Supersymmetry in Cosmology - PDF Free Download

Supersymmetry in Cosmology Raghavan Rangarajan Ahmedabad University raghavan@ahduni.edu.in

OUTLINE THE GRAVITINO PROBLEM SUSY FLAT DIRECTIONS AND THEIR COSMOLOGIAL IMPLICATIONS SUSY DARK MATTER SUMMARY 2

PREAMBLE A BRIEF HISTORY OF OUR UNIVERSE OBSERVATIONS + GENERAL THEORY OF RELATIVITY 14 b yr, COMPOSITION, EXPANDING, PAST HOT AND DENSE 3

A BRIEF HISTORY OF OUR UNVIERSE First second hot primordial plasma of electrons,.. photons, quarks/protons, neutrons, dark matter, 1 s 3 min light nuclei (helium, lithium,..) 400,000 years Atoms form, CMBR 300 million years First stars form 1 billion years First galaxies form 9 billion years Solar system formed, DE domin 14 billion years Today 4

THE FIRST SECOND 10-44 s Planck time (E ~ 10 19 GeV) [Q Gravity] Grand Unified Theory 10-38 s GUT Phase Transition (E ~ 10 16 GeV, T ~ 10 29 K) Standard Model [q, l, H, GB] /Modified SM 10-11 s Electroweak Phase Transition (E ~ 100 GeV, T ~ 10 15 K) 10-6 s quarks à protons, neutrons (E ~ 1 GeV, T ~ 10 13 K) 1 s Primordial Nucleosynthesis begins (E ~ 1 MeV, T ~ 10 10 K) 5

THE FIRST SECOND 10-44 s Planck time (E ~ 10 19 GeV) [Q Gravity] Grand Unified Theory 10-38 s GUT Phase Transition (E ~ 10 16 GeV, T ~ 10 29 K) Standard Model [q, l, H, GB] /Modified SM 10-11 s Electroweak Phase Transition (E ~ 100 GeV, T ~ 10 15 K) 10-6 s quarks à protons, neutrons (E ~ 1 GeV, T ~ 10 13 K).. 1 s Primordial Nucleosynthesis begins (E ~ 1 MeV, T ~ 10 10 K) 6

INFLATION and REHEATING INFLATION PERIOD OF ACCELERATED EXPANSION IN THE EARLY UNIVERSE (t ~ 10-38 s or later) WHEN THE ENERGY DENSITY OF A SLOWLY VARYING FIELD CALLED THE INFLATON Φ DOMINATES V(Φ) Φ e SLOW ROLL Φ OSCILLATE AND DECAY ENERGY DENSITY DOMINATES, DETERMINES EVOL OF UNIV 7

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INFLATION and REHEATING V(Φ) INFLATION Φ e Φ REHEATING DURING INFLATION, R~ exp(h I t) n OF ALL SPECIES 0. COLD INFLATON DECAY PRODUCTS THERMALISE, T reh THERMAL BATH HAS q, l, h, dm, BSM INCLUDING SUSY, GUT PARTICLES AND HEAVY NEUTRINOS REHEATING 9

MATTER-ANTIMATTER ASYMMETRY OF THE UNIVERSE SOLAR SYSTEM, MILKY WAY, CLUSTER (20 Mpc) ANTIMATTER RULED OUT TILL d~1000 Mpc SIZE OF OBSERVABLE UNIVERSE ~ 14000 Mpc (1 Mpc = 3 x 10 19 km = 3 x 10 6 lt-yr) MATTER-ANTIMATTER ASYMMETRY OF THE UNIV 10

HOW GENERATE ASYMMETRY? EARLY TIMES ( t << 1 s = PRIM. NUCL.) EQUAL AMOUNTS OF MATTER AND ANTIMATTER DISEQUILIBRIUM IN THE EARLY UNIVERSE 100 M + 100 A à 103 M + 101 A à 2 M X à M X à A r M > r A, GET MORE MATTER THAN ANTIMATTER X = GUT BOSONS (M X ~ 10 16 GeV), HEAVY NEUTRINOS (M N ~ 10 10 GeV) GUT BARYOGENESIS, LEPTOGENESIS 11

MATTER-ANTIMATTER ASYMMETRY WHEREFROM GUT BOSONS, HEAVY NEUTRINOS? In the hot early Universe when temperatures were very high (k B T > M) (k B =1) 12

THE GRAVITINO PROBLEM 13

GRAVITINOS SUPERSYMMETRIC PARTNER OF THE GRAVITON SUPERSYMMETRY EXTENSION OF THE STANDARD MODEL (GAUGE HIERARCHY) SUPERPARTNERS: FERMION BOSON PHOTON PHOTINO, ELECTRON SELECTRON LOCAL (spacetime dep) SUPERSYMMETRY: SUPERGRAVITY GRAVITON GRAVITINO BROKEN (EQUAL m, IF SUSY) 14

GRAVITINO MASS SUPERSYMMETRY BREAKING Þ SM SUPERPARTNERS GET A MASS m 0 ~ 100 GeV Þ GRAVITINO GETS A MASS GAUGE MEDIATED SUSY BREAKING (V. LIGHT, LIGHT < 100 GeV) GRAVITY MEDIATED SUSY BREAKING (HEAVY 100 GeV) ANOMALY MEDIATED SUSY BREAKING (V. HEAVY 100 GeV) 15

GRAVITINOS SUPERSYMMETRIC PARTNER OF THE GRAVITON PRODUCED AFTER INFLATION COSMOLOGICAL CONSEQUENCES (m, n) STABLE : AFFECTS EXPANSION RATE, (L/H) UNSTABLE : AFFECT EXPANSION RATE PRIOR TO DECAY DECAY PRODUCTS DESTROY LIGHT ELEMENTS (NUCLEOSYNTHESIS) GRAVITINO PROBLEM(S) 16

STANDARD PICTURE OF GRAVITINO PRODUCTION V(Φ) Φ e Φ INFLATION REHEATING (OSC. + DECAY) RADIATION DOMINATED UNIV (Relativistic particles) ALSO PROD DURING P/REHEATING THERMAL SCATTERING (gluons, quarks, squarks, gluinos) 18

GRAVITINO PRODUCTION PRODUCED BY THE SCATTERING OF INFLATON DECAY PRODUCTS A ~ G A G ~ B C B C e.g. q + q! g + G q + q! g + G g + g! g + G PRADLER AND STEFFEN

STANDARD CALC OF GRAVITINO PRODUCTION CALCULATE GRAVITINO PRODUCTION IN THE RAD DOM ERA MAINLY PRODUCED AT THE BEGINNING OF THE RAD DOM ERA WHEN, AND UPPER BOUND ON UPPER BOUND ON T reh OF 10 6 9 GeV (MASS 100 GeV 10 TeV) k B T in GeV k B =1 1 GeV =10 13 K 20

GRAVITINOS, REHEAT TEMPERATURE AND MATTER- ANTIMATTER ASYMMETRY 21

REHEATING, GRAVITINOS AND MATTER-ANTIMATTER ASYMMETRY THE UPPER BOUND ON THE REHEAT TEMPERATURE 10 6-9 GeV TO SUPPRESS GRAVITINO PRODUCTION 1 GeV =10 13 K 22

REHEATING, GRAVITINOS AND MATTER-ANTIMATTER ASYMMETRY THE UPPER BOUND ON THE REHEAT TEMPERATURE 10 6-9 GeV TO SUPPRESS GRAVITINO PRODUCTION MATTER-ANTIMATTER ASYMMETRY GENESIS MODELS REQUIRE HEAVY X, MASS 10 10, 10 16 GeV DIFFICULT TO HAVE ENOUGH HEAVY X IN THE RADIATION DOMINATED UNIV AFTER REHEATING n X ~ exp(- M c 2 /k B T) 24

SOLUTIONS TO THE GRAVITINO PROBLEM INCREASE GUT BOSON/HEAVY NEUTRINO PRODUCTION, OR SUPPRESS GRAVITINO PRODUCTION SCATTERINGS DURING REHEATING BEFORE TOTAL THERMALISATION (NOT X DECAYS) T: 0 à T max à T reh T max ~ 1000 T reh PREHEATING SUPPRESS GRAVITINOS USING SUSY FLAT DIRECTIONS CAVEAT (ALWAYS CHECK)

SUSY FLAT DIRECTIONS AND THEIR COSMOLOGIAL IMPLICATIONS 27

FLAT DIRECTIONS V = 0 ALONG BOTTOM. POTENTIAL IS FLAT MAG NOT CHANGE, PHASE DOES

SUSY FLAT DIRECTIONS STANDARD MODEL, H SCALAR (SPIN 0) MINIMISE V SCALAR POTENTIAL V IN SUSY IS A FUNCTION OF DIRECTIONS IN FIELD SPACE OF SCALARS ALONG WHICH THE SCALAR POTENTIAL IS MINIMISED V = 0, POTENTIAL IS FLAT FLAT DIRECTIONS [POTENTIAL IS CONSTANT AND ZERO ALONG FLAT DIRECTION NOT JUST PHASE CHANGE, MAGNITUDE CHANGE TOO]

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SUSY BREAKING FLAT DIRECTION à QUADRATIC POT WITH CURV m 0 2 DUE TO QUANTUM FLUCTUATIONS DURING INFLATION; OTHER REASONS A FIELD CONFIGURATION WITH THE FIELD AWAY FROM ITS MINIMUM IS OFTEN CALLED A CONDENSATE, CAN TREAT LIKE CLASSICAL FIELD, DO EOM

SUSY BREAKING FLAT DIRECTION à QUADRATIC POT WITH CURV m 0 2 DUE TO QUANTUM FLUCTUATIONS DURING INFLATION; OTHER REASONS WHEN t U ~ t F (OR H ~ m 0 ), OSCILLATES, THEN IT DECAYS (BEFORE EWSB t~10-11 s)

COSMOLOGICAL CONSEQUENCES AFFLECK-DINE BARYOGENESIS SUPPRESS GRAVITION PRODUCTION VIA DELAYED THERMALISATION DURING REHEATING GENERATION OF PRIMORDIAL MAGNETIC FIELDS 33

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sha1_base64="rtvvpcwv6+iqefyebvssqfgiwgm=">aaacfnicbvdlsgmxfm3uv62vuzdugkuqhdojgrorunfzwdpcp5q7adqgjjpt5i5ssv/cjb/ixowkw3hn35g+ftp6iha451xu7gktkqx63retwvhcwl7jrubw1jc2t9ztntstp5rxmotlrkshgc5fxmsoupjqojmoupjk2l0a+zv7ro2io1vsj7yuob2jlmcavmq4hqcfbhlaazaaanhuiggdp9decrccpj16rcejoa1kqcpnewvvddpp/cnjkylkdfcramysvtxcjsgymu8lwb+arsekh+ac1paewbfavgzpbiqb+mb815aewkvjw7g2l0i6vn9pdeaz01ehtsrajpn1ruj/xi3f1nl9ikikrr6xyajwkingdfqsbqrngcq+jcc0sh+lramagnoqc7yef/bkevi+kvwu/jvtfpfy2kaw7jf9ckh8ckak5jqusjkw8kieyst5c56cf+fd+zhem850zpf8gfp5azronus=</latexit> <latexit sha1_base64="rtvvpcwv6+iqefyebvssqfgiwgm=">aaacfnicbvdlsgmxfm3uv62vuzdugkuqhdojgrorunfzwdpcp5q7adqgjjpt5i5ssv/cjb/ixowkw3hn35g+ftp6iha451xu7gktkqx63retwvhcwl7jrubw1jc2t9ztntstp5rxmotlrkshgc5fxmsoupjqojmoupjk2l0a+zv7ro2io1vsj7yuob2jlmcavmq4hqcfbhlaazaaanhuiggdp9decrccpj16rcejoa1kqcpnewvvddpp/cnjkylkdfcramysvtxcjsgymu8lwb+arsekh+ac1paewbfavgzpbiqb+mb815aewkvjw7g2l0i6vn9pdeaz01ehtsrajpn1ruj/xi3f1nl9ikikrr6xyajwkingdfqsbqrngcq+jcc0sh+lramagnoqc7yef/bkevi+kvwu/jvtfpfy2kaw7jf9ckh8ckak5jqusjkw8kieyst5c56cf+fd+zhem850zpf8gfp5azronus=</latexit> AFFLECK-DINE BARYOGENESIS V ( ) =m 2 + i 2 ( 4 4 ) WHEN IS LARGE B AND CP VIOLATING QUARTIC COUPLINGS DOMINATE. n B IS CREATED LATER QUADRATIC TERMS DOMINATE. NO NEW n B DECAYS (e.g. q <latexit sha1_base64="fyjx9pkpa3xd4pnojcgdbdivkbg=">aaab6nicbvbnswmxej2tx7v+vt16crbbu9kvqb0vvxis4npcu5rsmm1dk2xiskjz+he8efdx6i/y5r8x2+5bqw8ghu/nmdmvvpwz6/tfxmvldw19o7pz29re2d2r7x88mdtthiyk5anuxthqziqnlbocdpwmwmscduljtef3hqk2ljx3dqpojpbisoqrbauprwwb1bt+058d/svbsrpqoj2of/ahkckelzzwbewv8jwncqwti5zoav3muixjbi9oz1gjbtvrpr91hk6cmkrjql1ji+bqz4kcc2ominadatuxwfyk8t+vl9nkmsqzvjmlkiwwjrlhnkxf42jincwwtx3brdn3kyjjrdgxlp6acyfyfvkvcc+av83g7rzrui7tqmirhmmpbhablbifnorayaxp8akvnvcevtfvfdfa8cqzq/gf7+mbkwoohg==</latexit> c! q/ q + ) AND GET BAU 36

SUSY FLAT DIRECTIONS DECREASE DELAYED THERMALISATION DURING REHEATING 37

e.g., q qa µ A µ NON-ZERO VALUE OF GIVES MASS TO GAUGE BOSONS (BREAKS GAUGE SYMMETRY), FLAT DIRECTION EXPECTATION VALUE CAN BE 10 13 GEV OR HIGHER THERMALISATION DURING REHEATING DUE TO PROCESSES MEDIATED BY GAUGE BOSONS PHOTONS (EM), GLUONS (STRONG) 38

IF ALL GAUGE BOSONS GET MASS [LLddd, QuQue], IT SLOWS DOWN THERMALISATION AFTER INFLATION A PHOTON C B D

STANDARD PICTURE OF REHEATING: INFLATON DECAYS THERMALISE KINETIC EQM CHEMICAL EQM FLAT DIRECTIONS: INFLATON DECAYS DELAYED THERMALISATION DILUTE PLASMA GRAVITINOS PRODUCED BY SCATTERING OF INFLATON DECAY PRODUCTS [n.n] ALLAHVERDI AND MAZUMDAR; RR AND A. SARKAR

GRAVITINO PROBLEM AGAIN! WITH SOME FLAT DIRECTIONS, HIT A RESONANCE GRAVITINO ABUNDANCE GENERATED IS VERY LARGE AND GREATER THAN THE COSMOLOGICAL UPPER BOUND FOR MOST PARAMETER SPACE COSMOLOGICAL UPPER BOUND IS Y < 10-14 FOR DIFFERENT SETS OF PARAMETERS WHY AMBIGUITY? Y = 10-8 10-2 MAHAJAN, RR AND A. SARKAR 41

SUSY FLAT DIRECTIONS GENERATE PRIMORDIAL MAGNETIC FIELDS 42

PRIMORDIAL MAGNETIC FIELDS DETECTED MAGNETIC FIELDS ON DIFFERENT COSMOLOGICAL LENGTH SCALES FROM GALAXIES TO CLUSTERS ORIGIN IS UNKNOWN DYNAMO THEORY: PRIMORDIAL MAGNETIC FIELD, AMPLIFIED BY DYNAMO PROCESS SOURCE OF PRIMORDIAL MAGNETIC FIELD UNKNOWN KANDASWAMY 43

<latexit sha1_base64="th3qaitzwztbyrnz0c8exffcfjw=">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</latexit> <latexit sha1_base64="th3qaitzwztbyrnz0c8exffcfjw=">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</latexit> <latexit sha1_base64="th3qaitzwztbyrnz0c8exffcfjw=">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</latexit> <latexit sha1_base64="th3qaitzwztbyrnz0c8exffcfjw=">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</latexit> PRIMORDIAL MAGNETIC FIELDS GENERATE THE PRIMORDIAL MAGNETIC FIELD DURING INFLATION GAUGE FIELD A µ (x) = X Z d 3 k µ (k)a k (t)exp(ik.x)a k + h.c. SOLVE EOM FOR A k IN CURVED SPACETIME A k (t) CAN GROW IF m A 0 EQUIVALENT TO CREATING E AND B FIELDS E DISAPPEARS. GET PRIMORDIAL B.

PRIMORDIAL MAGNETIC FIELDS q qa µ A µ NON-ZERO VALUE OF AFFLECK-DINE FIELD GIVES MASS TO A μ FLAT DIRECTIONS CAN GIVE RISE TO PRIMORDIAL MAGNETIC FIELDS ENQVIST, JOKINEN AND MAZUMDAR 45

SUSY DARK MATTER IF R PARITY IS CONSERVED, LSP IS STABLE IF IT IS FEEBLY INTERACTING WITH LIGHT AND OTHER PARTICLES (NEUTRAL, COLOURLESS), AND HAS THE RIGHT ENERGY DENSITY TODAY IT CAN BE THE DARK MATTER IT TURNS OUT THAT AN LSP (NEUTRALINO, SNEUTRINO) SATISFIES THESE PROPERTIES AND WITH THE MASS ~ 100 GeV HAS THE RIGHT ENERGY DENSITY (WIMP MIRACLE) 46

SUSY DARK MATTER EARLY UNIVERSE ALL SUSY AND SM PARTICLES IN THERMAL EQUILIBRIUM, Γ > H AS PARTICLES BECOME NON-RELATIVISTIC THEY TEND TO ANNIHILATE AND DISAPPEAR (HEAVY QUARKS, MUONS, TAU, HIGGS, SUSY PARTICLES) ONLY THE LIGHTEST SURVIVE (ELECTRON; u, d à p, n; PHOTON, LIGHT NEUTRINOS, LSP) 47

<latexit sha1_base64="jmrdim1payh6ow00aebqvc/mrjm=">aaacixicbzbnswmxeiazftb6terrs7aihqtsqqa9ceuvhqtyw2jqkk2zbwg2uyzzosz7w7z4v7x4uoln/dom2ylaohdy5j0zjvp6mwdko86nnte/sli0xfgprq6tb2zaw9t3kkokoxus8ug2fawoz4lwndocnmnjcehz2vd7l6n845fkxsjxqwcxbye4k1jacnzg8uxkecle5dkinsmqokphot+u0ocmokbikt7kj/vjzjbjlosknl1yyk4ecbbccztajgqepusdicqhfzpwrftldwldtrhujhcafvgiaixjh3dpy6daivxtnf8xg/tg6cagkuyidxp1d0ekq6ugow8qq6x7ajo3ev/ltridnlvtjujeu0hgg4keqx3bkv+wwyqlmg8myckz+sskpww80cbvkqnu9mqzud8qv8ru9umpejfxowb2wr44ac44bvvwbwqgdgh4ai/gdbxbz9ar9wenx6vz1qrnb/wj6+sbvl+hww==</latexit> <latexit sha1_base64="jmrdim1payh6ow00aebqvc/mrjm=">aaacixicbzbnswmxeiazftb6terrs7aihqtsqqa9ceuvhqtyw2jqkk2zbwg2uyzzosz7w7z4v7x4uoln/dom2ylaohdy5j0zjvp6mwdko86nnte/sli0xfgprq6tb2zaw9t3kkokoxus8ug2fawoz4lwndocnmnjcehz2vd7l6n845fkxsjxqwcxbye4k1jacnzg8uxkecle5dkinsmqokphot+u0ocmokbikt7kj/vjzjbjlosknl1yyk4ecbbccztajgqepusdicqhfzpwrftldwldtrhujhcafvgiaixjh3dpy6daivxtnf8xg/tg6cagkuyidxp1d0ekq6ugow8qq6x7ajo3ev/ltridnlvtjujeu0hgg4keqx3bkv+wwyqlmg8myckz+sskpww80cbvkqnu9mqzud8qv8ru9umpejfxowb2wr44ac44bvvwbwqgdgh4ai/gdbxbz9ar9wenx6vz1qrnb/wj6+sbvl+hww==</latexit> <latexit sha1_base64="jmrdim1payh6ow00aebqvc/mrjm=">aaacixicbzbnswmxeiazftb6terrs7aihqtsqqa9ceuvhqtyw2jqkk2zbwg2uyzzosz7w7z4v7x4uoln/dom2ylaohdy5j0zjvp6mwdko86nnte/sli0xfgprq6tb2zaw9t3kkokoxus8ug2fawoz4lwndocnmnjcehz2vd7l6n845fkxsjxqwcxbye4k1jacnzg8uxkecle5dkinsmqokphot+u0ocmokbikt7kj/vjzjbjlosknl1yyk4ecbbccztajgqepusdicqhfzpwrftldwldtrhujhcafvgiaixjh3dpy6daivxtnf8xg/tg6cagkuyidxp1d0ekq6ugow8qq6x7ajo3ev/ltridnlvtjujeu0hgg4keqx3bkv+wwyqlmg8myckz+sskpww80cbvkqnu9mqzud8qv8ru9umpejfxowb2wr44ac44bvvwbwqgdgh4ai/gdbxbz9ar9wenx6vz1qrnb/wj6+sbvl+hww==</latexit> <latexit sha1_base64="jmrdim1payh6ow00aebqvc/mrjm=">aaacixicbzbnswmxeiazftb6terrs7aihqtsqqa9ceuvhqtyw2jqkk2zbwg2uyzzosz7w7z4v7x4uoln/dom2ylaohdy5j0zjvp6mwdko86nnte/sli0xfgprq6tb2zaw9t3kkokoxus8ug2fawoz4lwndocnmnjcehz2vd7l6n845fkxsjxqwcxbye4k1jacnzg8uxkecle5dkinsmqokphot+u0ocmokbikt7kj/vjzjbjlosknl1yyk4ecbbccztajgqepusdicqhfzpwrftldwldtrhujhcafvgiaixjh3dpy6daivxtnf8xg/tg6cagkuyidxp1d0ekq6ugow8qq6x7ajo3ev/ltridnlvtjujeu0hgg4keqx3bkv+wwyqlmg8myckz+sskpww80cbvkqnu9mqzud8qv8ru9umpejfxowb2wr44ac44bvvwbwqgdgh4ai/gdbxbz9ar9wenx6vz1qrnb/wj6+sbvl+hww==</latexit> SOME LIGHTEST PARTICLES GO OUT OF EQUILIBRIUM WHEN THEY ARE RELATIVISTIC (LIGHT NEUTRINOS) AND SOME AFTER THEY BECOME NON- RELATIVISTIC (ELECTRON, n, p, LSP) Γ = H (FREEZE OUT CONDITION) AFTER OUT OF EQUILIBRIUM, n ~ 1/R 3, Y=n/s FROZEN 0 = mn 0 = mn eq R 3 eq R 3 0 R ~ 1/T IF NO ENTROPY RELEASE = mn(t eq ) T 3 0 T 3 eq 48

KNOWING T eq IS IMPORTANT. OBTAIN IT FROM Γ = n <! v > = H <.. > IS FOR THERMALLY AVERAGED CROSS SECTION WHEN A SPECIES BECOMES NON-RELATIVISTIC, n ~ exp(-m/t) AND! FALL, AND Γ < H FOR THE LSP, WE FIND T eq = m/20 (WEAK INTERACTIONS. FOR ELECTRON IT IS m/10 6 AND FOR PROTON IT IS m/10 9 ) 49

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sha1_base64="kf6azhqigk8k/k1aw+/ju6bsko4=">aaab+nicbzbps8mwgmbt+w/of3uevqsh4gm0iqghyaghl8ie6wzbkwmwbmfpupjuhkvfxyshfa9+em9+g7oub918ipdjed+x980tjowq7tjfvmvpewv1rbpe29jc2t6xd+spsqqsew8ljmq3riowyomnqwakm0ic4pcrtji+mty7j0qqkvi9nitej9gq04hipi0v2pw+hinagrewgoz6ng/shtn0csffcetogfltwp7qdwroy8i1zkipnusk2s+q1bqzktf6qsijwmm0jd2dhmve+vlxew4pjtoakzdmcq0l9/dehmkljnfoomokr2q+njx/q/vshz35gevjqgnhs0vryqawcboehfbjsgytawhlam6feiqkwtrevtmhupnfxgtvuhnedo9ogq3lmo0q2ach4ai44bs0wa1oaw9g8asewst4s3lrxxq3pmatfauc2qn/zh3+ac9xk3e=</latexit> FOR THE LSP, WE FIND T eq = m/20 = mn(t eq ) T 3 0 T 3 eq n(t )=g mt 2 3/2 e m/t FOR m ~ 100 GeV, 0 = DM WIMP MIRACLE 50

CANDIDATE SUSY DARK MATTER NEUTRALINOS (LIGHTEST COMBO OF WINO, BINO, 2 NEUTRAL HIGGSINOS) SNEUTRINOS m ~ 100 GeV; WIMP MIRACLE NEUTRALINO NOT SEEN YET (MODEL DEPENDENT) SNEUTRINOCURRENTLY RULED OUT IN MSSM 51

CANDIDATE SUSY DARK MATTER GRAVITINO VERY WEAKLY COUPLED, DIFFICULT TO DETECT; CREATED THROUGH DECAY OF NLSP AS NOT THERMAL IN EARLY UNIV DUE TO VERY WEAK COUPLING, m ~ ev AXINO CREATED THROUGH THERMAL SCATTERING OF PARTICLES (LIKE GRAVITINO) OR OUT OF EQM DECAY OF NLSP m ~ kev - TeV 52