4 P. Grang´eet al.: The fine-tuning problem revisited in the light of the Taylor-Lagrange renormalization scheme
the necessary (ultra-soft) cut-o in the calculation of the integral. After an evident change of variable, we get 3M 4 X M 2 ⇥ = H dX f H X (16) 1b,H 32⌅2v2 X +1 2 ↵0 ⌃ ⌥ 3M 4 1 M 2 = H dX 1 f H X . 32⌅2v2 X +1 2 ↵0 ⌃ ⌥ ⌃ ⌥ The first term under the integral can be reduced to a pseudo-function, using (11). Indeed, with Z =1/X,we have dZ M 2 1 dXf(X)= f H (17) Z2 2 Z ↵0 ↵0 ⌃ ⌥ 1 = dZ Pf Z2 ↵0 ⌃ ⌥ 1 = =0. Z ⇧ where the complications start ⇧ a ⇧ one explicit mass scale of the Standard Model is a mass-squared parameter The notation f(u) simply indicates⇧ that f(u) should be taken at the value |u = a, the lower limit of integration be- defining the leading orderFig. shape 1. Radiativeof the Mexican corrections Hat to the Higgs mass in the Stan- dard Model in second order of perturbation theory. For simplic- ing taken care of by the definition of the pseudo-function. V()ϕ D 2 n mass. The “cancellation” of massless bosons to give ity, we have not shown contributions from ghosts or Goldstone This result is reminiscent of the property d p(p ) = 0, a massive boson, as anticipated by Anderson and • to get the correct shape for electroweak developed in the 1964 papers, is the famous Higgs for any n, in DR [15]. mechanism; for their contributions to its discovery, bosons. 2 Englert and Higgs received this year’s Nobel Prize symmetry breaking, m0 < 0 (tachyonic) ⌦ in Physics. (For more, see page 10 of this issue.) The self-energy thus writes As recounted in his 2010 talk “My Life as a 1 Boson,” Higgs submitted his second paper of 1964 2 2 4 to Physics Letters, which promptly rejected it.10 ! V0 = m0 H + H 4 2 Shocked at that setback, he revised and expanded shown in Fig. 1. We have| | left out,2 | for| simplicity, all contri- 3MH 1 MH the manuscript, adding the key observation that ⇥1b,H = dX f X . (18) when applied to a charged spinless boson, the Higgs butions coming from ghosts and Goldstone bosons. Each 2 2 2 mechanism leaves behind a neutral spinless boson. 32⌅ v 0 X +1 That neutral particle—the Higgs boson—has a mass • assume electroweak symmetry ↵ ⌃ ⌥ determined by the shape of the Mexican-hat poten- Re ϕ diagram in this figure gives a contribution to the self- tial energy density, but that mass cannot be expressed 2 2 2 in terms of the mass generated for the gauge boson. 4 P. Grang´eetIm ϕ al.: The fine-tuning problem revisited in the light of the Taylor-Lagrangebreaking, renormalization scheme and start computing quantum Higgs sent the improved revision to a different jour- energy i⇥(p ), where p is the four-momentum of the The constant factor MH / in the argument of the test nal, Physical Review Letters, and it was promptly Figure 2. The Mexican-hat potential energy density considered by the necessary (ultra-soft) cut-o in the calculation of the accepted. Jeffrey Goldstone in his seminal 1961 paper.2 The energy density is a external particle,corrections and we involving have the Higgs boson function has no physical meaning since it can be absorbed At first, theorists thought that the most suitable integral. function of the real (Re) and imaginary (Im) values of a spinless field ϕ. After an evident change of variable, we get 2 application of spontaneous symmetry breaking to In the context of the electroweak theory developed later in the decade, by a rescaling of the arbitrary dimensionless scale ⇤ .This particle physics was in the arena of the strong inter- the yellow ball at the top of the hat would represent the symmetric 4 2 2 2 2 actions. Only in 1967 did Weinberg, and, independ- 3MH X MH solution for the potential, in which the photon, W bosons, and Z boson ⇥1b,H = dX f X (16) ently, Salam, realize that the Higgs mechanism of- •2 2 The leadingM2 = orderM + corrections⇥(M ) . involve (13) are all massless. The blue ball in the trough represents the solution after 32⌅ v 0 X +1 H 0 H can be easily seen by applying the Lagrange formula (6) fered an elegant explanation of the weak interactions. ↵ ⌃ ⌥ symmetry breaking. In that solution the W and Z bosons are massive 3M 4 1 M 2 2 2 In their model, which is now the electroweak portion = H dX 1 f H X . and the photon remains massless. The steepness of the trough is related 2 2 2 with the intrinsic scale a = M / and k = 0. It can thus of the standard model, four Higgs fields are related 32⌅ v 0quadratically-divergent X +1 integrals over H to the mass of the Higgs boson. ↵ ⌃ ⌥ ⌃ ⌥ by a gauge symmetry of the type introduced by 1 Yang and Mills. Three Goldstone bosons are eaten The first term under the integral can be reduced to a safely be removed . to give large masses to the W+, W−, and Z bosons that decay process into two virtual Z bosons, each of pseudo-function,Using using avirtual (11).na¨ıve Indeed, momenta. cut-o with Z =1/Xto,we regularize Keep going the amplitudes, by cutting these mediate the weak interactions. An added bonus, not which, in turn, decays into an electron–positron or have We can now apply the Lagrange formula for k = 0. foreseen by Higgs and the rest, is that the Higgs muon–antimuon pair. The other shows the Higgs dZ M 2 1 field also gives mass to quarks and leptons, the ele- decay into two photons. The image on pages 28 and radiativedXf( correctionsXoff)= thef integralsH lead(17) to in thethe well UV with known some mass correc- Z2 2 Z Using the boundary condition on the support of the test mentary fermions that make up matter. 29 shows a visualization of the data produced by a ↵0 ↵0 ⌃ ⌥ The mass of the Higgs boson left behind is not Higgs boson candidate at the LHC; the four decay 1 tion = dZ Pf predicted, but the interactions of the Higgs with products are muons or antimuons—a pair of each— arbitraryZ 2 ΛC cut-off scale function other elementary particles can be precisely com- whose tracks are depicted as red lines. ↵0 ⌃ ⌥ puted as a function of its mass and the masses of the The experimental results so far suggest that the 1 2 = =0. other particles. Furthermore, the exchange of virtual particle observed at the LHC is indeed a Higgs Z 2 Xt H(X)=⇤ Xg (X) , (19) ⇧ 3 Higgs bosons generates an attractive short-range boson, though not necessarily possessing exactly 2 2 ⇧ C 2 2 2 2 ⇥ force. If the Higgs boson is an elementary particle, the properties postulated by the standard model. a ⇧ TheM notation=f(uM) simply+ indicates⇧ that f(u) shouldM be +2M + M 4m + ... , as so far appears to be the case, then that force is The discovery itself is based on large excesses of H | 0 2 2 H W Z t Fig. 1. Radiative corrections to the Higgs mass in the Stan- taken at the value u = a, the lower limit of integration be- we finally get, in the limit f 1 every bit as fundamental as the gauge-boson-medi- Higgs-like events in the two decay channels de- 8⌅ v dard Model in second order of perturbation theory. For simplic- ing taken care of by the definition of the pseudo-function. ated forces of the standard model. In that case, the scribed above, supported by less conclusive but D 2 n ⇤ ity, we have not shown contributions from ghosts or Goldstone This result is reminiscent of the property d p(p ) = 0, (14) Higgs would be the first fundamental force media- compatiblein absence excesses observed of insomething other channels. (a symmetry,for any n, in DR or [15]. other conspiracy),⇤ the electroweak scale can⌅ tor ever detected that is not a gauge boson. Figurebosons. 4 displays CMS data for the four-lepton The self-energy thus writes ⌦ 4 ⇥ channel. The measured mass is about 126 GeV/c2, where mt,MW,Z and MH are the2 masses of the top quark, 3M X dt The discovery intermediate between the mass of the Z boson and H onlyshown inbe Fig. obtained 1. We have left out, by for simplicity, fine-tuning all contri- a bare3M parameter4 1 Magainst2 (cut-off) dependent radiative The ATLAS and CMS (Compact Muon Solenoid) ex- the mass of the top quark. ⇥ = H dX f H X . (18) ⇥1b = dX X butions coming from ghosts and Goldstone bosons. Each W,1 Zb,H and 32⌅2v2 HiggsX +1 bosons 2 respectively, and v is the vacuum 2 2 periments at the LHC were built to probe the mech- The new particle cannot be a spin-1 particle be- ↵0 ⌃ ⌥ 32⌅ v X +1 t anisms of electroweak symmetry breaking and the causecorrections thediagram decay of in such this an figure object (or gives into the two a photons contribution so -iscalled to the self-naturalness mess) rc 0 1 2 2 2 particle origins of dark matter. Wired up with about energy i⇥(p ), where p is the four-momentum of the The constant factor M / in the argument of the test ↵ ⌃ ⌥ ↵ forbidden by a general result known as the Landau– expectationH value of the Higgs potential in the Standard a hundred million readout channels each and made Yang external theorem. particle, Its wavefunction and we have does not change function has no physical meaning since it can be absorbed 4 up of many thousands of tons of material that inter- sign when operated on by CP (a product of the dis- by a rescaling of the arbitrary dimensionless scale ⇤2.This 3MH 2 2 2 2 Model. The dots include logarithmic corrections in C as acts with the particles emanating from the LHC’s crete symmetries of chargeM conjugationH = M0 + ⇥and(M coordi-H ) . (13) can be easily seen by applying the Lagrange formula (6) = ln ⇤ . (20) high-energy proton–proton collisions, the two de- nate inversion, or parity), as the pion wavefunction with the intrinsic scale a = M 2 / 2 and k = 0. It can thus 2 2 H 32⌅ v tectors have already managed to capture and recon- does. So the new particle is either unchanged by CP, wellsafely be asremoved contributions1. independent of C in the large C 11 struct many rare Higgs boson candidate events. as a HiggsUsing boson a na¨ıve is, or cut-oit couldto be regularize a CP-violating the amplitudes, these We can now apply the Lagrange formula for k = 0. Since Higgs bosons decay into other particles admixtureradiative if there corrections exists a new lead source to the of well matter– known mass correc- limit.Using the boundary condition on the support of the test ⇥ −22 after about 100 yoctoseconds (10 seconds), the col- antimattertion asymmetry related to the Higgs. The pro- function We shall come back in Sec. 4 to the meaning of the limiting lider searches involve several different decay signa- duction rate of the particle and the degree to which 2 2 Xt H(X)=⇤ Xg (X) , (19) tures or channels. Figure 3 illustrates the two most it decays into2 different2 3 channels C 2 appear consistent2 2 2 The calculation⇥ of the four di erent types of contribu- MH = M0 + MH +2MW + MZ 4mt + ... , procedure f 1 in the presence of a physical cut-o important channels used by ATLAS and CMS in with the standard-model8⌅2 vpredictions2 for the Higgs we finally get, in the limit f 1 ⇤ their quest for the Higgs. One represents the Higgs boson, although the experimental⇤ uncertainties are ⌅ (14) tions shown in Fig. 1 is very easy in TLRS. Let us first ⇤ 4 ⇥ where mt,MW,Z and MH are the masses of the top quark, 3MH X dt eff to define the domain of validity of the (e ective) www.physicstoday.org December 2013 Physics Today 31 ⇥1b = dX X W, Z and Higgs bosons respectively, and v is the vacuum 32⌅2v2 X +1 t expectation value of the Higgs potential in the Standard illustrate the↵0 calculation⌃ ⌥ ↵1 of the simple Higgs loop contri- 3M 4 underlying theory. Model. The dots include logarithmic corrections in C as = H ln ⇤2 . (20) bution 32 in⌅2v2 Fig. 1.b. In Euclidean space one has 2 well as contributions independent of C in the large C It is easy to see that using a na¨ıve cut-o on k one limit. We shall come back in Sec. 4⇥ to the meaning of the limiting E The calculation of the four di erent types of contribu- procedure f 1 in the presence of a physical cut-o tions shown in Fig. 1 is very easy in TLRS. Let us first ⇤ would have obtained, in the large C limit eff to define the domain of validity of2 the (e ective) 4 2 illustrate the calculation of the simple Higgs loop contri- underlying theory. 3iMH d kE 1 kE bution in Fig. 1.b. In Euclidean space one has 2 Iti is⇥ easy1b,H to see that= using a na¨ıve cut-o on kE one f , (15) would have obtained, in the large limit2 4 2 2 2 2 2 3iM 2 d4k 1 k2 2Cv (2⌅) k + M H E E 0 E H C 3MH 2 2 C i⇥1b,H = 2 4 2 2 f 2 , (15) 2 2 2v 0 (2⌅) kE + MH C 3MH 2 2 C ↵ ⌃ ⌥ ⇥ = M ln . (21) ↵ ⌃ ⌥ ⇥1b,H = C MH ln . (21) 1b,H C H 2 32⌅2v2 M 2 2 2 2 ⌃ H ⌥ 32⌅ v M where kE is the square of the four-momentum k in Eu- 2 H clidean space. As already mentioned in Sec. 2, is an where1 This couldk also be doneis more the directly square by choosing a par-of the four-momentum k in Eu- ⌃ ⌥ arbitrary momentum scale. The test function f provides ticular value for E. clidean space. As already mentioned in Sec. 2, is an 1 This could also be done more directly by choosing a par- arbitrary momentum scale. The test function f provides ticular value for . the sure cure: SUSY SUSY introduces superpartner particles, and the extra diagrams with the superpartners cancel the divergences of the Standard Model diagrams
SUSY models have many other nice features: The electroweak scale is derived from the SUSY-breaking scale, and the Higgs mass- squared parameter is automatically tachyonic due to quantum effects Once you have superpartners at the electroweak scale, SUSY models make sense up to around the Planck scale ~ 1019 GeV, where quantum gravity presumably becomes important
SUSY models are the expected lower energy outcome of string theory, which may be the correct description of quantum gravity And of course you predict the imminent discovery of all the superpartner particles, since they are connected to the electroweak scale. in the next set of lectures we are going to go back an forth between Dark Matter, SUSY and other frameworks that attempt to solve the gauge hierarchy problemUPHFUIFSXJUIUIF%.QSPCMFN
Monday, Part 1
Dark Matter from astrophysical observations Dark Matter from Cosmological observations Dark Matter and the Electroweak Scale
Monday, WhatWhat isis DarkDark Matter?Matter?
Dark Matter Luminous Matter FirstFirst detectiondetection ofof darkdark mattermatter
FritzFritz ZwickyZwicky (1933):(1933): DarkDark mattermatter inin thethe ComaComa ClusterCluster HowHow MuchMuch DarkDark MatterMatter isis ThereThere inin TheThe Universe?Universe?
ΩΩΜ == ρρΜ // ρρc ~2% RecentRecent measurements:measurements: (Luminous)
ΩΩΜ ∼∼ 0.3,0.3, ΩΩΛ ∼∼ 0.70.7
ΩΩLum ∼∼ 0.0050.005 ~98% (Dark) HowHow DoDo WeWe KnowKnow ThatThat itit Exists?Exists?
!! CosmologicalCosmological ParametersParameters ++ InventoryInventory ofof LuminousLuminous materialmaterial !! DynamicsDynamics ofof galaxiesgalaxies !! DynamicsDynamics andand gasgas propertiesproperties ofof galaxygalaxy clustersclusters !! GravitationalGravitational LensingLensing @galactic, sub-galactic and cluster of galaxies scale: 1. galactic rotation curves 2. weak gravitational lensing of distant galaxies by foreground structure 3. weak modulation of strong lensing of massive elliptical galaxies 4. velocity dispersions of stars in galaxies imply that contain O(103) more mass than can be attributed to their luminosity
Monday, @cosmological scales The cosmic microwave background anisotropies
Monday, May 16, 2011 Monday, May 16, 2011 23% CDM
Monday, 23% of critical density of Universe 84% of non relativistic matter in universe gravitationally clumps, necessary for galaxy formation and cluster formation DARK (no electromagnetic interactions) (nearly) collisionless much weaker than weak cross section for direct detection
Monday, May 16, 2011 40 years ago
Monday, May 16, 2011 40 years ago
Monday, DynamicsDynamics ofof GalaxiesGalaxies II
Galaxy ≈ Stars + Gas + Dust + Supermassive Black Hole + Dark Matter DynamicsDynamics ofof GalaxiesGalaxies IIII
Visible galaxy
Observed
Vrot
Expected R
R Dark matter halo Visible galaxy 73 years ago
Monday, May 16, 2011 Zwicky-virial theorem-DM Zwicky used the virial theorem on the Coma Cluster and concludes that something is fishy with the mass budget of the cluster
Monday, CHANDRA X-ray Virial on Coma
Given that the gas observed by Chandra has a radius of 1 Mpc, estimate the total mass inside this radius including DM using the virial theorem units
max energy of photon detected by Chandra is 10 keV=1.6 10-15 Joules -27 Constraints on the mass distribution in Coma derived mp=1.7 10 kg from kinematical and X-ray techniques. 1pc=3.1 1016 m 3 -1 -2 GN=6.7 10-11 m kg s
1 M=1.98 1030 kg
Monday, DynamicsDynamics ofof GalaxyGalaxy ClustersClusters
Balance between kinetic and potential energy → Virial theorem: v2 R M = vir G HotHot GasGas inin GalaxyGalaxy ClustersClusters
High mass required to keep the hot gas from leaving the cluster!
If gas in hydrostatic equilibrium → Luminosity and temperature profile → mass profile X-ray gas, T=107—108 K Going to the 90’s
K. G. Begeman, A. H. Broeils and R. H. Sanders, 1991, MNRAS, 249, 523 It is unclear to-date whether galaxies present DM profiles that are cuspy or shallow in their innermost regions Optical, X-ray (pink) and gravitational lens map (blue) of the "bullet cluster" of galaxies. GravitationalGravitational LensingLensing GravitationalGravitational LensingLensing IIII BaryonicBaryonic andand NonNon--BaryonicBaryonic DarkDark MatterMatter II Baryons: Ordinary matter made out of three quarks, like protons and neutrons BBNS modelling + measurements of primordial abundances
or CMBR analysis →Ωbaryons≈0.045
ΩBaryonic≈ 0.045 →
ΩNon-baryonic≈ 0.25 →
ΩM = ΩBaryonic + ΩNon-baryonic ≈ 0.3 Dark Matter What DM? HEPAP/AAAC DMSAG Subpanel (2007) How much DM? DM characterization
Interaction strength (cross section) mass of DM candidate 10-36 - 10+34 (pb) 10-33 - 10+18 (GeV)
Monday, May 16, 2011 The Weak Scale
From contact interaction 2 to a gauge boson: the GFE behavior was tamed at short length scales weak scale~100 GeV
Monday, May 16, 2011 DM-Weak Scale Serendipity A schematic of the comoving number density of a stable species as it evolves through the process of thermal freeze-out.
<σv> is the thermally averaged cross section for two “wimps” to annihilate to ordinary particles (annihilation cross section)
The relic density (relic abundance) is
for: mX~mWeak~100 GeV gX~gW~0.6
Kolb, Turner Ωx=0.1 we discussed a lot of caveats in the form of “spherical cows”
Monday, May 16, 2011 Annihilation, Scattering, Production
!" !" Efficient annihilation now (Indirect detection) (Particle colliders)
q q production now Efficient
Efficient scattering now (Direct detection)
Monday, May 16, 2011 Monday, May 16, 2011 Indirect Signals of Dark Matter Annihilation (in the news)
Photons (Fermi/LAT?) Charged Cosmic Rays antiprotons (not!) positrons (yes?) electrons (high energy excess?) Monday, May 16, 2011
Monday, May 16, 2011 indirect detection of WIMP annihilation in the galaxy? usual annihilation into weak bosons/higgses would give too many anti protons Pamela, Atic, Fermi, Hess signals imply 100-1000X larger rate than the <σ v> which gives observed relic abundance for standard WIMP (3 x 10-26 cm3/s) not dark matter? (maybe nearby pulsar?) non thermal dark matter production astrophysical boost factor from clumpiness
fashionable: “Sommerfeld enhancement” Hisano et al, Pospelov & Ritz, Arkani Hamed et al
Monday, May 16, 2011 Summary of experimental situation on direct, indirect
PAMELA, Fermi and other cosmic ray expts may have provided first clues to identity of dark matter or found high energy charged particles created by a pulsar or other astrophysical source if dark matter, must explain large annihilation cross section and lack of antiprotons DAMA increases the puzzle if correct waiting for CDMS new results and the LHC Monday, May 16, 2011 Summary Part 1 we have a big [huge] problem with the DM in the universe we have many ways to go about it but what we know is outdated very fast (i.e. DM distributions in galaxies, clusters etc) the particle physics input and understanding is essential but still far from complete
Monday, May 16, 2011 GSPNIUUQBSYJWPSHQEGWQEG
Dark Matter and Dark Energy 39
6. Glossary of Technical Terms and Acronyms‡ ACBAR (Arcminute Cosmology Bolometer Array Receiver). Abolometer- based CMB temperature experiment that characterized the damping tail of CMB temperature fluctuations. It had a 16-element array and 4 arc-minute resolution at 150 GHz (http://cosmology.berkeley.edu/group/swlh/acbar/). Acoustic peaks. Wiggles in the CMB temperature and polarization power spectra that arise from acoustic oscillations in the primordial baryon-photon fluid. Adiabatic perturbations. Primordial density perturbations in which the spatial distribution of matter is the same for all particle species (photons, baryons, neutri- nos, and dark matter). Such perturbations are produced by thesimplestinflation models. AdS/CFT (Anti-de Sitter space/conformal field theory) correspondence. Aconjecturedequivalencebetweenstringtheoryinonespaceandaconformalgauge theory on the boundary of that space. AMANDA. An astrophysical-neutrino observatory in deep Antarctic ice (http://amanda.uci.edu). AMS (Alpha Magnetic Spectrometer). ANASAspace-basedcosmic-ray- antimatter experiment (http://ams.cern.ch). APEX-SZ (Atacama Pathfinder EXperiment-Sunyaev-Zel’dovich). Abolometer- based experiment designed to search for galaxy clusters via the Sunyaev-Zel’dovich effect. The 12-meter diameter APEX telescope gives one arc-minute resolution at 150 GHz (http://bolo.berkeley.edu/apexsz/). Axion. AscalarparticlethatarisesinthePeccei-Quinnsolutionto the strong-CP problem. If the axion has a mass near 10−5 eV, then it could make up the dark matter. Baksan experiment. ARussianundergroundastrophysical-neutrinotelescope (http://www.inr.ac.ru/INR/Baksan.html). BICEP (Background Imaging of Cosmic Extragalactic Polarization). A bolometer-based CMB polarization experiment sited at the South Pole. It uses a small refractive telescope to achieve 0.6 degree resolutionat150GHz (http://www.astro.caltech.edu/ lgg/bicep front.htm). ∼ Baryons. In cosmology, this term refers to ordinary matter composed ofneutrons, protons, and electrons. BBN (Big-bang nucleosynthesis). The theory of the assembly of light nuclei from protons and neutrons a few seconds to minutes after the big bang. BBO (Big Bang Observer). Amissionconcept,currentlyunderstudy,fora post-LISA space-based gravitational-wave observatory designed primarily to seek inflationary gravitational waves (http://universe.nasa.gov/program/bbo.html).
‡Prepared in collaboration with Adrian Lee. Dark Matter and Dark Energy 40
BESS (Balloon-borne Experiment with a Superconducting Spectrome- ter). AJapanese-UScollaborativeseriesofballoon-borneexperiments to measure antimatter in cosmic rays (http://www.universe.nasa.gov/astroparticles/programs/bess/). Big rip. ApossibleendfatefortheUniverseinwhichtheUniverseexpands to infinite size in finite time, ripping everything apart as it does so. Boltzmann equations. Equations for the evolution of the momentum distribu- tions for various particle species (e.g., baryons, photons,neutrinos,anddark-matter particles). BOOMERanG. Aballoon-borneCMB-fluctuationexperimentthatreportedin 2000 the first measurement of acoustic-peak structure in the CMB. It used a bolome- ter array and had 10 arc-minute resolution at 150 GHz (http://cmb.phys.cwru.edu/boomerang). Brane or p-brane.Ap-dimensional subspace of some higher-dimensional subspace. As an example, in some string theories, there may be many extradimensions,but standard-model fields are restricted to lie in a 4-dimensional volume that is our 3+1-dimensionalspacetime. CACTUS. Aheliostatarrayfor> 40 GeV gamma-ray astronomy (http://ucdcms.ucdavis.edu/solar2). CAPRICE (Cosmic AntiParticle Ring Imaging Cherenkov Experiment). A1994balloon-bornecosmic-ray-antimatterexperiment (http://www.roma2.infn.it/research/comm2/caprice). CBI (Cosmic Background Imager). An interferometric CMB telescope de- signed to measure the smallest-angular-scale structure of the CMB (http://www.astro.caltech.edu/ tjp/CBI). ∼ CAPMAP (Cosmic Anisotropy Polarization MAPper). ACMBpolariza- tion experiment using the Lucent Technologies 7-meter diameter telescope at Craw- ford Hill NJ and coherent detectors (http://quiet.uchicago.edu/capmap/). CDMS (Cryogenic Dark Matter Search). AU.S.experimentdesignedtolook for WIMPs (http://cdms.berkeley.edu). CELESTE. Aheliostatarrayfor 100 GeV gamma-ray astronomy. ∼ CMB (Cosmic microwave background). A2.7Kgasofthermalradiationthat permeates the Universe, a relic of the big bang. CMBPOL. Amissionconcept,currentlyunderstudy,forapost-PlanckCMB satel- lite experiment designed primarily to search for inflationary gravitational waves. COBE (Cosmic Background Explorer). ANASAsatelliteflownfrom1990– 1993 with several experiments designed to measure the properties of the CMB. John Mather and George Smoot, two of the leaders of COBE, were awarded the 2006 Nobel prize for physics for COBE (http://lambda.gsfc.nasa.gov/product/cobe). Cosmic jerk. Aparameterthatquantifiesthetimevariationofthecosmicaccel- eration. Dark Matter and Dark Energy 41
Cosmic shear (CS). Gravitational lensing of distant cosmological sources by cos- mological density perturbations along the line to those sources. Cosmological constant (Λ). An extra term in the Einstein equation that quan- tifies the gravitating mass density of the vacuum. Critical density. The cosmological density required for a flat Universe. If the density is higher than the critical density, then the Universe is closed, and if it is smaller, then it is open. DAMA. An Italian experiment designed to look for WIMPs (http://people.roma2.infn.it/ dama/web/home.html). ∼ Dark energy (DE). Aformofnegative-pressurematterthatfillstheentireUni- verse. It is postulated to account for the accelerated cosmological expansion. Dark matter (DM). The nonluminous matter required to account for the dy- namics of galaxies and clusters of galaxies. The preponderance of the evidence suggests that dark matter is not made of baryons, and it thus often referred to as “nonbaryonic dark matter.” The nature of dark matter remainsamystery. DASI (Degree Angular Scale Interferometer). An interferometric CMB ex- periment sited at the South Pole that characterized the acoustic peaks in the CMB power spectrum and first detected the E-mode polarization in the CMB (http://astro.uchicago.edu/dasi/). DECIGO (Deci-hertz Interferometer Gravitational Wave Observatory). Amissionconcept,currentlyunderstudyinJapan,foranevenmoreambitious version of BBO. DGP (Dvali-Gabadadze-Porrati) gravity. Atheoryforgravity,thatmayex- plain cosmic acceleration, based on the introduction of one extra spatial dimension. Dirac neutrino. Atypeofneutrinothathasanantiparticle. DMR (Differential Microwave Radiometer). An experiment on COBE that measured temperature fluctuations in the CMB (http://lambda.gsfc.nasa.gov/product/cobe). EDELWEISS. A French experiment designed to look for WIMPs (http://edelweiss.in2p3.fr). EGRET (Energetic Gamma Ray Experiment Telescope). Ahigh-energy gamma-ray experiment flown aboard NASA’s Compton Gamma-Ray Observatory in the early 1990s (http://cossc.gsfc.nasa.gov/docs/cgro/cossc/EGRET.html). Einstein’s equations. The equations of general relativity. Electroweak (EW) phase transition. The phase transition at a temperature 100 GeV that breaks the electroweak symmetry at low energies to distinct elec- ∼ tromagnetic and weak interactions. Friedmann equation. The general-relativistic equation that relates the cosmic expansion rate to the cosmological energy density. Friedman-Robertson-Walker (FRW) spacetime. The spacetime that de- scribes a homogeneous isotropic Universe. Dark Matter and Dark Energy 42
Galaxy clusters. Gravitationally bound systems of hundreds to thousands of galaxies. General relativity (GR). Einstein’s theory that combines gravity with relativity. GLAST (Gamma Ray Large Area Space Telescope). ANASAtelescope,to be launched within a year, for high-energy gamma-ray astronomy (http://www-glast.stanford.edu). Grand-unified theories (GUTs). Gauge theories that unify that electroweak and strong interactions at an energy 1016 GeV. ∼ Gravitational lensing. The general-relativistic bending of light by mass concen- trations. Gravitational waves (GWs). Propagating disturbances, which arise in general relativity, in the gravitational field, analogous to electromagnetic waves (which are propagating disturbances in the electromagnetic field). Hawking radiation. Radiation emitted, as a result of quantum-mechanical pro- cesses, from a black hole. HEAT (High Energy Antimatter Telescope). Aballoon-bornecosmic-ray- antimatter telescope from the 1990s. HESS (High Energy Stereoscopic System). Aground-basedairCerenkov telescope for GeV–TeV gamma-ray astronomy (http://www.mpi-hd.mpg.de/hfm/HESS/HESS.html). Hubble constant. The constant of proportionality between the recessional veloc- ity of galaxies and their distance. The Hubble constant is also the expansion rate. When used in this context, the term is a misnomer, as the expansion rate varies with time. IceCube. An astrophysical-neutrino observatory (a successor to AMANDA) now being built at the South Pole (http://icecube.wisc.edu). IMAX (Isotopie Matter Antimatter Telescope). A1992balloon-bornecosmic- ray-antimatter telescope (http://www.srl.caltech.edu/imax.html). Inflation. AperiodofacceleratedexpansionintheearlyUniversepostulated to account for the isotropy and homogeneity of the Universe. Inflationary gravitational waves (IGWs). Acosmologicalbackgroundofgrav- itational waves produced via quantum processes during inflation. IMB (Irvine-Michigan-Brookhaven) experiment. AU.S.undergroundde- tector designed originally to look for proton decay, but usedultimately(from1979– 1989) as an astrophysical-neutrino detector (http://www-personal.umich.edu/ jcv/imb/imb.html). ∼ JDEM (Joint Dark Energy Mission). AspacemissioninNASA’sroadmap that aims to study the cosmic acceleration (http://universe.nasa.gov/program/probes/jdem.html). Kaluza-Klein (KK) modes. Excitations of a fundamental field in extra dimen- sions in a theory with extra dimensions. These modes appear asmassiveparticles in our 3+1-dimensional spacetime. Dark Matter and Dark Energy 43
Kamiokande and Super-Kamiokande. AJapaneseundergroundastrophysical- neutrino telescope (and proton-decay experiment) and its successor (http://www-sk.icrr.u-tokyo.ac.jp/sk/index.html). Large extra dimensions. Acurrentlypopularideainparticletheorythatthe Universe may contain more spatial dimensions than the three that we see, and that the additional dimensions may be large enough to have observable consequences. Large-scale structure (LSS). The spatial distribution of galaxies and clusters of galaxies in the Universe. Laser Interferometric Space Antenna (LISA). Asatelliteexperimentplanned by NASA and ESA to detect gravitational waves from astrophysical sources (http://lisa.nasa.gov). LEP (Large Electron-Positron) Collider. The electron-positron collider at CERN (European Center for Nuclear Research) which from 1989 to 2000 tested with exquisite precision the Standard Model. LHC (Large Hadron Collider). The successor the LEP at CERN, the LHC will be (starting November 2007) a proton-proton collider, and the world’s most powerful particle accelerator. LSP (Lightest superpartner). The lightest supersymmetric particle (and a can- didate WIMP) in supersymmetric extensions of the Standard Model. LIGO (Laser Interferometric Gravitational-Wave Observatory). An NSF experiment, currently operating, designed to detect gravitational waves from astro- physical sources (http://www.ligo.caltech.edu). Local Group. The group of galaxies that the Milky Way belongs to. LSST (Large Synoptic Survey Telescope). A proposed wide-field survey tele- scope (http://www.lsst.org/lsst home.shtml). Lyman-alpha forest or Ly-α forest.Theseriesofabsorptionfeatures,inthe spectra of distant quasars, due to clouds of neutral hydrogenalongthelineofsight. Majorana neutrino. Atypeofneutrinothatisitsownantiparticle. MACRO (Monopoles and Cosmic Ray Observatory). An underground astrophysical-neutrino telescope (and proton-decay experiment) that ran at the Gran Sasso Laboratory in Italy from 1988 to 2000. MASS (Matter Antimatter Superconducting Spectrometer). A1989–1991 balloon-borne cosmic-ray-antimatter telescope (http://people.roma2.infn.it/ aldo//mass.html). ∼ MAT/TOCO (Mobile Anisotropy Telescope on Cerro TOCO). ACMB experiment using coherent detectors that gave early resultsonthelocationofthe first acoustic peak in the CMB angular power spectrum (http://www.physics.princeton.edu/cosmology/mat/). MAXIMA (Millimeter Anisotropy eXperiment Imaging Array). Aballoon- borne experiment that reported in 2000 measurements of temperature fluctuations on degree angular scales. It had a 16 element bolometer array operated at 100 mK and 10 arc-minute beams at 150 GHz (http://cosmology.berkeley.edu/group/cmb). Dark Matter and Dark Energy 44
MAXIPOL. Aballoon-borneCMBpolarizationexperimentbasedontheMAX- IMA experiment (http://groups.physics.umn.edu/cosmology/maxipol/). Naturalness problem. In grand-unified theories without supersymmetry, the parameter that controls the EW symmetry-breaking scale mustbetunedtobe extremely small. NET (Noise-equivalent temperature). Aquantitythatdescribesthesensitiv- ity (in units of µK √sec) of a detector in a CMB experiment. ∼ Neutralino. The superpartner of the photon and Z0 and Higgs bosons, and an excellent WIMP candidate in supersymmetric extensions of the standard model. PAMELA. A space-based cosmic-ray-antimatter experiment flown in 2006 (http://wizard.roma2.infn.it/pamela). Peccei-Quinn mechanism. Amechanism,involvingtheintroductionofanew scalar field, that solves the strong-CP problem. Phantom energy. An exotic form of dark energy that is characterized by an equation-of-state parameter w< 1. − Planck satellite. AcollaborativeNASA/ESAsatelliteexperimentaimedtomea- sure temperature fluctuations in the CMB with even more precision and sensitivity than WMAP (http://www.rssd.esa.int/Planck). Planck-scale physics. Acolloquialtermthatreferstoquantumgravityorstring theory. POLARBeaR (POLARization of the Background Radiation). Aplanned bolometer-based CMB polarization experiment to be sited in Chile (http://bolo.berkeley.edu/polarbear/index.html). Primordial density perturbations or sometimes just primordial perturba- tions. The small-amplitude primordial density inhomogeneities (which may have arisen during inflation) that were amplified via gravitational instability into the large-scale structure we see today. Pseudo-Nambu-Goldstone boson. Anearlymasslessscalarparticlethatarises in a theory with an explicitly broken global symmetry. PVLAS. Alaserexperimentdesignedtolookforthevacuummagneticbirefrin- gence predicted in quantum electrodynamics (http://www.ts.infn.it/physics/experiments/pvlas/pvlas.html). Q-balls. Extended objects, composed of a a spinning scalar field, that appear in scalar field theories with a U(1) symmetry (i.e., a cylindrical symmetry in the internal space). QCD (Quantum chromodynamics). The theory of the strong interactions that confine quarks inside protons and neutrons. QuaD (Q and U Extra-galactic Sub-Millimetre Telescope and DASI). A bolometer-based CMB polarization experiment at the South Pole. It has 4 arc- minute resolution at 150 GHz (http://www.stanford.edu/ schurch/quad.html). ∼ Dark Matter and Dark Energy 45
Quantum gravity. Atermthatreferstoatheory—stilltobedeterminedbut widely believed to be string theory—that unifies quantum mechanics and gravity. Quark-hadron phase transition or QCD phase transition.Thetransitionat temperature 100 MeV at which quarks are first bound into protons and neutrons. ∼ Quintessence. Amechanismpostulatedtoexplaincosmicaccelerationbythe displacement of a scalar field (the quintessence field) from the minimum of its po- tential. Recombination. The formation of atomic hydrogen and helium at a redshift z 1100. ≃ Redshift (z). The recessional velocity of a galaxy divided by the speed of light. The redshift is used as a proxy for distance or time after the big bang, with higher redshift indicating larger distances and earlier times. SKA (Square-Kilometer Array). Alargeradio-telescopearrayplannedbyNSF (http://www.skatelescope.org). SNAP (Supernova Acceleration Probe). Aproposedspace-basedtelescope dedicated to measuring the cosmic expansion history (http://snap.lbl.gov). SPIDER. Aballoon-bornebolometer-basedCMBpolarizationexperiment with six refractive telescopes (http://www.astro.caltech.edu/ lgg/spider front.htm ). ∼ Spintessence. Avariantofquintessenceinwhichthescalarfieldistakentobe complex with a U(1) symmetry. SPUD (Small Polarimeter Upgrade for Dasi ). AproposedCMBexperiment to be attached to the DASI mount at the South Pole. STACEE (Solar Tower Atmospheric Cerenkov Effect Experiment). A ground-based air Cerenkov telescope designed to detect gamma rays in the 100 ∼ GeV range (http://www.astro.ucla.edu/ stacee). ∼ Standard Model (SM). The theory of strong, weak, and electromagnetic inter- actions. String theory. Atheorythatpostulatesthatallelementaryparticlesareexcita- tions of fundamental strings. The aim of such theories is to unify the strong and electroweak interactions with gravity at the Plank scale,anenergyscale 1019 ∼ GeV. Strong-CP problem. Although the strong interactions are observed to be parity conserving, there is nothing in QCD that demands that parity be conserved. Supersymmetry (SUSY). Asymmetrybetweenfermionsandbosonspostulated primarily to solve the naturalness problem. It is an essential ingredient in many theories for new physics beyond the Standard Model. Triangle anomaly. Acoupling,mediatedbytheexchangeofvirtualfermions, between a scalar particle and two photons. This coupling is responsible for neutral- pion decay to two photons. TS93. A1993balloon-bornecosmic-ray-antimattertelescope (http://people.roma2.infn.it/ aldo//ts93.html). ∼ Universal extra dimensions (UED). Aclassoftheoriesfornewphysicsat Dark Matter and Dark Energy 46 the electroweak scale in which the Universe has extra large dimensions in which standard-model fields propagate. Vacuum energy. The energy of free space. VERITAS (Very Energetic Radiation Imaging Telescope ArraysSys- tem). Aground-basedairCerenkovtelescopeforGeV–TeVgamma-rayastronomy (http://veritas.sao.arizona.edu). VSA (Very Small Array). A ground-based CMB interferometer that is sited in the Canary Islands. It is sensitive to a wide range of angular scales with a best resolution of 10 arc-minute (http://www.mrao.cam.ac.uk/telescopes/vsa/index.html). WIMP (Weakly-interacting massive particle). Adark-mattercandidatepar- ticle that has electroweak interactions with ordinary matter. Examples include massive neutrinos, supersymmetric particles, or particlesinmodelswithuniversal extra dimensions. WMAP (Wilkinson Microwave Anisotropy Probe). ANASAsatellitelaunched in 2001 to measure, with better sensitivity and angular resolution than DMR, the temperature fluctuations in the CMB (http://map.gsfc.nasa.gov). ZEPLIN An experiment designed to look for WIMPs.