1 / 59

Connections between Dark Energy and Particle Physics

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. Outline. Brief Introduction Properties of Dark Energy Theoretical Considerations

wilson
Télécharger la présentation

Connections between Dark Energy and Particle Physics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 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

  2. 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

  3. 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

  4. General approach to Dark Energy M2pl=1/8p G = 1 • Can introduce Dark Energy via • New Particles (modification of Tun ) • Scalar-Tensor (non-minimal coupling f(f) R ) • f(R) modification (e.g. MOND) • Inhomogeneities (live in a huge Bubble) • for reviews see • Dynamics of dark energy. E. Copelandet al Int.J.Mod.Phys.D15:1753,2006. hep-th/0603057 • Dark Energy and the Accelerating Universe. J. Friemanet al, Ann.Rev.Astron.Astrophys.46:385, 2008, arXiv:0803.0982 • The Dynamics of Quintessence, The Quintessence of Dynamics. E. Linder Gen.Rel.Grav.40:329-356,2008, arXiv:0704.2064 Cosmology on the Beach, Playa del Carmen, January 2010

  5. 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

  6. 5 year WMAP, Komatsu et al w = cte Cosmology on the Beach, Playa del Carmen, January 2010

  7. 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

  8. Improved Dark Energy Constraints from ~100 New CfA Supernova Type Ia Light Curves.M.Hicken et al Astrophys.J.700:1097-1140,2009. Vector Fields i.e. w = - 0.87 +/- 0.06 Cosmology on the Beach, Playa del Carmen, January 2010

  9. Reconstruction from Hubble diagram V, w(z) • Reconstruction: • Model independent • or • Piece wise w(z) for z+Dz • 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

  10. 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

  11. 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

  12. Parametrization of w • w = wo constant • w = wo + w1 z • w = wo + w1 z/(1+z) The values and evolution of w(z) depend heavily on the parametrization used 4 free parameters Yellow no cross over the w = -1 line Yellow = 95% C.L. Corasaniti et al PRD’04

  13. 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 …

  14. Dark Energy Properties A. Riess et al ‘06 • 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

  15. Dark Energy Properties for scalar fields • Slow roll conditions must be satisfied • |V’/V| << 1 • |V’’/V| << 1 • Weakly coupled to SM particles • Scalar field light mass (induces a long range force) Present values of mass and dark energy M2pl=1/8p G = 1 Cosmology on the Beach, Playa del Carmen, January 2010

  16. 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 ? • Derive the potential V(f ) • Small number of free parameters • Reasonable choice of values for the free parameters • (i.e no fine tuning of parameters) • Initial condition of scalar field f and energy density r(f) • Account for the long period of radiation and matter domination • 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

  17. 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

  18. 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

  19. Particle Phsyics and Dark Energy • 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) • 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> • 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 e.g. A Vi/VDE Cosmology on the Beach, Playa del Carmen, January 2010

  20. Evolution of Energy Densities Radiation w = p/r DE 120 orders of magnitude log[Energy] Matter CosmologicalConstant • initial size of universe log[a] today COINCIDENCE PROBLEM dynamics, e.g. scalar field • Cosmologial constant w = -1 • Quintessence (scalar field) w = w(a)

  21. 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.... • Wet fluid • Equivalent to the sum of a constant w component and a cosmological constant (Holman & Naidu, 04) • Oscillating Models • Dynamics corresponding to a circle in phase space • (Barenboim & Lykken 06; Barenboim, Mena Requejo, & Quigg 06) • Quintom Models • Scalar fields that cross over the w = -1 line • (Vikman, Odintosov et al, Hu et al) • Pseudo Nambu-Godstone Bosons, pNGB • Scalar fields that acquiere a small mass trough non-perturbative symmetry breaking (mass is protected from quantum corrections) but need fine-tuning of the initial conditions (Frieman et al, Choi) • Chameleon Models • DE potential and mass depends on the environment • (Khoury, Brax et al 04) • Interaction Models • Interaction between DE and other fluid, e.g. dark matter or neutrinos • (Amendola, van de Bruck) • Condensate Models • effective scalar field produced by a late time phase transition • (Bienetruy, A.M.) • Mocker Models • Transition from matter like behavior to cosmological constant like behavior along curves of dw/da = C w(1 + w) (Linder 06) • Skating Models, • Go from free field behavior w = +1 to cosmological constant like behavior along the curve dw/da = -3(1- w^2) [physically corresponding to a field moving across a constant potential] (Linder 05; Liddle et al, 05)] • Quartessence and Chaplygin gas models • Attempt to unify dark matter and dark energy • (Makler, de Oliveira, & Waga 03 for an overview) • Late Generation of DE • Late time production of scalar field (F.Briscese, A.M.) • Tracking Models • scalar fields that redshift (track) as the dominate energy component, • they are insensitive to initial conditions buy w >-0.7 (Steinhardt et al) • Leveling Models • Approach a cosmological constant as the density nears a limiting value and have parabolic tracks, respectively dw/da =-3(1 + w)(w- wa) and dw/da = -3(1 + w)(w + w_a). (Linder, 06) • Assisted Inflation • Slow roll of the DE depends on having multiple fields • (Liddle et al, Coley et al)

  22. Quintessence large number of DE models, e.g. acceleration acceleration if Cosmology on the Beach, Playa del Carmen, January 2010

  23. Evolution of Scalar Fields e =1 quintessence e = -1 phantom Friedmann eq. e = 1 canonical e = -1 phantom Autonomous evolution eqs. Classify the models by the limit of l = - V’/V , g = 1 + w, for e =1 Cosmology on the Beach, Playa del Carmen, January 2010

  24. Stability issues perturbations around the solution the perturbations have an eq. of motion Cosmology on the Beach, Playa del Carmen, January 2010

  25. 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

  26. 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

  27. V = m2f2 The field oscillates around the minimum with w = 0 V=x^2 V = L9/f5 Runaway. n = 5, wtr = -0.3, L = 10 TeV, w = - 0.75, W = 0.72 n = 1, wtr = -2/3 L = keV, w = - 0.87, W = 0.72 V = L5/f

  28. 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 D-branes and V has a form both give a w = 0 Cosmology on the Beach, Playa del Carmen, January 2010

  29. Tachyon Potentials Copeland et al PRD 05 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

  30. 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

  31. 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)

  32. 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 L.Sorbo et al ‘05 Cosmology on the Beach, Playa del Carmen, January 2010

  33. At the maximum the pGNB is tachyonic so instabilities arise Cosmology on the Beach, Playa del Carmen, January 2010

  34. pNGB are scalar fields with mass protected by the symmetry • however, • Models with fa < 0.1 Mplare extremely fine-tuned • Models with fa > Mplhave a V with instanton contributions Cosmology on the Beach, Playa del Carmen, January 2010

  35. Possibe way out • fa > mpl not good from strings or GR • Many pNGB • 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

  36. 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 the Beach, Playa del Carmen, January 2010 • A. de la Macorra Inst. de Física, UNAM

  37. Observational constraints on an interacting dark energy model, R. Maartens et al, arXiv:0907.4987 Cosmology on the Beach, Playa del Carmen, January 2010

  38. 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, Inst. de Física, UNAM Cosmology on the Beach, Playa del Carmen, January 2010 • A. de la Macorra Inst. de Física, UNAM

  39. “Cosmology of mass-varying neutrinos driven by quintessence …” A, W. Brookfield, et al Phys.Rev.D73:083515,2006, astro-ph/0512367 CDM f n n Cosmology on the Beach, Playa del Carmen, January 2010

  40. 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 Cosmology on the Beach, Playa del Carmen, January 2010

  41. = - 1.06 w < -1 can be an “optical effect” • Describe the universe with • non-interacting DE and DM • wDE and wm = 0 • ii) Interacting DE and DM • wIDE = wf and wm = 0 Non Interacting Interacting wDE : apparent eq. of state as seen for the non-interaction DE wDE can be < -1 if x > 0 wDE< - 1 i) For x = 0 wap = wf ii) For x > 0 wap < wf we can have wDE < - 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

  42. 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 ! Acosmological constant isnot within the 95 % CL A.Melchiorri, P.Serra, R.Bean A.M. Astropart.Phys. ‘07.

  43. 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. Condensation or phase transition scale one loop evolution

  44. What happens to elementary particles when the coupling becomes strong ? The particles form neutral bound states. Quarks form: pions, protons, neutrons Dark Energy is a bound states made out of fundamental particles Dark Energy Scalar field Initial Conditions for V and f Cosmology on the Beach, Playa del Carmen, January 2010

  45. 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): Phase Transition or condensation scale The potential V is generated below the energy scale when the coupling constant g becomes large A. de la Macorra, Inst. de Física, UNAM Cosmology on the Beach, Playa del Carmen, January 2010

  46. radiation DE matter • i) For E > LDEfundamental particles are massless and we have w = 1/3 • 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

  47. 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

  48. Late time generation of Dark Energy F.Briscese, A.M. 08, 09 • Overview • The universe contains no dark energy field f • At late time the field f is generated by a relativistic field j, via a quantum transition • The scale of the re-generation is dynamically obtained G/H > 1 • given in terms of the coupling “g” between f, j • we can unify inflation with dark energy with inflation • We can use the same interaction for the inflaton f decay and its the late time re-generation A. de la Macorra, IFUNAM, IAC Cosmology on the Beach, Playa del Carmen, January 2010

  49. Inflation – Dark Energy Unification • Inflation (accelerates univ.) => Flat at high energy • Dark Energy (accelerates univ.) => Flat al low energy • 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? • Require a V: |V’/V|<1 , |V’’/V| < 1 • and dr/r =10-5 and V(fo)=Vo V(f) f coupling Vint (j relativistic field c , y SM particles) Cosmology on the Beach, Playa del Carmen, January 2010 • A. de la Macorra Inst. de Física, UNAM

  50. Inflaton- Dark Energy Unification f coupling Vint (j relativistic field c , y SM particles) The process takes place when 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 A. de la Macorra, IFUNAM, IAC Cosmology on the Beach, Playa del Carmen, January 2010

More Related