flux from the best fit DM candidate (a 3 TeV DM particle annihilating into τ+ τ- with a cross section of cm3/sec) is the lower dashed line and is summed to the supposed background, giving the pink flux which fits the data. Left, center and right like in previous figure

ARE THESE DARK MATTER? Pulsars can explain PAMELA
Energy spectrum shape consistent with WIMP dark matter candidates BUT to produce the PAMELA and ATIC signals WIMPs must annihilate dominantly to charged leptons (to produce sufficiently hard spectrum, and to avoid the overproduction of cosmic ray antiprotons) Furthermore very large annihilation rate required: times higher than is naively expected for a thermal relic -> this require a large annihilation cross Solution: -- Local inhomogeneities in the dark matter distribution boost the annihilation rate Alternative production mechanism (non thermal mech.) WIMPS interacting through exchange of very light particles can annihilate through non-perturbative processes -> Cirelli, Kadastik, Raidal, Strumia (2008) Arkani-Hamed, Finkbeiner, Slatyer, Weiner (2008) Feldman, Liu, Nath (2008); Ibe, Murayama, Yanagida (2008) Guo, Wu (2009); Arvanitaki et al. (2008) Pulsars can explain PAMELA Zhang, Cheng (2001); Hooper, Blasi, Serpico (2008) Yuksel, Kistler, Stanev (2008); Profumo (2008) Fermi-LAT Collaboration (2009) Dark matter particles which annihilate directly to e+e- generate an edge in cosmic ray e- spectrum that drops suddenly at Ee = mX. Pulsars produce spectra which fall off more gradually. KK dark matter with m ~ 600 GeV ATIC (2008) Fermi-LAT Collaboration (2009) Blue line: pulsars model now Freez-out 57

WMAP As A Synchrotron Telescope
In addition to CMB photons, WMAP was used to provide the best measurements to date of the standard interstellar medium emission mechanisms: thermal dust, spinning dust, ionized gas, and synchrotron. Data is “contaminated” by a number of galactic foregrounds that must be accurately subtracted Thermal Dust Soft Synchrotron Free-Free WMAP Soft Synchrotron - From SN shocks; morphology traced by the 408 MHz Haslam map Free-Free - Hot gas electron/ion thermal Bremsstrahlung; morphology traced by the H recombination line map (Finkbeiner, 2003) Thermal/Spinning Dust -Emission from vibrating and spinning dust grains; morphology traced by the SFD98 dust map (Schlegel et al.) and the 94 GHz Finkbeiner map

22 GHz After known foregrounds are subtracted, an excess appears in the residual maps within the inner ~20 around the Galactic Center Synchrotron + 22 GHz Free-free _ = … + T & S Dust WMAP + CMB

Dark Matter and the WMAP Haze
Initial interpretation: thermal bremsstrahlung gas K Ruled out by the lack of a corresponding H recombination (X-ray) line Appears to be hard synchrotron emission from a new population of energetic electrons/positrons in the inner galaxy -Too hard to be supernovae shocks -Too extended to be a singular event (GRB, etc.) Very Difficult to explain astrophysically 22 GHz 2004 Doug Finkbeiner: WMAP Haze could be synchtrotron from electrons/positrons produced in dark matter annihilations in the inner galaxy 1) Assuming an NFW profile, a WIMP mass of 100 GeV and an annihilation cross section of 3x10-26 cm3/s, the total power in dark matter annihilations in the inner 3 kpc of the Milky Way is ~1.2x1039 GeV/sec 2) The total power of the WMAP Haze is between 0.7x1039 and 3x1039 GeV/sec Coincidence?

Fitting The Haze To The Dark Matter Halo Profile
When the effects of diffusion are accounted for, an NFW halo profile (  R-1) under produces the WMAP haze at small angles Angular distribution of the haze matches that found for a cusped halo profile, with   R-1.2 Although the precise result of this fit depends on the diffusion parameters adopted (magnetic fields, starlight density, etc.), the approximate result (slope of -1.1 to -1.3) is fairly robust (R)  R-1.2 (R)  R-1 (NFW) Significant systematic errors

The Dark Matter Annihilation Cross Section
For a given annihilation mode, diffusion parameters and halo profile, we can calculate the annihilation cross section needed to normalize the observed intensity of the WMAP Haze Hooper, G. Dobler and D. Finkbeiner (2007) b-b+ ZZ W-W+ -+ -+ WIMP annihilation cross section (times boost factor) required to produce the intensity of the WMAP haze. e-e+ For a typical GeV WIMP, the annihilation cross section needed is within a factor of 2-3 of the value needed to generate the density of dark matter thermally (3x10-26 cm3/s); No boost factors are required!

Other (OLDER) Claims of Evidence For Dark Matter Annihilation
The HEAT positron excess 511 keV emission from the galactic bulge EGRET’s galactic gamma ray spectrum EGRET’s extragalactic gamma ray spectrum

The HEAT Positron Excess
In its , 2000 flights, the HEAT balloon-based cosmic ray detector observed an excess of positrons relative to electrons in the 7-30 GeV range Measurements from AMS add some support Combined statistical significance of several (4-5) sigma, neglecting (likely important, but difficult to evaluate) systematic uncertainties E. Baltz and J. Edsjo, PRD, astro-ph/

The HEAT Positron Excess
Strengths: Fit to data can be easily improved if dark matter component is included Weaknesses: Messy astrophysics Requires annihilation boost of ~50 or more (possible, but unlikely), or non-thermal dark matter production Prospects: Confirmed by PAMELA (excess in the GeV range) data and by FERMI (extended to about 200 GeV)

511 keV Emission from the Galactic Bulge
2003: INTEGRAL/SPI spectrometer observed bright 511 keV emission from the bulge of the Milky Way (1.3 x 1043 positrons injected per second) Gaussian, spherically symmetric morphology (FWHM of 8˚) Type Ia supernovae are unable to generate the observed injection rate (too few escape) Hypernovae (type Ic SNe) or gamma ray bursts could potentially generate enough positrons if high estimates for rates are considered Even if the injection rate is sufficient, a mechanism is required to transport from disk to bulge - appears to be somewhat difficult 1-10 MeV dark matter particles annihilating to e+e- could simultaneously generate the measured dark matter relic abundance, and the observed 511 keV emission (particle much lighter than the DM particles in the theoretical most attractive models (Boem et al. 2003, astro-ph/ )

511 keV Emission and MeV Dark Matter
Strengths: Challenging to explain 511 signal with non-exotic astrophysics Weaknesses: Somewhat difficult to construct a viable particle physics model with an MeV WIMP Prospects: No clear path to confirmation or exclusion of the MeV dark matter hypothesis (perhaps 511 emission from dwarf galaxies?) De Cesare et al. (2012) : line from Galactic X-Ray Binaries INTEGRAL all-sky picture of positronium gamma line (511 keV) emission (J. Knödlseder et al., astro-ph/ ) 1. Although neutralinos should be heavier (by relic abundance considerations) than 20 GeV they can be much lighter in extended supersymmetric models in which light Higgs bosons can mediate neutralino annihilations 2. ∼500 GeV dark matter particles could be collisionally excited to states which are ∼1 MeV heavier, which produce electron-positron pairs in their subsequent de-excitations to the ground state

EGRET’s Galactic Gamma Ray Spectrum
EGRET observed an excess of gamma rays above 1 GeV, compared to the the most simple galactic cosmic ray models Could be the product of a ~ GeV WIMP (W. de Boer et al, PLB, hep-ph/ ; Astron.Astrophys, astro-ph/ ; astro-ph/ ) The same dark matter annihilation spectrum can fit the shape of the GeV excess in all regions of the sky Problem: To accodomate the required normalization for the annihilation rate in various regions of the Galaxy, however, requires a departure from a simple halo profile De Boer, et al. introduce two rings of dark matter near the galactic plane at 4 and 14 kpc from galactic center (8x1010 M tidally disrupted dwarf galaxy? motivated by rotation curves) (W. de Boer et al, A.A., astro-ph/

Problem: With a standard treatment of cosmic ray diffusion, far too many antiprotons are produced in this scenario To reconcile, anisotropic diffusion, strong convection away from (and outside of) the disk and local spatial variations are required Predicted in de Boer model Prediction from standard secondary cosmic ray production (Bergstrom, Edsjo, Gustafsson and Salati, JCAP, astro-ph/ )

Strengths: Consistent with a neutralino or other EW-scale WIMP(50- 100 GeV WIMP) Similar spectral shape over sky Weaknesses: Non-standard dark matter distribution is needed (two rings) Conflict with antiprotons unless non-standard comic ray diffusion is invoked The GeV excess can plausbily be reduced or eliminated without dark matter by modifying the diffusion model FERMI data on diffuse gamma rays compared with EGRET data in the mid-latitude range (100 < b < 200)

EGRET’s Extragalactic Gamma Ray Spectrum
EGRET has also detected a diffuse, extragalactic gamma ray signal, which becomes more intense above 1 GeV Integrated signal from dark matter annihilations throughout the universe could produce a potentially observable signal (Ullio, Bergstrom,Edsjo 2002) Intensity depends critically on DM distribution – cuspy halos and substructure are required The EGRET extragalactic diffuse spectrum can be fit by annihilations from a ~500 GeV neutralino (or other WIMP) ___steep power law plus annihilation spectrum EGB (Extra Galactic γ-ray Background) spectrum has two components: a steep-spectrum power law with index -2.33 (dashed-blue) and a strong bump at a few GeV. (higgsino mass parameter µ; gaugino mass parameter m2; mass of the cp-odd higgs mA; ratio of the higgs vacuum Expectation values tan ; scalar mass parameter mS and Trilinear soft-breaking parameters for the third generation squarks At and Ab) Elsasser and Mannheim, PRL, astro-ph/ Ψ=boost factor

EGRET’s Extragalactic Gamma Ray Spectrum
Strengths: Consistent with a (somewhat heavy) neutralino or other WIMP Weaknesses: Not a particularly distinctive signal, could easily be astrophysical High annihilation rate needed; either large degree of very cusped substructure, or a non-thermal WIMP Signal from our galactic center would have been seen, unless cusp is removed by tidal effects (S. Ando, PRL, astro-ph/ )

Summary Searches for dark matter signatures in gamma rays from the Milky Way halo and dwarf galaxies exclude canonical thermal relic dark matter annihilation cross-sections for masses less than a few tens of GeV • Fermi LAT CRE data provide a valuable probe of dark matter models that could explain the measured rise in the local cosmic-ray positron fraction • More observations are needed

Non-Baryonic Dark Matter in Cosmology

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