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Instituto Avanzado de Cosmología Connections between Dark Energy and Particle Physics Axel de la Macorra Instituto de Física, UNAM Instituto Avanzado de Cosmologia Cosmology on the beach, Playa del Carmen, Jaunuary 2010 El Universo Invisible 1er Congreso de Cosmología IAC Outline • Brief Introduction • Properties of Dark Energy • Theoretical Considerations • Dynamics of Dark Energy (Scalar Fields) • Specific models: pNGB Condensates Coupled (interacting) DE Models Late time generation of DE • Conclusions Cosmology on the Beach, Playa del Carmen, January 2010 Dark Energy • Dark Energy has been established in the last 10 years • It is one of the most interesting and open question in physics • But the nature and dynamics of Dark Energy “DE” is still not well know How detectable is DE on earth? A volume of the earth size filled with DE weights less than 0.001 gr It was a big surprise for most scientist even though there were some hints from • age of globular cluster (age ~ 13.5 billion years) • structure formation both required a larger age of the universe Without DE 8-10 billion years with DE 13.7 billion years Cosmology on the Beach, Playa del Carmen, January 2010 General approach to Dark Energy M2pl=1/8p G = 1 Can introduce Dark Energy via 1) New Particles (modification of Tun ) 2) Scalar-Tensor (non-minimal coupling f(f) R ) 3) f(R) modification (e.g. MOND) 4) Inhomogeneities (live in a huge Bubble) for reviews see • Dynamics of dark energy. E. Copeland et al Int.J.Mod.Phys.D15:1753,2006. hep-th/0603057 • Dark Energy and the Accelerating Universe. J. Frieman et al, Ann.Rev.Astron.Astrophys.46:385, 2008, arXiv:0803.0982 • The Dynamics of Quintessence, The Quintessence of Dynamics. E. Linder Gen.Rel.Grav.40:329356,2008, arXiv:0704.2064 Cosmology on the Beach, Playa del Carmen, January 2010 Basics Einstein eqs. in a FRW metric eq. of state w = 1/3 radiation w = 0 matter w = -1 cosmo. cte acceleration requires w < -1/3 Cosmology on the Beach, Playa del Carmen, January 2010 5 year WMAP, Komatsu et al w = cte Cosmology on the Beach, Playa del Carmen, January 2010 5 year WMAP, Komatsu et al w = cte -1.11 < w < 0.86 (95% CL) w = wo + w’ z/(1+z) w’=dw/dz ( at z = 0 ) - 1.32 < w < 0.86 (95% CL) Cosmology on the Beach, Playa del Carmen, January 2010 Improved DarkVector Energy Constraints from ~100 New CfA Supernova Type Ia Light Curves. Fields M.Hicken et al Astrophys.J.700:1097-1140,2009. i.e. w = - 0.87 +/- 0.06 Cosmology on the Beach, Playa del Carmen, January 2010 Reconstruction from Hubble diagram V, w(z) Reconstruction: i) Model independent or i) Piece wise w(z) for z+Dz ii) Choose a parametrization of w(z) But • Involves an integration and is not precise enough to extract w(z) • Results depend on the priors used • require extra data sets (LSS, BAO, WL) see Tegmark, Takada, Zaldariaga courses and Bean, Crawford, Roe, Suntzeff talks or all “Cosmologia en la Playa” Cosmology on the Beach, Playa del Carmen, January 2010 There is a strong degeneracy in w(z) and Wm on the expansion history due to the integration on the luminosity distance Steinhardt et al ‘02 Cosmology on the Beach, Playa del Carmen, January 2010 Improved Cosmological Constraints from New, Old and Combined Supernova Datasets. Supernova Cosmology Project (M. Kowalski et al.). Astrophys.J.686:749-778,2008. Cosmology on the Beach, Playa del Carmen, January 2010 Parametrization of w i) w = wo constant ii) w = wo + w1 z iii) w = wo + w1 z/(1+z) The values and evolution of w(z) depend heavily on the parametrization used 4 free parameters Yellow = 95% C.L. Yellow no cross over the w = -1 line Corasaniti et al PRD’04 How to solve the nature of Dark Energy ? Need two fundamental ingredients Inspiration (go to the top of a pyramid and recieve the “energy”) e.g. Sun pyramid or Tulum careful thinking … A. Riess et al ‘06 Dark Energy Properties Generic Properties DE models must satisfy: • Amount of Dark Energy WDE = 0.72 +/- 0.03 • Present mass density Wm = 0.28 +/- 0.03 • Constraint from NS Bean et al Wf < 0.045 • Distance to last scattering, z=1089: RCMB = 1.70 +/- 0.03 • SDSS luminous red galaxy, baryon acoustic oscillation (BAO) distance parameter z = 0.35 gives A with n = 0.95 • Distance ratio from z = 0.35 to z =1089 gives R0.35 = 0.0979 +/- 0.0036 Cosmology on the Beach, Playa del Carmen, January 2010 Dark Energy Properties for scalar fields • Slow roll conditions must be satisfied 1) |V’/V| 2) |V’’/V| << 1 • Weakly coupled to SM particles • Scalar field light mass (induces a long range force) << 1 Present values of mass and dark energy M2pl=1/8p G = 1 Cosmology on the Beach, Playa del Carmen, January 2010 Particle Phsyics and Dark Energy • What is the Nature of Dark Energy? • Is it a cosmological constant w= -1 or a particle w(z) ? • Why is DE relevant today ? “Coincidence Problem” What do we expect from a good theoretical model ? 1) Derive the potential V(f ) 2) Small number of free parameters 3) Reasonable choice of values for the free parameters (i.e no fine tuning of parameters) 4) Initial condition of scalar field f and energy density r(f) 5) Account for the long period of radiation and matter domination 6) and of course have a good fit to the data e.g. Scalar potential V (f) = L4 f (f /M) need to derive the functional form f (f /M) and explain the parameters L, M A. de la Macorra, Inst. de Física, UNAM, IAC Ultra violet Vacuum Energy Vacuum Energy L = 0.003 eV Quantum field vacuum corrections k = Planck mass 1019 GeV? k = Electroweak Scale 100-1000 GeV? r is too large ! The Standard Model “SM” has no cutoff k --> Planck mass • The mass of the Higgs is expected to be O(100-1000) GeV (quntum corrections give m =O(mpl) or to the scale of SM validity) • need new physics beyond TeV • e.g. Supersymmetry (scalar + fermion loops cancel) scalar loop fermion loop =0 + j=spin, susy ameliorates the UV problem but it is still too large Cosmology on the Beach, Playa del Carmen, January 2010 Naturalness We measure a parameter A(m) at a scale m << L (e.g. Mpl) we should be able to determine it from A(L) with L >> m • We do not want a fine tuning between A(L) delta A • We would like to have A(L) ~ d A ~ A(m) • For mass m with V ~ f4 one has dm ~ L • For gauge coupling constant g one has d g ~ Log[ L/m ] Potential one loop effective potential Potential it is not enough to derive Vo to give Dark Energy and but we should ensure that the radiative corrections do not spoil the DE behavior Cosmology on the Beach, Playa del Carmen, January 2010 Particle Phsyics and Dark Energy A) Scalar fields f (spin cero particles) present at high energies (after inflation) Mpl > L >>TeV • Fundamental scalar fields f (e.g. tracker behavior of scalar fields) B) Produce DE scalar field at a late time and low energy scale L << TeV a) Fundamental field generated dynamically at small scale L e.g. produced by the decay of other particles b) Composite scalar field f generated at a phase transition scale L ( e.g. can have mpl >> L ) i) fermion condensate f = <YY> ii) vector condensate A = <Vm Vm> • L = L gut e 2 8p 2 / g gut b LQCD 200 MeV since L is closer to present scale of DE we have less fine tuning of the parameters in the DE potential • help to explain the coincidence problem Phase transition we expect V = O(L4 ) with L the scale of sym. breaking A e.g. Vi/VDE Cosmology on the Beach, Playa del Carmen, January 2010 Radiation log[Energy] 120 orders of magnitude Evolution of Energy Densities w = p/r DE 1 rrad a , wr = 3 rmat a 3 , wm = 0 4 Matter Cosmological Constant initial size of universe log[a] COINCIDENCE PROBLEM 1) Cosmologial constant w = -1 2) Quintessence (scalar field) w = w(a) rL a 0 = cte, wL = 1, today dynamics, e.g. scalar field rf a 3(1 w) , wf (a) Dark Energy Models Generic Properties: Scalar fields with weak coupling to the SM • Quintessence Scalar field with standard (canonical) kinetic term, a slow roll potential V and w > -1 • K-essence (include Tachyons) Scalar field with non standard kinetic term • Phantom Scalar field with negative kinetic term, can have w < -1 Mixture of any of the above Model buliding: • Tracking Models • Pseudo Nambu-Godstone Bosons, pNGB • Condensate Models • Assisted Inflation • Interacting (coupled) Models • Chameleon Models • Late Generation of DE • Oscillating Models • Mocker Models • Quartessence and Chaplygin gas models • Skating Models, • Wet fluid • Leveling Models • Quintom Models many others.... •Tracking Models • •Quartessence •Wet •Quintom •Condensate •Interaction •Chameleon Pseudo Oscillating •Mocker •Skating fluid Nambu-Godstone Models Models Models, Models Models Models Models Bosons, pNGB •Late scalar Generation fields and that ofChaplygin DE redshift gas (track) models as the dominate energy component, •Leveling Models •Assisted Inflation Dynamics Equivalent Scalar effective Interaction DE Transition Go potential from fields scalar free corresponding to between from that the and field field acquiere cross sum matter mass behavior DE produced of over depends like and ascalar to a constant a small the behavior other w circle =by w+1 on mass = afluid, w to in -1 late the to component phase cosmological line trough e.g. cosmological time environment dark space phase non-perturbative matter and transition constant aconstant cosmological or neutrinos like like symmetry behavior behavior constant along Attempt Late they time to are unify insensitive dark matter of to initial and field dark conditions (F.Briscese, energy buy A.M.) w >-0.7 et al) Approach aproduction cosmological constant as the density nears a (Steinhardt limiting value and Slow rollcurves of the DE depends having multiple breaking (Barenboim (Holman (Vikman, (Bienetruy, (Amendola, (Khoury, along the curve & Odintosov (mass Brax Naidu, dw/da A.M.) & van Lykken et of is de al 04) =protected dw/da 04) -3(1Bruck) et&06; al, = w^2) Hu Barenboim, C on from w(1 et [physically al) +quantum w) (Linder Mena corresponding corrections) Requejo, 06)fields & Quigg but to aneed field 06)dw/da fine-tuning moving across of a (Makler, de Oliveira, Waga 03 for an overview) have parabolic tracks, respectively dw/da =-3(1 + w)(wwa) and = -3(1 + (Liddle et conditions al, Coley et(Frieman al) the constant initial potential] (Linder 05; et al, Liddle Choi) et al, 05)] w)(w + w_a). (Linder, 06) Quintessence large number of DE models, e.g. acceleration acceleration if Cosmology on the Beach, Playa del Carmen, January 2010 Evolution of Scalar Fields e =1 quintessence e = -1 phantom Friedmann eq. Autonomous evolution eqs. Classify the models by the limit of l = - V’/V , e = 1 canonical e = -1 phantom g = 1 + w, for e =1 Cosmology on the Beach, Playa del Carmen, January 2010 Stability issues perturbations around the solution the perturbations have an eq. of motion Cosmology on the Beach, Playa del Carmen, January 2010 Tracker Fields Tracker behavior = scalar field evolves as the dominant fluid eq.motion eq. of state Tracker condition Cosmology on the Beach, Playa del Carmen, January 2010 Tracker Fields However, tracking behavior may be reach later than present time, e.g. For IPL tracker needs n > 5 and has (n=5) w > - 0.75 trackers have w > - 0.7 For V = Cosmology on the Beach, Playa del Carmen, January 2010 V = m2 f2 The field oscillates around the minimum with w = 0 1 1 0.8 0.8 0.6 0.4 0.5 0 w 0.6 V=x^2 0.2 0.4 0.5 0 0.2 0.2 1 0 1 2 t 3 4 0 0.5 V = L9/f5 1 1.5 t 2 2.5 0 3 0.5 1 1.5 t 2 2.5 Runaway. n = 5, wtr = 0.3, L = 10 TeV, w = - 0.75, W = 0.72 1 1 0.5 0.8 0.5 0.4 w 0.6 0.3 0 0.4 0.5 0.2 0.2 0.1 1 0 0 0 0 1 2 3 4 2 6 8 10 12 0 14 2 4 6 5 n = 1, wtr = 2/3 L = keV, L5/f 8 10 12 14 t t t V= 4 1 w = - 0.87, W = 0.72 1 2 0.8 0.5 1.5 1 w 0.6 0.4 0.5 0.5 0.2 0 0 1 2 3 t 4 5 0 0 1 0 1 2 3 t 4 5 0 1 2 3 t 4 5 Tachyons Tachyon: the lowest string excitation in D-brane or D-antiD brane systems Tachyons were motivated by String. They represent the lowest energy state in Dbranes and V has a form both give a w = 0 Cosmology on the Beach, Playa del Carmen, January 2010 Copeland et al PRD 05 Tachyon Potentials n = 2, acceleration depends on Vo 0 < n < 2, gives acceleration (1) cases (2) and (3) 2 < n, in case (1), (4) and (5) with w = 0 at late times Cosmology on the Beach, Playa del Carmen, January 2010 K-essence: Scalar fields with non canonical kinetic terms string motivation: at weak coupling g field, conformal transformation obtain acceleration w < -1/3 for X < 2/3 Cosmology on the Beach, Playa del Carmen, January 2010 Phantoms: Fields with negative kinetic term acceleration Big Rip: as t => ts H and r go to infinity at finite time (but avoided if V has a maximum) p-Nambu-Goldstone Bosons pNGB • A global continuos symmetry has massless Nambu-Godlstone bosons • Non-perturbative effects may break the symmetry and give a small mass • The mass is protected from loop corrections by the global symmetry • e.g. axion fields • Typical potential is: Slow roll V’/V << 1 fa > Mpl helps inflation but V will have corrections from instanton contributions expand around the extrema duration of inflation Cosmology on the Beach, Playa del Carmen, L.Sorbo et al ‘05 January 2010 60 1 3 2.5 2 1.5 1 0.5 0 50 V V' w 0.5 0 40 30 20 0.5 10 0 1 0 2 4 6 8 t 10 12 14 0 2 4 6 t 8 10 12 0 2 4 6 At the maximum the pGNB is tachyonic so instabilities arise Cosmology on the Beach, Playa del Carmen, 8 t January 2010 10 12 14 • pNGB are scalar fields with mass protected by the symmetry however, • Models with fa < 0.1 Mpl are extremely fine-tuned • Models with fa > Mpl have a V with instanton contributions Cosmology on the Beach, Playa del Carmen, January 2010 Possibe way out 1) fa > mpl not good from strings or GR 2) Many pNGB 3) Two pNGB (mixing with QCD type hidden sector) v = 10 eV, M = 1019 GeV m = 0.001 eV pNGB may work if the scale m can be brought close to DE scale, i.e. late time phase transition. Cosmology on the Beach, Playa del Carmen, January 2010 Interacting Dark Energy General Analysis Define effective equations of state which fluid dominates depends on the sign of Dweff e.g. for d = c H r dm , c constant a late time attractor Cosmology on la the Beach, Inst. Playa Carmen, A. de Macorra de del Física, UNAM January 2010 Observational constraints on an interacting dark energy model, R. Maartens et al, arXiv:0907.4987 Cosmology on the Beach, Playa del Carmen, January 2010 Interacting Dark Energy f e.g. Scalar Field f and Fermions y mass Fermi-Dirac distribution with a field dependent mass M gs degrees of freedom Density Pressure A. de la Macorra, on la the Beach, Inst. Playa Carmen, Inst. Cosmology de Física, UNAM A. de Macorra de del Física, UNAM January 2010 “Cosmology of mass-varying neutrinos driven by quintessence …” A, W. Brookfield, et al Phys.Rev.D73:083515,2006, CDM f astro-ph/0512367 n n Cosmology on the Beach, Playa del Carmen, January 2010 How to How to obtain w < -1 ? 1) For the interacting fluids 2) For the non-interacting fluids using get Cosmology on the Beach, Playa del Carmen, January 2010 = - 1.06 w < -1 can be an “optical effect” Describe the universe with i) non-interacting DE and DM wDE and wm = 0 ii) Interacting DE and DM Non Interacting Interacting wIDE = wf and wm = 0 wDE : apparent eq. of state as seen for the non-interaction DE wDE can be < -1 if x > 0 wDE i) For x = 0 wap = wf ii) For x > 0 wap < wf we can have wDE < - 1 ! <-1 even though wIDE = wf > -1 (for a growing function f(f) i.e. f (a<1) /fo(ao=1) < 1 Cosmology on the Beach, Playa del Carmen, January 2010 Neutrinos in Cosmology Neutrinos density From HM experiment Implications to Dark Energy With out HM: -0.94 < w < -1.28 95%CL with HM: -1.09 < w < -1.67 95%CL w is more negative ! A cosmological constant is not within the 95 % CL A.Melchiorri, P.Serra, R.Bean A.M. Astropart.Phys. ‘07. Condensate Model A.M. PRL ‘01, JHEP ’03,PRD‘05 Evolution of coupling constants vs energy SU(3) QCD Dark Energy SU(Nc=3), Nf = 6, b = 3 SU(2) Weak interact. SU(1) E.M. interact. one loop evolution 1 g 2 (L) = 1 g 2 (L gut) b = 3N c N f L gut 10 GeV , 16 g 2 gut 1 / 2 b L Log [ ] 2 L gut 8p Condensation or phase transition scale L = L gut e 2 8p 2 / g gut b L QCD 200 MeV L DE 40 eV What happens to elementary particles when the coupling becomes strong ? The particles form neutral bound states. Quarks form: p =< d d pions, p =< uud , n =< udd protons, neutrons LQCD 200MeV Dark Energy is a bound states made out of fundamental particles f = (< YY ) 1/ 3 L DE 40 eV Dark Energy Scalar field Initial Conditions for V and f fi = (< YY )1/ 3 = LDE V (fi ) = L DE 4 2 / 3fi 2 / 3 = L DE 4 mf (fi ) = 2 2V f 2 = L DE 4 2 / 3fi 2 2 / 3 = L DE 2 Cosmology on the Beach, Playa del Carmen, January 2010 Dark Energy Model Dark Group: SU(Nc=3), Nf=6 using supersymmetry y non perturbative and exact results we determine the potential V (Affleck-Dine-Seiberg): 1 /( N c N f ) W = ( N c N f )(LbDE / det < Y Y ) V = | f = (< YY )1/ 3 dW 2 4 n | = L DE f n df L DE 40 eV Phase Transition or condensation scale The potential V is generated below the energy scale L DE when the coupling constant g becomes large A.Cosmology de la Macorra, Física, UNAM onInst. the de Beach, Playa del Carmen, January 2010 r r a 4 radiation DE r m a 3 rf a 3(1 w) matter i) For E > LDE fundamental particles are massless and we have w = 1/3 ii) At E = LDE, phase transition ! Effective scalar field and potential V are generated w is dynamical for E < LDE. V(f ) Effective potential Effective potentital f Dark Energy evolution (after phase transition) wo = - 0.92 Having extra particles coupled at high energies with the standard model gives a smaller energy density for our Dark Group Late time generation of Dark Energy F.Briscese, A.M. 08, 09 Overview 1) The universe contains no dark energy field f 2) At late time the field f is generated by a relativistic field j, via a quantum transition 4) The scale of the re-generation is dynamically obtained given in terms of the coupling “g” between G/H > 1 f, j 5) we can unify inflation with dark energy with inflation 6) We can use the same interaction for the inflaton f decay and its the late time re-generation Cosmology on A.the de la Beach, Macorra, Playa IFUNAM, del Carmen, IAC January 2010 Inflation – Dark Energy Unification i) Inflation (accelerates univ.) => Flat at high energy ii) Dark Energy (accelerates univ.) => Flat al low energy iii) but we require a long period of deceleration dominated by radiation and later by matter (nucleosynthesis, formation of galaxies, stars etc) Are the 2 inflation periods connected ? Can we have a single field producing inflation? iii) and Require a V: |V’/V|<1 , |V’’/V| < 1 dr/r =105 and V(fo)=Vo f coupling Vint (j relativistic field c , y SM particles) Cosmology on la the Beach, Inst. Playa Carmen, A. de Macorra de del Física, UNAM January 2010 V(f) Inflaton- Dark Energy Unification f coupling Vint (j relativistic field c , y SM particles) The process takes place when 1) G/H > 1 Inflaton Decay f --> j j j 2) Reheating with Standard model with SM particles 3) Dark Energy Re-generation f and j relativistic if we take Cosmology on A.the de la Beach, Macorra, Playa IFUNAM, del Carmen, IAC January 2010 Re-generation process: • Start with No f particles • E > Egen with n = V = r = 0 • Only for E < Egen f particles are produced • Potential V is generated Cosmology on the Beach, Playa del Carmen, January 2010 Linear evolution of perturbations • DE Homogenous via Equation of state w(t) (Adiabatic sound speed ca(t) ) • DE Perturbations via Sound speed cs(t) • Dark Matter General fluid (e.g. Dark Energy) with ca2 = w ^ = rest frame of the D. E. fluid q = fluid velocity perturbation x = Dark Energy • DE perturbations are crucial to distinguish between different DE models • sound speed cs • adiabatic sound speed ca A. deBeach, la Macorra Inst. de Física, Cosmology on the Playa delUNAM Carmen, January 2010 Linear growth cs2 = w and w = wo + wa z/(1+z) Nonlinear growth w = wo + wa z/(1+z) Collapsed halos of mass M + dM Total number of halos with M > Minf L. Abramo et al astro-ph/0707.2882 Conclusiones • Our universe is dominated today by Dark Energy • Do not know the nature of Dark Energy • Cosmological Constant or dynamical DE ? • Determination of the cosmological parameters depend on the priors used (e.g. parametrization of dark energy w(z) ) • Many models of Dark Energy in the market • Perhaps the best (simplest) candidates are scalar fields but need to derive the potential V = L f (f) and explain the smallness of the scale L and the functional form f (f) • DE perturbations are important to break degeneracy (Cosmological constant has no perturbations or interaction) • scalar fields produced at late time have less fine tuning on the parameters, could explain the coincidence problem (e.g. condensates models) • or protected by symmetries (e.g. pNGB) • or …. Cosmology on the Beach, Playa del Carmen, January 2010 Cosmology on the Beach, Playa del Carmen, January 2010 Lagrangian Eq. of motion perturbations around the classical background account for the quantum states (particles) Eqs. of motion and Boltzmann equations Cosmology on A.the de la Beach, Macorra, Playa IFUNAM, del Carmen, IAC January 2010 Initial Energy Densities Initial Conditions gi = r DE p2 = g D TD 4 , 30 r rad p2 = g r Tg 4 30 (bos. deg 7 ferm. deg) 8 g rad = 228 for MSSM E 1 TeV g rad = 3.36 for E < 0.1 MeV g D = 97.5 for Dark Group E L DE = 42 eV i) Initial = Unification Scale E = Lgut W rad (L gut ) = we have Tg = TDE and all particles are massless, i.e. radiation. ii) At phase transition E ~ LDE = 40 eV W D (L gut ) = W rad (L DE ) = W DE (L DE ) = g rad g rad g D gD g rad g D = 0.3 g rad g rad g D (TD / Tg ) 4 g DE (TDE / Tg ) 4 g rad g D (TD / Tg ) = 0.7 4 = 0.9 = 0.1 Cosmology on the Beach, Playa del Carmen, January 2010 Cosmology on the Beach, Playa del Carmen, January 2010