Dark Matter and Dark Energy: Summary and Future Directions arXiv:astro-ph/0304183v1 10 Apr 2003 BY JOHN ELLIS TH Division, CERN, Geneva, Switzerland CERN–TH/2003-086 astro-ph/0304183 April 2003 This paper reviews the progress reported atisinthis Society Discussion Meeting and advertizes some possible future directions ourRoyal drive to understand dark matterInnew and dark energy. Additionally, a firstof attempt made to place in context the exciting results from the WMAP satellite, which were published shortly afterhere this Meeting. the first part ofdark this review, pieces observational evidence shown that bear on are the amounts of matter and dark energy are reviewed. Subsequently, particle candidates for dark matter are mentioned, and detection strategies are discussed. Finally, ideas presented for tocalculating relating them laboratory the data.amounts of dark matter and dark energy, and possibly Keywords: cosmology, particle physics, dark matter, dark energy 1. The Density Budget of the Universe It istheir convenient to relative express the mean densities ρi of Ω various quantities in theto Universe in terms of fractions tothat the critical density: ≡ ρidata /ρ Thethe theory of cosmological ishould crit.very inflation suggests the the total density be close the critical one: Ω 1,−5and this is supported by the available on cosmic microwave tot ≃ strongly background radiation (CMB) (Bond 2003). The fluctuations observed inwaves, thebe CMB at a level ∼ 10 in amplitude exhibit a peak at a partial wave ℓ ∼ 200, as would produced by acoustic oscillations in a flat Universe with Ω ≃ 1. At lower partial ℓ ≪to200, tot the CMB fluctuations believed to be dominated by the due the gravitational potential,are and more acoustic oscillations areSachs-Wolfe expected at effect larger ℓ > 200, > whose relative heights depend on the baryon density Ωbmade . At even larger ℓ ∼ (Bond 1000,2003) these oscillations should be progressively damped away. Fig. 1 compares measurements of CMB fluctuations before WMAP with the WMAP data themselves (Bennett et al. 2003; Hinshaw et al. 2003), that were released shortly this2003), Meeting. The of the first acoustic peak indeed corresponds to a after flatet Universe with ≃position inh2particular, WMAP finds Ω = tot more tot 1.02±0.02 (Spergel al. and Ω two acoustic peaks are established with high significance, providing a new determination of1:Ω = 0.0224 ±now 0.0009, where hlikelihood ∼ 0.7 is b units the presentfor Hubble expansion rate measured inthe of The functions various cosmological parameters shown in100km/s/Mpc. Fig. 2. Remarkably, there is excellent consistency between theH, estimate ofare present-day Hubble constant H ∼ 72km/s/Mpc from WMAP (Spergel et Article submitted to Royal Society TEX Paper 2 J. Ellis Figure 1. Spectrum of fluctuations in the cosmic microwave background measured by WMAP (darker points with smaller error bars), compared with previous measurements (lighter points with larger error bars, extending to greater ℓ) (Hinshaw et al. 2003). al. 2003) with that inferred from the local distance ladder based, e.g., on Cepheid variables. Figure 2. The likelihood functions for various cosmological parameters obtained from the WMAP data analysis (Spergel et al. 2003). The panels show the baryon density Ω h2, the b matter density Ωm h2, the Hubble expansion rate h, the strength A, the optical depth τ , the spectral index ns and its rate of change dns/lnk, respectively. As seen in Figb)3,favour the2003; combination data with those high-redshift Type-Ia supernovae (Perlmutter Perlmutter &Universe Schmidt 2003) and on on largestructure (Peacock strongly a of flatCMB about 30 % of (mainly dark) matter and2003a, 70 % of vacuum (dark) energy. Type-Ia with supernovae probe thescale geometry of the Universe at redshifts z < ∼ 1. They disagree with a flat Article submitted to Royal Society Dark Matter and Dark Energy 3 Figure 3. The density of matter Ωm and dark energy ΩΛ inferred from WMAP and other CMB data (WMAPext), and from combining them with supernova and Hubble Space Tele- scope data (Spergel et al. 2003). Ω that has no supernovae vacuum energy, and also1 appear with anto open Ω m against ≃quate 0.3 Universe tot = 1 Universe (Perlmutter 2003; Perlmutter Schmidt 2003). be adestandard candles, and twothat observed with z They > argue strongly dustThe or evolution effects would be&zsufficient to cloud their cal interpretation. supernovae indicate that theofexpansion of the Universe isgeometricurrently accelerating, though it had been decelerating when was > 1. There are good prospects for improving substantially the accuracy the supernova data, by a combination of continued groundbased and subsequent space observations using the SNAP satellite project (Perlmutter 2003; Perlmutter & Schmidt 2003). It is impressive that the baryon density inferred from WMAP data (Spergel et al. 2003) is in good agreement with the value calculated previously on the basis of Big-Bang 2 nucleosynthesis (BBN), which depends ondata completely different (nuclear) physics. Fig. compares abundances of light elements calculated WMAP value ofon Ω bh4 with thosethe inferred from astrophysical (Cyburt etlight-element al. the 2003). the astrophysical assumptions that are made in extracting theusing abundances from astrophysical data, theory there is respectable overlap. As we heard at other thisDepending Meeting, several pillars of inflation have now been verified by WMAP and CMB data (Bond 2003): the Sachs-Wolfe effect due to fluctuations in the large-scale gravitational potential were first byofthe satellite, the first acoustic peak was and seen the CMB spectrum at ℓseen ∼ tail 210 andCOBE this has been followed by two more peaks theinintervening dips, the damping Article submitted to Royal Society 4 J. Ellis Figure 4. The likelihood functions forb the primordial abundances of light elements inferred from astrophysical observations (lighter, yellow shaded regions) compared with those cal- culated using the CMB value of Ω h2 (darker, blue shaded regions). The dashed curves are likelihood functions obtained under different astrophysical assumptions (Cyburt et al. 2003). the fluctuation spectrum expected at ℓof> 1000 has been seen, polarization has been ∼ the observed, and the Universe primary anisotropies are predominantly Gaussian. WMAP additionally, the thickness last scattering surface andto observed the reionization ofmeasured the when zare ∼ secondary 20 by the first generation ofe.g., stars (Kogut ethas, al. 2003). Remaining to be established anisotropies, due, the SunyaevZeldovich effect, weak lensing and inhomogeneous reionization, and tensor perturbations induced by gravity waves. As we also heard at this meeting, the values of Ω inferred from X-ray studies of CDM gas in rich clusters using the Chandra satellite (Rees 2003), which indicate Ω = CDM 0.325±0.34, gravitational lensing (Schneider 2003) and data on large-scale structure, e.g., from the by 2dFwith galaxy redshift survey (Peacock 2003a, b), are very consistent with that 2 inferred combining CMB andΩCDM supernova data. The WMAP data confirm this concordance higher precision: h = 0.111 ± 0.009 (Spergel et al. 2003). The 2dF galaxy survey has examined two wedges through the Universe. Significant structures are seen at low redshifts, which die away at larger redshifts where the Universe becomes more homogeneous and isotropic. The perturbation power spectrum at these large scales matches nicely with that in seen the CMB data, whilst the structures small scales wouldofnot present a in baryondominated Universe, or one seen with ata significant fraction hot be dark matter. Indeed, Article submitted to Royal Society Dark Matter and Dark Energy 5 the 2dF data were usedwhich to inferhas an recently upper limit onimproved the sum ofusing the neutrino of 1.8 eV (Elgaroy et 2002), been WMAPmasses data (Spergel et al. 2003) to al. Σνi mνi < 0.7 eV, (1.1) as seen in Fig. 5. This impressive upper limit is substantially better than even the stringent laboratory upperalso limit onthe anthree individual as discussed inmost the next Section. Thw WMAP data provide (Crotty et al.neutrino 2003) a mass, new limit on the effective number ofdirect light neutrino species, beyond within the Standard Model: ν eff −1.5 < ∆N < 4.2. (1.2) This limitthat is not as not stringent as that in from LEP, but applies to additional light degrees of freedom might be produced Z decay. ν Figure 5. The likelihood function for the total neutrino density Ω h2 derived by WMAP (Spergel et al. 2003). The upper limit mν < 0.23 eV applies if there are three degenerate neutrinos. 2. What is it? As discussed here by −15(2003), particle candidates for dark matter range from the > Kolb +15 axion a mass GeV Benakli (van Bibber to via cryptons withwith masses < GeV (Ellis∼ et10al. 1990; et al.2003) 1999), neutrinos masses ∼ 10 with −10 < ∼ 10 GeV, the gravitino and the lightest supersymmetric particle with a mass 2 > ∼ 10 GeV (Ellis et al. 1984; Goldberg 1983). In recent years, there has been Article submitted to Royal Society J. Ellis 6 considerable experimental progress in understanding masses, so I start them, even though cosmology now disfavours the another hot dark matter theynow would provide (Spergel etwhich al. 2003). All others are candidates forneutrino cold dark matter, except forwith the gravitino, might constitute warm dark matter, bility disfavoured by the WMAP evidence for the reionization when z ∼ 20 (Kogut etpossial. 2003). (a) Neutrinos Particle theorists expectofparticles to have masses that vanish exactly only if they are protected by some unbroken gauge symmetry, much as the photon is massless because of the U(1) so gauge symmetry electromagnetism, thatto isacquire associated with the conservation of electric charge. There is corresponding exact gauge symmetry to protect lepton number, we expect itoftoby beno violated and neutrinos masses. This is indeed the accepted interpretation the observed oscillations between different types of neutrinos, which are made possible mixing into non-degenerate mass eigenstates (Wark 2003); Pakvasa & Valle 2003). Neutrino masses could arise even theet Model of particlebephysics, without adding any new particles, at thewithin expense ofStandard introducing a interaction tween two neutrino fields and two Higgs fields (Barbieri 1980): ⟨ al. 0|H0⟩ 2 1 M νH · νH → mν M . (2.1) = However, such an thought interaction would be non-renormalizable, andsome therefore is not thought to be is fundamental. The (presumably large) M et appearing the denominator of (2.1) generally to originate frommass the scale exchange of massive fermionic particle that mixes with the light neutrino (Gell-Mann al. 1979; Yanagida 1979; Mohapatra & Senjanovic 1980): 0 MD , (2.2) νL (νL, N ) T MD M Diagonalization of this yields small neutrino since we that mass termmatrix mD direct is naturally of the same order as quark andonmasses, lepton masses, andexpect M ≫ m .the Dirac W We have the following upper limits neutrino masses. From measurements ofetthe end-point in experimental Tritium β decay, we know that (Weinheimer et al. 1999; Lobashov al. 1999): mνe < (2.3) ∼ 2.5 eV, Nabout 0.5 eV with the pro- posed and there are prospects to improve this limit down to KATRIN know thatexperiment (Hagiwara (Osipowicz et al. 2002):et al. 2001). From measurements of π → µν decay, we mνµ < 190 KeV, (2.4) and there arewe prospects to improve this et limit a factor ∼ 20. From measurements of τ → nπν decay, know that (Hagiwara al. by 2002): mντ < 18.2 MeV, Article submitted to Royal Society (2.5) Dark Matter and Dark Energy 7 and there are prospects to improve this limit to ∼ 5 MeV. However, the weighted most stringent laboratory limit on neutrino may from searches for neutrinoless double-β decay, which constrain themasses sum of thecome neutrinos’ Majorana masses by their couplings to electrons (Klapdor-Kleingrothaus et al. 2001): i i ei ⟨ mν⟩ e ≡ |Σν mν U 2 | < (2.6) ∼ 0.35 eV and there are prospects to improve this limit to ∼further 0.01 in a futureinput round of experiments. The impact of the limit (2.6) in relation to the eV cosmological upper limit (1.1)The is neutrino discussed below, after we have gathered experimental from neutrino-oscillation experiments. mass matrix (2.2) mass should be regarded also as general, a matrix in incide flavour space. When is diagonalized, the neutrino eigenstates will not, in cothe flavouritbetween eigenstates partner mass eigenstates of leptons. Thewith mixing matrix themthat (Maki et al.the 1962) may be written in the the charged form c13 0 s13 c12 s12 0 1 0 0 0 0 1 0 −s23 c23 −s130e−iδ 0 c13e0−iδ V = −s12 c12 0 0 c23 s23 1 . (2.7) where the symbols c, θs12,23,31 the standard trigonometric functions of the three real ij denote ‘Euler’ mixing angles , and δ is a CP-violating phase that can in principle also be observed in neutrino-oscillation experiments (De Rújula et al. 1999). Additionally, are The twoneutrino CP-violating phases φ1,2 that appear inother the double-β observable (2.6), butthat dothere not affect oscillations. pioneering Super-Kamiokande and experiments have shown atmospheric neutrinos oscillate, with the following difference in squared masses and mixing angle (Fukuda et al. 1998): δm2 ≃ 2.4 × 10−3 eV2, sin2 2θ23 ≃ 1.0, (2.8) which very consistent the reactor neutrino experiment al. 2002), as seen inisSNO the left panel et ofwith Fig. 6. K2K A b), flurry recent solar neutrino experiments, notably (Ahmad al. 2002a, haveofestablished beyond any(Ahn doubtetthat theymost also oscillate, with δm2 ≃ 6 × 10−5 eV2, tan2 θ31 ≃ 0.5. (2.9) Most recently, the KamLAND experiment has2 reported deficit set of electron antineutrinos from nuclear power reactors, leading to eta al. verya data, similar of parameters, asrange seen in the right panel Fig. 6 (Eguchi Using the of allowed byof solar and KamLAND onePre-WMAP, can es-preferred tablish 12 correlation between the relic neutrino density Ω h& and the 2003). neutrinoless double-β decay νset observable ⟨m as⟨θseen Fig. 7the (Minakata Sugiyama 2002). thea ν⟩ e,on experimental limit m be used to the bound (Minakata & Sugiyama ν ⟩ in e could 2002) 2 −1 10−3 < ∼ Ων h < ∼ 10 . Article submitted to Royal Society (2.10) J. Ellis 8 m2(eV2) 10-3 -2 m2 [eV2] 10 -3 10-4 10 10 -4 -5 10 -1 10 100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 2 2 tan sin 2 Figure 6. Left panel: The region of neutrino oscillation parameters (sin2 2θ, ∆m2) inferred from the K2K reactor experiment (Ahn et al. 2002) includes the central values favoured by the SuperKamiokande atmospheric-neutrino experiment, indicated by the star (Fukuda et al. 1998). Right panel: The region of neutrino oscillation parameters (tan2 θ, ∆m2) in- ferred from solar-neutrino experiments is very consistent with derived from the KamLAND reactor neutrino experiment (Eguchi et al. 2003). The shaded regions show the combined probability distribution (Pakvasa & Valle, 2003). Alternatively, now that WMAP hasbound: set a tighter upper bound Ωνh2 < 0.0076 (1.1), one can use this correlation to set an upper < mν >e < ∼ 0.1 eV, (2.11) which is‘Holy difficult to reconcile with the signal inin(Klapdor-Kleingrothaus et al. 2002). The is CPreported violation neutrino oscillations, which would manifestGrail’ itself as neutrino a difference between the oscillation probabilities for neutrinos and antineutrinos (De of Rújula et al.physics 1999): P (νe → νµ) − P (ν¯e → ν¯µ) = 16s12c12s13c2 13 s23c23 sin δ 2 12 L 2 13 L (2.12) 2 23 L , ∆m ∆m ∆m sin sin sin 4E 4E 4E For this to be observable, ∆m12 and θ12 have to be large, as SNO and KamLAND have to in bethe theminimal case,oscillations andseesaw also θ13(Casas has to& beIbarra large2001). enough which remains to bethat seen. Inshown fact, even model contains many additional parameters are not observable neutrino In-three addition to the three masses of the charged leptons, there are three light-neutrino light-neutrino mixing angles and three CP-violating the light-neutrino sector: the oscillation and the thatin are relevantmasses, to neutrinoless double-β decayδ experiments. AsMajorana well,CP-violating therephases arephases three heavy neutrino masses, three morephase mixing angles andtwo three more phases that singlet- Article submitted to Royal Society Dark Matter and Dark Energy 9 0.1 (b) h2 0.01 0.001 0.0001 0.001 0.01 0.1 1 max (eV) <m> Figure 7. Correlation between Ω νh2 and ⟨ m ν⟩ e . The different diagonal lines correspond to uncertainties in the measurements by KamLAND and other experiments (Minakata & Sugiyama 2002). become observable insothe heavy-neutrino sector, making a total ofknown, 18 parameters. Out of all masses these parameters, far just fourthought light-neutrino parameters are twobetween differences in squared and two mixing As discussed later, itsector isreal often that there may be Universe, athree connection CP violation in the neutrino and theangles. baryon density in the via leptogenesis. Unfortunately, this connection is somewhat indirect, since the CP-violating phases measurable in the light-neutrino sector to not contribute to leptogenesis, which is controlled bycontribute the other to phases that are not observable directly at low energies (Ellis & Raidal 2002). However, ifthe the seesaw model combined with supersymmetry, these extra renormalization ofissoft superymmetry-breaking parameters at lowphases energies, and hence may have indirect observable effects (Ellis et al. 2002a, b). (b) Problems with Cold Dark Matter? A recurring question isobservational whether thea data cold darkhalo. matter paradigm for structure formation is compatible with all the (Navarro 2003; Abadi et this al. 2002). One of the issues is the mass profile at the corehaloes of galactic As weto heard at meeting, density profiles clearly differ from naive power andseem are much than simple isothermal models. However, the oflaws, γstill <though, 2.5 be inγshallower reasonable agreement with CDM sumulations, though there are problems with > 2.5 galaxies. The theoretical predictions are not yet conclusive, with questions such as triaxiality, departures from equilibrium and time dependence remaining to be resolved. Another issue is halo substructure and the abundance of Article submitted to Royal Society 10 J. Ellis Figure 8. Exclusion domains for the halo density of different types of axion, as functions of the frequency corresponding to the possible axion mass, as obtained from microwave cavity experiments (van Bibber 2003; Asztalos et al. 2001). Milky Waybetween satellites. However, the latest is that there is aapparently better agreement the number Milky Way satellites and the number of massive halo substructures predicted in CDM simulations. Itnews has been argued that Milky Way-like stellar disk would thickened if of there were substructures in the but simulations do display anybe significant effect (Navarro Abadi etthere al. 2002). Thus, the latest advice simulators be thathalo, isrecent no showstopper for not the CDM paradigm, so from let such us the examine someseems of 2003; the to candidates for the CDM. (c) Axions As to weexplain heard here vaninteractions: Bibber (vanin Bibber 2003), axions were invented in order to conserve CP in thefrom strong thetable picturesque analogy of Sikivie (Sikivie 1996), why strong-interaction pool isg apparently horizontal. Axion-like particles may characterized by to a two-dimensional parameter space, consisting of the axion mass mbe and itsthe coupling pairs teleof photons, areas of this parameter a by aγ. Many space are excluded by laser experiments, scopes, searches for solar axions currently being extended the CAST experiment at CERN (Irastorza et al. 2002), astrophysical constraints et as al. 2002) and searches forexcluding halo using microwave (Asztalos et(Hagiwara 2001), seen inbest Fig. 8.matter. These and axions searches using Rydbergcavities atoms (Yamamoto etal.al. 2001) have thecold chances of ragions of parameter space where the axion might constitute dark Article submitted to Royal Society Dark Matter and Dark Energy (d) 11 1 Supersymmetric Dark Matter 19 Thethe appearance of supersymmetry at the scale 1981) wasmass originally motivated by10 the hierarchy problem (Maiani 1979; ’tpotential Hooft 1979; - why is m mPNewton ∼ W GeV, only candidate we for ainTeV fundamental scale in ≪the physics, or 2 have alternatively why anWitten atom so much larger than 2 The 2 former 2is theisCoulomb potential? ∝m eis =a typical O(1), whereas the latter is It is ∝ G m ∼ m /m , where particle mass scale. not sufficient simply N to set particle masses such as m ≪ m , since quantum corrections will increase them W P again. Many one-loop quantum corrections each yield P 2 δmW α ≃ O π Λ2, (2.13) where Λ is anand effective cut-off, representing the Standard to 16be valid, new physics appears. If Λthe≃scale mP atorwhich the GUT scale ∼Model ceases 10 GeV, the ‘small’ correction (2.13) will be much larger than the physical value of m2W. It would require ‘unnatural’ fine-tuning to choose the bare value of m2 to W be almost equal andright opposite tonumbers the ‘small’ correction (2.13), sowith that their combination happens to have the magnitude. Alternatively, supersymmetry introduces ancouplings, effective cut-off Λ by postulating equal of bosons and fermions identical in which case the corrections (2.13) cancel among themselves, leaving α δm2 ≃ O (m2 − m2 ), (2.14) W B F π 2 which is < ∼ m Wif 2 2 < 2 |mB − mF | ∼ O(1) TeV , (2.15) i.e., if supersymmetry appears at relatively low energy. Thisofnaturalness argument for low-energy is supported byconsistent several pieces indirect empirical evidence. One is supersymmetry that atthe of ric theparticles different gauge interactions measured atenergies low energies, thestrengths LEP accelerator, are with unification at high if thereparticularly are&low-mass supersymmet(Ellis et al. Amaldi etlight al. 1991; Langacker Luo Giunti et the al. 1991). A second is that1991b; LEP other precision are1991; fitted well by Standard Model if there is a and relatively Higgslow-energy boson withdata mass < 200 GeV, very consistent with the range m 130 GeV predicted by supersymmetry h < ∼ (Okada et al. 1991; Ellis et al. 1991a; Haber & Hempfling 1991). A third is that the minimal supersymmetric extension of the (MSSM) contains a good candidate χ<for cold dark matter, which hasStandard a suitableModel relic density if the supersymmetric mass scale ∼magnetic 1 TeV (Ellis et of al.the 1984; Goldberg 1983). Aet fourth mayBennett beprediction. provided by the anomalous moment muon, gµ −2 (Brown al. 2001; et al. on 2002), if itsWhen experimental value deviates significantly from the Standard Model the experimental, cosmological and theoretical constraints the MSSM, it considering is common assume the unseen spin-0 supersymmetric particles have some masstwo mto some that GUTall scale, and similarly for the unseen fermion 0 at massesuniversal m parameters ofinput this constrained 1/2. These MSSM (CMSSM) are restricted by the absences of supersymmetric particles at LEP: mχ± > ∼ 103 GeV, me˜ > ∼ 99 GeV, and at the Fermilab Tevatron collider. Article submitted to Royal Society J. Ellis 12 They are also restricted indirectly by the absence of a Higgs boson at LEP: mh > 114.4 GeV, andbybythethe factmeasurement that b → sγ of decay Standard Model, and potentially BNL gµ −is2,consistent as seen in with Fig. 9the (Ellis et al. 2003a; Lahanas & Naopoulos 2003). 800 700 700 600 600 m0 (GeV) m0 (GeV) tan = 10 , > 0 800 500 400 500 400 300 300 200 200 100 100 0 100 200 300 400 500 600 700 m1/2 (GeV) 800 900 1000 tan = 10 , < 0 0 100 200 300 400 500 600 700 800 900 1000 m1/2 (GeV) Figure 9. The (m1/2, m0) planes for (left panel) tan β = 10, µ > 0, and (right panel) tan β = 10, µ < 0. In each panel, the region allowed by the older cosmological constraint 2 0.1 ≤ Ωχh ≤ 0.3 has light shading, and the region allowed by the newer WMAP cosmological constraint 0.094 ≤ Ωχ h2 ≤ 0.129 has very dark shading. The region with dark (red) shading is disallowed because there the lightest supersymmetric particle would be charged. The regions excluded by b → sγ have medium (green) shading, and those in panels (a,d) that are favoured by gµ − 2 at the 2-σ level have medium (pink) shading. LEP constraints on the Higgs and supersymmetric particle masses are also shown (Ellis et al. 2003a). 2 also restricted by cosmological As shown the CMSSM 2 the relic bounds on the there, amount cold darkparameter matter, Ωspace . Since ρχ ...) =For mχnsome , and CDM χ1/m number density nχ increases ∝ of1/σ (χχ → ...) where σhis (χχ → , time, the2001a, relic ann ann density generically with increasing sparticle masses. the conservative upper limit on Ω h2Dutta hasAs been <but 0.3 (Lahanas et∝ al. 2000, CDM & 2001b; Barger & Kao 2001; Arnowitt 2002), the recent WMAP data allow this to be reduced to < 0.129 at the 2-σ level. seen in Fig. 9, this improved upper limit significantly improves the cosmological upper limit on the sparticle mass scale (Ellis et al. 2003a, Lahanas & Nanopoulos 2003). If there are other important components of the cold dark matter, the CMSSM parameters could lie below the dark (blue) strips in Fig. 9. In order todetecting facilitate discussion of physics reaches of different accelerators and strategies for dark matter, it the is convenient to focus onwould a limited number of benchmark scenarios that illustrate the various different supersymmetric possibilities (Battaglia et al. 2001). In many of these scenarios, supersymmetry be very easy to observe at the LHC, and many different types of super- Article submitted to Royal Society Dark Matter and Dark Energy 13 symmetric particleis might be for discovered. However, searches astrophysical dark matter may be competitive forlook some scenarios (Ellis etthe al.cosmic 2001). One strategy to relic annihilations out in (Pearce thefor galactic halo, which might produce detectable antiprotons or positrons in rays (Silk Srednicki As discussed here by Carr (2003), both the PAMELA et & al. 2002) and AMS (Aguilar et al. 2002) space experiments will be looking for these signals, though the1984). rates are not very promising in the benchmark scenarios we studied (Ellis et al. 2001). Alternatively, one might look for annihilations in the core of our galaxy, which might produce detectable gamma rays. As seen in the left panel of Fig. 10, this may be possible in certain benchmark scenarios (Ellis et al. 2001), although the rate is rather uncertain because of the unknown enhancement of relic particles in our galactic core. A third strategy is to look for annihilations inside the Sun or Earth (Silk et al. 1985), where the local density ofthem relic partiis enhanced in a calculable way bybound. scattering off matter, which causes to losecles energy and become gravitationally signature would be energetic neutrinos that might produce detectable muons. As also discussed by Carr (2003), several underwater and ice experiments areThe underway or plannedthen tohere look for this and strategy promising for several benchmark scenarios, as seen in thesignature, right panel of this Fig. 10 †. looks Figure 10. Left panel: Spectra of photons from the annihilations of dark matter particles in the core of our galaxy, in different benchmark supersymmetric models (Ellis et al. 2001). Right panel: Signals for muons produced by energetic neutrinos originating from annihila- tions of dark matter particles in the core of the Sun, in the same benchmark supersymmetric models (Ellis et al. 2001). The most satisfactory way look for supersymmetric relic particlesGoodis directly their scattering on dominant nuclei infor atoheavier low-background laboratory experiment man via & Witten 1985). There are two scattering matrix elements, independent normally nuclei, and spin-dependent -which whichare could fortypes lighterofHowever, elements such asand fluorine. Thespinbest experimentalasensitivities sobe farinteresting are for et spin-independent scattering, onebeen experiment has claimed positive signal (Bernabei al. 1998). this has not † It will be interesting to have such neutrino telescopes in different hemispheres, which will be able to scan different regions of the sky for astrophysical high-energy neutrino sources. Article submitted to Royal Society 14 J. Ellis confirmed by sensitivities, aInnumber ofbut other experiments, as for discussed herethe by sensitivity Kraus (2003) and Smith (2003). thealso benchmark scenarios the rates are considerably theFig. present experimental there prospects improving into the interesting range, as discussed byare Kraus (2003) and Smith (2003), asbelow seen in 11. Figure 11. Rates calculated for the spin-independent elastic scattering of dark matter par- ticles off protons in the same benchmark supersymmetric models (Ellis et al. 2001) as in Fig. 10. Overall, the et searches for that astrophysical supersymmetric matter dis- covery prospects (Ellis al. 2001) are comparable with thosedark of the LHChave (Battaglia et al. 2001). (e) Superheavy Dark Matter As discussed by Kolb (2003), it has beenand realized that interesting amounts oforsuperheavy particles with masses ∼recently 1014±5 GeV might have been produced non-thermally inofhere the very early Universe, either via prereheating following inflation, during bubble collisions, or cosmic by gravitational effects in be the expanding Universe. If any these superheavy particles were metastable they might able, seen in Fig. 12, to explain the ultra-high-energy rays Zatsepin-Kuzmin that seem (Takeda etchallenges, al.ascutoff 2002; Abu-Zayyad et al. 2002) to appear beyond the Greisen(GZK) (Greisen 1966; Zatsepin & Kuzmin 1966). Such models have to face some notably from upper limits on fractions of12±2 gamma at ultra-high energies, but might exhibit distinctive signatures such as a∼ galactic anisotropy (Sarkar 2002). Examples of such superheavy particles arethe the cryptons found inrays some models derived from string theory, which naturally have masses 10 GeV metastable protons), decaying viaAuger higher-order multiparticle interactions (Ellis etare al. 1990; Benakli et al. 1999). The Pierre experiment (Cronin et al. 2002) willand be able to tell us (like whether ultrahigh-energy Article submitted to Royal Society Dark Matter and Dark Energy 15 cosmic rays top-down really Auger, existmechanism, beyond are the ideas GZK cutoff, and, if so,some whether they areastrophysical due(Petrolini to some such or whether they bottom-up origin. Following for space experiments such as EUSO et al. exotic 2002) that could havethere even better sensitivities tohave ultra- high-energy cosmic rays. log10 E 3J(E) (eV 2m -2s -1sr -1) 26.0 25.5 25.0 AGASA Akeno 1 km2 Stereo Fly’s Eye Haverah Park Yakutsk 24.5 24.0 23.5 23.0 17 18 19 log10 E (eV) 20 21 Figure 12. Calculation of the spectrum of ultra-high-energy cosmic rays that might be produced by the decays (Sarkar 2002) of metastable superheavy particles. 3. Calculate it! Now that we a good ideadata. of the and energy content the Universe, and some prospects for have detecting it, the next taskmatter is to calculate it from firstofprinciples on violation the basis of microphysics and laboratory • Ωconjugation : As Sakharov taught usthermal (Sakharov baryogenesis the of bB, charge C and its combination CP1967), with parity, interactions that violate baryon number and aexpected departure from equilibrium. The first tworequires have been observed for quarks, and are within the Standard Model. B violation is also expected in the Standard Model, at the non-perturbative level. One might therefore wonder whether the observed cosmological baryon asymmetry have generated by the Standard Model alone, but(Carena the answer toAnbe nocould (Gavela etbeen al. 1994). However, it might be possible in the MSSM, itseems contains additional sources violation beyond the Standard Model etif 0, al. 2003). attractive alternative isCP leptogenesis & Yanagida 1986), according to which first the of converted heavyof singlet create a CPviolating asymmetry ∆L /= and then this isdecays partially intoneutrinos a baryon(Fukugita asymmetry by non-perturbative weak interactions. At the one-loop level, the asymmetry in the decays of one heavy singlet neutrino Article submitted to Royal Society J. Ellis 16 Ni due to exchanges of another one, Nj, is 1 1 ǫ = Im (Y ij ν ν ij 2 Mj 8π (Y Y †) Y †) f Mi , (3.1) ν ν ii where Yν is a matrix of Yukawa couplings between heavy singlet and light doublet neutrinos. The expression (3.1) involves a δare sum over the light leptons, henceit is independent the CP-violating MNS phase andnot thedirectly Majorana phases φ1,2 . Instead, is controlled byof extra phase parameters that accessible toand low-energy experiments. This leptogenesis scenario produces effortlessly athe baryon-to-photon ratio YB ofother the right order of magnitude. However, as seen in Fig. 13, CP-violating decay asymmetry (3.1) is explicitly independent of δ (Ellis & Raidal 2002). On the other hand, observables such as the charged-lepton-flavour-violating decays µ → eγ and τ → µγ may cast some indirect light on the mechanism of leptogenesis (Ellis et al. 2002a, b). Predictions for these decays may be refined if one makes extra hypotheses. MN1 GeV 1 1 MN1 GeV Figure 13. Comparison of the CP-violating asymmetries in the decays of heavy singlet neutrinos giving rise to the cosmological baryon asymmetry via leptogenesis (left panel) without and (right panel) with maximal CP violation in neutrino oscillations (Ellis & Raidal 2002). They are indistinguishable. One possibility is that the inflaton be heavy sneutrino (Murayama et al. 1993, 1994). would require amight ≃ a2perturbations, ×inflaton 1013singlet GeV, which is well within the range favoured by This seesaw models. The sneutrino model predicts (Ellis etdata al. 2003b) values of the spectral index ofmass scalar the fraction ofwithin tensor perturbations and other CMB observables that are consistent with the WMAP (Peiris et al. 2003) . Moreover, this model predicts a branching ratio for µ → eγ a couple of orders of magnitude of the present experimental upper limit. • ΩCDM : The relic density of supersymmetric matter The is calculable supersymmetric particle masses and Standard Model dark parameters. sensitivityin terms of Article submitted to Royal Society Dark Matter and Dark Energy 17 to theseAtparameters isfrom quitethese small in generic but mayonspace besupersymmetlarger in some exceptional regions corresponding toregions, ‘tails’ ofdata the regions, MSSM parameter (Ellis & Olive 2001). least away from the LHC ric parameters should enable the cold dark matter density to constant be calculated quite reliably. • Ω : The biggest challenge may be the cosmological vacuum energy. For a long time, Λ theorists tried to find reasons why the cosmological should vanish, but no convincing symmetry to guarantee this was ever found. Now cosmologists tell us that the vacuum energy actually does not vanish. Perhaps theorists’ previous failure should be reinterpreted as a success? If the vacuum isorindeed a constant, the hope that it could beSteinhardt calculated from perhaps first principles inenergy string M theory. Alternatively, asis argued here by 2003, the vacuum energy is presently relaxing towards zero, as in quintessence models (Maor et al. 2002). Such models are getting to be quite strongly constrained by the cosmological data, in particular those from high-redshift supernovae and WMAP (Spergel et al. 2003) as seen in Fig. 14, and it seems that the quintessence equation of state must be quite similar to that of a true cosmological constant (Spergel et al. 2003). Either way, the vacuum energy is a fascinating discovery that provides an exciting new opportunity for theoretical physics. Figure 14. Constraints on the equation of state of the dark energy from WMAP and other CMB data (WMAPext) combined with data on high-redshift supernovae, from the 2dF galaxy redshift survey and from the Hubble Space Telescope (Spergel et al. 2003). 4. Test it! 19 Laboratory experiments have the energy range up to about GeV, and quantum must become important around the There Planckare energy ∼ 10 where will new gravity physics appear in thisexplored vast energy range? reasons to 100GeV: Article submitted to Royal Society 18 J. Ellis < think thatIfthe origin ofisparticle masses will be found at some energy 103the GeV. If dark they ∼ a prototype are indeed due to some elementary scalar Higgs field, this willfor provide for the inflaton. the Higgs accompanied by supersymmetry, this may provide cold matter that fills the Universe. Some circumstantial evidence supersymmetry may be provided by the anomalous magnetic moment of the muon and by measurements offirst the 16 electroweak mixing angle θ the framework of grand unified theories. These would W , in operate at energy scales ∼ 10 GeV, far beyond the direct reach of accelerators. The hints in favour of such theories have already been provided by experiments on astrophysical (solar and atmospheric) neutrinos, and cosmology may provide the best probes of grand unified theories, e.g., via inflation and/or super-heavy relic particles, which might be responsible for the ultra-high-energy cosmic rays. Cosmology may also be providing our first information about quantum in the form of the vacuum energy. The LHC will extend the gravity, direct exploration of the energy frontier upmany ∼ideas 103 GeV. However, as these examples indicate, the unparallelled energies attained intothe early Universe and in some astrophysical sources may provide the most direct tests of for physics beyond the Standard Model. The continuing dialogue between the two may tell us the origins of dark matter and dark energy. References Abadi, M. G. et al. 2002 arXiv:astro-ph/0211331. Abu-Zayyad, T. et al. 2002 arXiv:astro-ph/0208301. Aguilar, M. et al. 2002 Phys. Rept. 366, 331. Ahmad, Q. R. et al. 2002a Phys. Rev. Lett. 89, 011301 [arXiv:nucl-ex/0204008]. Ahmad, Q. R. et al. 2002b Phys. Rev. Lett. 89, 011302 [arXiv:nucl-ex/0204009]. Ahn, M. H. et al. 2003 Phys. Rev. Lett. 90, 041801 [arXiv:hep-ex/0212007]. Amaldi, U., de Boer, W. & Furstenau, H. 1991 Phys. Lett. B 260, 447. Arnowitt, R. & Dutta, B. 2002 arXiv:hep-ph/0211417. Asztalos, S. J. et al. 2002 Astrophys. J. 571, L27 [arXiv:astro-ph/0104200]. Barbieri, R., Ellis, J. R. & Gaillard, M. K. 1980 Phys. Lett. B 90, 249. Barger, V. & Kao, C. 2001 Phys. Lett. B518, 117 [arXiv:hep-ph/0106189]. Battaglia, M. et al. 2001 Eur. Phys. J. C 22, 535 [arXiv:hep-ph/0106204]. Benakli, K., Ellis, J. R. & Nanopoulos, D. V. 1999 Phys. Rev. D 59, 047301 [arXiv:hepph/9803333]. Bennett, C. L. et al. 2003 arXiv:astro-ph/0302207. Bennett, G. W. et al. 2002 Phys. Rev. Lett. 89, 101804 [Erratum-ibid. 89, 129903] [arXiv:hep-ex/0208001]. Bernabei, R. et al. 1998 Phys. Lett. B 436, 379. Bond, J. R. 2003 talk at this meeting. Bond, J. R. & Crittenden, R. G. 2001 arXiv:astro-ph/0108204. Brown, H. N. et al. 2001 Phys. Rev. Lett. 86, 2227 [arXiv:hep-ex/0102017]. Carena, M. et al. 2003 Nucl. Phys. B 650, 24 [arXiv:hep-ph/0208043]. Carr, J. 2003 talk at this meeting. Casas, J. A. & Ibarra, A. 2001 Nucl. Phys. B 618, 171 [arXiv:hep-ph/0103065]. Chung, D. J., Crotty, P., Kolb, E. W. & Riotto, A. 2001 Phys. Rev. D 64, (2001) 043503 [arXiv:hep-ph/0104100]. Cronin, J. et al. 2002 http://www.auger.org/. Article submitted to Royal Society Dark Matter and Dark Energy 19 Crotty, P., Lesgourgues, J. & Pastor, S. 2003 arXiv:astro-ph/0302337. Cyburt, R. H., Fields, B. D. & Olive, K. A. 2003 arXiv:astro-ph/0302431. De Rú jula, A., Gavela, M. B. & Hern´andez, P. 1999 Nucl. Phys. B547, 21 [arXiv:hepph/9811390]. Eguchi, K. et al. 2003 Phys. Rev. Lett. 90, 021802 [arXiv:hep-ex/0212021]. Elgaroy, O. et al., 2002 Phys. Rev. Lett. 89, 061301 [arXiv:astro-ph/0204152]. Ellis, J. R. & Olive, K. A. 2001 Phys. Lett. B 514, 114 [arXiv:hep-ph/0105004]. Ellis, J. R. & Raidal, M. 2002 Nucl. Phys. B 643, 229 [arXiv:hep-ph/0206174]. Ellis, J. R., Hagelin, J. L., Nanopoulos, D. V., Olive, K. A., & Srednicki, M. 1984 Nucl. Phys. B 238, 453. Ellis, J. R., Lopez, J. L. & Nanopoulos, D. V. 1990 Phys. Lett. B 247, 257. Ellis, J. R., Ridolfi, G. & Zwirner, F. 1991a Phys. Lett. B 257, 83. Ellis, J. R., Kelley, S. & D. V. Nanopoulos 1991b Phys. Lett. B 260, 131. Ellis, J. R. et al. 2001 Eur. Phys. J. C 24, 311 [arXiv:astro-ph/0110225]. Ellis, J. R. et al. 2002a Nucl. Phys. B 621, 208 [arXiv:hep-ph/0109125]. Ellis, J. R., et al. 2002b Phys. Lett. B 528, 86 [arXiv:hep-ph/0111324]. Ellis, J. R. et al. 2003a arXiv:hep-ph/0303043. Ellis, J. R., Raidal, M. & Yanagida, T. 2003b arXiv:hep-ph/0303242. Fukuda, Y. et al. 1998 Phys. Rev. Lett. 81, 1562 [arXiv:hep-ex/9807003]. Fukugita, M. & Yanagida, T. 1986 Phys. Lett. B174, 45. Gavela, M. B. et al. Nucl. Phys. B 430, 382 [arXiv:hep-ph/9406289]. Gell-Mann, M., Ramond, P. & Slansky, R. 1979 Proceedings of the Supergravity Stony Brook Workshop, New York, 1979 (eds. P. Van Nieuwenhuizen and D. Freedman). NorthHolland, Amsterdam. Giunti, C., Kim, C. W. & Lee, U. W. 1991 Mod. Phys. Lett. A 6, 1745. Goldberg, H. 1983 Phys. Rev. Lett. 50, 1419. Goodman, M. W. & Witten, E. 1985 Phys. Rev. D 31, 3059. Greisen, K. 1966 Phys. Rev. Lett. 16, 748. Haber, H. E. & Hempfling, R. 1991 Phys. Rev. Lett. 66, 1815. Hagiwara, K. et al. 2002 Phys. Rev. D 66, 010001. Hinshaw, G. et al. 2003 arXiv:astro-ph/0302217. Irastorza, I. G. et al. 2002 arXiv:astro-ph/0211606. Klapdor-Kleingrothaus, H. V. et al. 2001 Eur. Phys. J. A 12, 147 [arXiv:hep-ph/0103062]. Klapdor-Kleingrothaus, H. V., et al. I. V. 2002 Mod. Phys. Lett. A 16, 2409 [arXiv:hepph/0201231]. Kogut, A. et al. 2003 arXiv:astro-ph/0302213. Kolb, E. W. 2003 talk at this meeting. Kraus, H. 2003 talk at this meeting. Lahanas, A. B. & Nanopoulos, D. V. 2003 arXiv:hep-ph/0303130. Lahanas, A. B., Nanopoulos, D. V. & Spanos, V. C. 2000 Phys. Rev. D 62, 023515 [arXiv:hep-ph/9909497]. Lahanas, A. B., Nanopoulos, D. V. & Spanos, V. C. 2001a Mod. Phys. Lett. A 16, 1229 [arXiv:hep-ph/0009065]. Lahanas, A. B., Nanopoulos, D. V. & Spanos, V. C. 2001b Phys. Lett. B518, 94 [arXiv:hepph/0107151]. Langacker, P. & Luo, M. X. 1991 Phys. Rev. D 44, 817. Lobashev, V. M. et al. 1999 Phys. Lett. B 460, 227. Maiani, L. 1979 Proceedings of the 1979 Gif-sur-Yvette Summer School on Particle Physics. Article submitted to Royal Society 20 J. Ellis Maki, Z. Nakagawa, M. & Sakata, S. 1962 Prog. Theor. Phys. 28, 870. Maor, I. et al. 2002 Phys. Rev. D 65, 123003 [arXiv:astro-ph/0112526]. Minakata, H. & Sugiyama, H. 2002 arXiv:hep-ph/0212240. Mohapatra, R. & Senjanovic, G. 1980 Phys. Rev. Lett. 44, 912. Murayama, H. et al. 1993 Phys. Rev. Lett. 70, 1912. Murayama, H. et al. 1994 Phys. Rev. D 50, 2356 [arXiv:hep-ph/9311326]. Navarro, J. 2003 talk at this meeting. Okada, Y., Yamaguchi, M. & Yanagida, T. 1991 Prog. Theor. Phys. 85 (1991), 1. Osipowicz, A. et al. 2001 arXiv:hep-ex/0109033. Pakvasa, S. & Valle, J. W. 2003 arXiv:hep-ph/0301061. Peacock, J. A. 2003a arXiv:astro-ph/0301042. Peacock, J. A. 2003b talk at this meeting. Pearce, M. et al. 2002 Nucl. Phys. Proc. Suppl. 113, 314. Peiris, H. V. et al. 2003 arXiv:astro-ph/0302225. Perlmutter, S. 2003 talk at this meeting. Perlmutter, S. & Schmidt, B. P. 2003 arXiv:astro-ph/0303428. Petrolini, A. et al. 2002 Nucl. Phys. Proc. Suppl. 113, 329. Rees, M. 2003 talk at this meeting. Sakharov, A. D. 1967 Pisma Zh. Eksp. Teor. Fiz. 5, 32 Sarkar, S. 2002 arXiv:hep-ph/0202013. Schneider, P. 2003 talk at this meeting. Sikivie, P. 1996 Phys. Today 49N12, 22 [arXiv:hep-ph/9506229]. Silk, J. & Srednicki, M. 1984 Phys. Rev. Lett. 53, 624. Silk, J., Olive, K. A. & Srednicki, M. 1985 Phys. Rev. Lett. 55, 257. Smith, P. 2003 talk at this meeting. Spergel, D. N. et al. 2003 arXiv:astro-ph/0302209. Steinhardt, P. 2003 talk at this meeting. Takeda, M. et al. 2002 arXiv:astro-ph/0209422. ’t Hooft, G. 1979 Recent Developments in Gauge Theories, Proceedings of the Nato Ad- vanced Study Institute, Cargese, 1979 (eds. G. ’t Hooft et al.). Plenum Press, NY, 1980. van Bibber, K. 2003 talk at this meeting. Wark, D. 2003 talk at this meeting. Weinheimer, W. et al., 1999 Phys. Lett. B 460, 219. Witten, E. 1981 Phys. Lett. B 105, 267. Yamamoto, K. et al. 2001 arXiv:hep-ph/0101200. Yanagida, T. 1979 Proceedings of the Workshop on Unified Theories and Baryon Number in the Universe, Tsukuba, Japan 1979 (eds. A. Sawada and A. Sugamoto). KEK Report No. 79-18, Tsukuba. Zatsepin, G. T. & Kuzmin, V. A. 1966 JETP Lett. 4, 78. Article submitted to Royal Society
