1. Dunkle Energie – Ein kosmisches Raetsel Quintessence

2. Quintessence – a fifth force from a fifth force from variation of the variation of the fundamental scale ? fundamental scale ? Durham 04

3. Quintessence C.Wetterich A.Hebecker,M.Doran,M.Lilley,J.Schwindt, C.Müller,G.Schäfer,E.Thommes, R.Caldwell

4. What is our Universe made of ?

5. fire, air, water, soil ! Quintessence !

6. critical density ρ c =3 H² M² ρ c =3 H² M² critical energy density of the universe critical energy density of the universe ( M : reduced Planck-mass, H : Hubble parameter ) ( M : reduced Planck-mass, H : Hubble parameter ) Ω b =ρ b /ρ c Ω b =ρ b /ρ c fraction in baryons fraction in baryons energy density in baryons over critical energy density energy density in baryons over critical energy density

7. Composition of the universe Ω b = 0.045 Ω b = 0.045 Ω dm = 0.225 Ω dm = 0.225 Ω h = 0.73 Ω h = 0.73

8. gravitational lens, HST

9. spatially flat universe theory (inflationary universe ) theory (inflationary universe ) Ω tot =1.0000……….x Ω tot =1.0000……….x observation ( Boomerang,WMAP ) observation ( Boomerang,WMAP ) Ω tot =1.02 (0.02) Ω tot =1.02 (0.02) Ω tot = 1

10. picture of the big bang

11. mean values Ω tot =1.02 Ω m =0.27 Ω b =0.045 Ω dm =0.225

12. Ω tot =1

13. Dark Energy Ω m + X = 1 Ω m + X = 1 Ω m : 30% Ω m : 30% Ω h : 70% Dark Energy Ω h : 70% Dark Energy h : homogenous, often Ω Λ instead of Ω h

14. Dark Energy : homogeneously distributed

15. Dark Energy : prediction: The expansion of the Universe accelerates today !

16. Perlmutter 2003

17. Supernova cosmology Riess et al. 2004

18. Structure formation : fluctuation spectrum Waerbeke CMB agrees with galaxy distribution Lyman – α forest and gravitational lensing effect !

19. consistent cosmological model !

20. Composition of the Universe Ω b = 0.045 visible clumping Ω b = 0.045 visible clumping Ω dm = 0.225 invisible clumping Ω dm = 0.225 invisible clumping Ω h = 0.73 invisible homogeneous Ω h = 0.73 invisible homogeneous

21. What is Dark Energy ? Cosmological Constant or Quintessence ?

22. Cosmological Constant Constant λ compatible with all symmetries Constant λ compatible with all symmetries No time variation in contribution to energy density No time variation in contribution to energy density Why so small ? λ/M 4 = 10 -120 Why so small ? λ/M 4 = 10 -120 Why important just today ? Why important just today ?

23. Cosm. Const. | Quintessence static | dynamical

24. Cosmological mass scales Energy density Energy density ρ ~ ( 2.4×10 -3 eV ) - 4 ρ ~ ( 2.4×10 -3 eV ) - 4 Reduced Planck mass M=2.44×10 18 GeV Newton’s constant G N =(8πM²) Only ratios of mass scales are observable ! homogeneous dark energy: ρ h /M 4 = 6.5 10ˉ¹²¹ homogeneous dark energy: ρ h /M 4 = 6.5 10ˉ¹²¹ matter: ρ m /M= 3.5 10ˉ¹²¹ matter: ρ m /M 4 = 3.5 10ˉ¹²¹

25. Time evolution ρ m /M 4 ~ aˉ ³ ~ ρ m /M 4 ~ aˉ ³ ~ ρ r /M 4 ~ aˉ 4 ~ t -2 radiation dominated universe ρ r /M 4 ~ aˉ 4 ~ t -2 radiation dominated universe Huge age small ratio Huge age small ratio Same explanation for small dark energy? Same explanation for small dark energy? tˉ ² matter dominated universe tˉ 3/2 radiation dominated universe

26. Quintessence Dynamical dark energy, generated by scalar field generated by scalar field (cosmon) (cosmon) C.Wetterich,Nucl.Phys.B302(1988)668, 24.9.87 P.J.E.Peebles,B.Ratra,ApJ.Lett.325(1988)L17, 20.10.87

27. Cosmon Scalar field changes its value even in the present cosmological epoch Scalar field changes its value even in the present cosmological epoch Potential und kinetic energy of cosmon contribute to the energy density of the Universe Potential und kinetic energy of cosmon contribute to the energy density of the Universe Time - variable dark energy : Time - variable dark energy : ρ h (t) decreases with time ! ρ h (t) decreases with time !

28. Cosmon Tiny mass Tiny mass m c ~ H m c ~ H New long - range interaction New long - range interaction

29. “Fundamental” Interactions Strong, electromagnetic, weak interactions gravitationcosmodynamics On astronomical length scales: graviton + cosmon

30. Evolution of cosmon field Field equations Field equations Potential V(φ) determines details of the model Potential V(φ) determines details of the model e.g. V(φ) =M 4 exp( - φ/M ) e.g. V(φ) =M 4 exp( - φ/M ) for increasing φ the potential decreases towards zero ! for increasing φ the potential decreases towards zero !

31. Cosmic Attractors Solutions independent of initial conditions typically V~t -2 φ ~ ln ( t ) Ω h ~ const. details depend on V(φ) or kinetic term early cosmology

32. Quintessence becomes important “today”

33. Equation of state p=T-V pressure kinetic energy p=T-V pressure kinetic energy ρ=T+V energy density ρ=T+V energy density Equation of state Equation of state Depends on specific evolution of the scalar field

34. Negative pressure w < 0 Ω h increases (with decreasing z ) w < 0 Ω h increases (with decreasing z ) w < -1/3 expansion of the Universe is w < -1/3 expansion of the Universe is accelerating accelerating w = -1 cosmological constant w = -1 cosmological constant late universe with small radiation component :

35. small early and large present dark energy fraction in dark energy has substantially increased since end of structure formation fraction in dark energy has substantially increased since end of structure formation expansion of universe accelerates in present epoch expansion of universe accelerates in present epoch

36. How can quintessence be distinguished from a cosmological constant ?

37. Time dependence of dark energy cosmological constant : Ω h ~ t² ~ (1+z) -3 M.Doran,…

39. Early dark energy A few percent in the early Universe Not possible for a cosmological constant

40. Quintessence and solution of cosmological constant problem should be related !

41. Fundamental mass scale Unification fixes parameters with dimensions Unification fixes parameters with dimensions Special relativity : c Special relativity : c Quantum theory : h Quantum theory : h Unification with gravity : Unification with gravity : fundamental mass scale fundamental mass scale ( Planck mass, string tension, …) ( Planck mass, string tension, …)

42. Fundamental mass scale Fixed parameter or dynamical scale ? Fixed parameter or dynamical scale ? Dynamical scale Field Dynamical scale Field Dynamical scale compared to what ? Dynamical scale compared to what ? momentum versus mass momentum versus mass ( or other parameter with dimension ) ( or other parameter with dimension )

43. Cosmon and fundamental mass scale Assume all mass parameters are proportional to scalar field χ (GUTs, superstrings,…) Assume all mass parameters are proportional to scalar field χ (GUTs, superstrings,…) M p ~ χ, m proton ~ χ, Λ QCD ~ χ, M W ~ χ,… M p ~ χ, m proton ~ χ, Λ QCD ~ χ, M W ~ χ,… χ may evolve with time : cosmon χ may evolve with time : cosmon m n /M : ( almost ) constant - observation ! m n /M : ( almost ) constant - observation ! Only ratios of mass scales are observable Only ratios of mass scales are observable

44. Example : Field χ denotes scale of transition from higher dimensional physics to effective four dimensional description in theory without fundamental mass parameter (except for running of dimensionless couplings…)

45. Dilatation symmetry Lagrange density: Lagrange density: Dilatation symmetry for Dilatation symmetry for Conformal symmetry for δ=0 Conformal symmetry for δ=0

46. Dilatation anomaly Quantum fluctuations responsible for Quantum fluctuations responsible for dilatation anomaly dilatation anomaly Running couplings: hypothesis Running couplings: hypothesis Renormalization scale μ : ( momentum scale ) Renormalization scale μ : ( momentum scale ) λ~(χ/μ) -A λ~(χ/μ) -A

47. Dilatation anomaly V~χ 4-A, M p (χ )~ χ V~χ 4-A, M p (χ )~ χ V/M p 4 ~ χ -A : V/M p 4 ~ χ -A : decreases for increasing χ !! decreases for increasing χ !! E>0 : crossover quintessence E>0 : crossover quintessence

48. Cosmology Cosmology : χ increases with time ! ( due to coupling of χ to curvature scalar ) for large χ the ratio V/M 4 decreases to zero Effective cosmological constant vanishes asymptotically for large t !

49. Weyl scaling Weyl scaling : g μν → (M/χ) 2 g μν, φ/M = ln (χ 4 /V(χ)) φ/M = ln (χ 4 /V(χ)) Exponential potential : V = M 4 exp(-φ/M) No additional constant !

50. Crossover Quintessence ( like QCD gauge coupling) ( like QCD gauge coupling) critical χ where δ grows large critical φ where k grows large k²(φ )=δ(χ)/4 k²(φ )= “1/(2E(φ c – φ)/M)” k²(φ )= “1/(2E(φ c – φ)/M)” if  c  ≈ 276/M ( tuning ! ) if  c  ≈ 276/M ( tuning ! ) Relative increase of dark energy in present Relative increase of dark energy in present cosmological epoch cosmological epoch

52. Realistic cosmology Hypothesis on running couplings Hypothesis on running couplings yields realistic cosmology yields realistic cosmology for suitable values of A, E, φ c for suitable values of A, E, φ c

53. Dilatation anomaly Computation of running couplings ( beta functions ) needs unified theory ! Computation of running couplings ( beta functions ) needs unified theory ! Dominant contribution from modes with momenta ~χ ! Dominant contribution from modes with momenta ~χ ! No prejudice on “natural value “ of anomalous dimension should be inferred from tiny contributions at QCD- momentum scale ! No prejudice on “natural value “ of anomalous dimension should be inferred from tiny contributions at QCD- momentum scale ! Almost flat direction in potential for φ : Almost flat direction in potential for φ : Pseudo-Goldstone boson of dilatation symmetry Pseudo-Goldstone boson of dilatation symmetry

54. Are fundamental “constants” time dependent ? Fine structure constant α (electric charge) Ratio nucleon mass to Planck mass

55. “Fifth Force” Mediated by scalar field Mediated by scalar field Coupling strength: weaker than gravity Coupling strength: weaker than gravity ( nonrenormalizable interactions ~ M -2 ) ( nonrenormalizable interactions ~ M -2 ) Composition dependence Composition dependence violation of equivalence principle violation of equivalence principle Quintessence: connected to time variation of Quintessence: connected to time variation of fundamental couplings fundamental couplings R.Peccei,J.Sola,C.Wetterich,Phys.Lett.B195,183(1987) C.Wetterich, Nucl.Phys.B302,645(1988)

56. Quintessence and Time dependence of “fundamental constants” Fine structure constant depends on value of Fine structure constant depends on value of cosmon field : α(φ) cosmon field : α(φ) (similar in standard model: couplings depend on value of Higgs scalar field) (similar in standard model: couplings depend on value of Higgs scalar field) Time evolution of φ Time evolution of φ Time evolution of α Time evolution of α Jordan,…

57. Field dependent gauge coupling ( gauge invariance maintained ) for GUT : C.Hill ; Q.Shafi, CW

58. GUT : running of electromagnetic and strong gauge coupling related strong effect from variation of nucleon mass for time dependent couplings ! X.Calmet, H.Fritzsch

59. Where to look for time variation of fundamental couplings ? Nucleosynthesis Nucleosynthesis Molecular absorption lines in the light of distant Quasars Molecular absorption lines in the light of distant Quasars Oklo natural reactor Oklo natural reactor Atomic clocks Atomic clocks CMB CMB

60. A.Coc Abundancies of primordial light elements fromnucleosynthesis

61. Relative change of He 4 – abundance vs. relative change of couplings C.Mueller, G.Schaefer, …

62. if present 2-sigma deviation of He –abundance from CMB/nucleosynthesis prediction would be confirmed : Δα/α ( z=10 10 ) = -1.0 10 -3 GUT 1 Δα/α ( z=10 10 ) = -2.7 10 -4 GUT 2

63. Variation of fine structure constant as function of redshift Webb et al Srianand et al

64. Variation of fine structure constant Three independent data sets from Keck/HIRES Three independent data sets from Keck/HIRES Δ α/α = - 0.54 (12) 10 -5 Δ α/α = - 0.54 (12) 10 -5 Murphy,Webb,Flammbaum, june 2003 Murphy,Webb,Flammbaum, june 2003 VLT VLT Δ α/α = - 0.06 (6) 10 -5 Δ α/α = - 0.06 (6) 10 -5 Srianand,Chand,Petitjean,Aracil, feb.2004 Srianand,Chand,Petitjean,Aracil, feb.2004 z ≈ 2

65. Crossover quintessence and time variation of fundamental “constants” Upper bounds for relative variation of the Upper bounds for relative variation of the fine structure constant fine structure constant Oklo natural reactor Δ α/α < 10 -7 z=0.13 Oklo natural reactor Δ α/α < 10 -7 z=0.13 Meteorites ( Re-decay ) Δ α/α < 3 10 -7 z=0.45 Meteorites ( Re-decay ) Δ α/α < 3 10 -7 z=0.45 Crossover Quintessence compatible with QSO Crossover Quintessence compatible with QSO and upper bounds ! and upper bounds !

66. Time evolution of fundamental couplings traces time evolution of quintessence today w h close to -1 : today w h close to -1 : Small kinetic energy Small kinetic energy Slow change of φ Slow change of φ Slow change of α Slow change of α Very small Δα/α for low z ! Very small Δα/α for low z !

67. Variation of fine structure constant as function of redshift Webb et al

68. Atomic clocks and OKLO assumes that both effects are dominated by change of fine structure constant

69. Time variation of coupling constants is tiny – would be of very high significance ! Possible signal for Quintessence

70. Παντα ρει

71. Cosmodynamics Cosmon mediates new long-range interaction Range : size of the Universe – horizon Range : size of the Universe – horizon Strength : weaker than gravity Strength : weaker than gravity photon electrodynamics photon electrodynamics graviton gravity graviton gravity cosmon cosmodynamics cosmon cosmodynamics Small correction to Newton’s law

72. Violation of equivalence principle Different couplings of cosmon to proton and neutron Differential acceleration Violation of equivalence principle earth p,n cosmon

73. Differential acceleration η For unified theories ( GUT ) : Q : time dependence of other parameters η=Δa/2a

74. Link between time variation of α and violation of equivalence principle typically : η = 10 -14 if time variation of α near Oklo upper bound to be tested by MICROSCOPE

75. Summary o Ω h = 0.7 o Q/Λ : dynamical und static dark energy will be distinguishable will be distinguishable o Q : time varying fundamental coupling “constants” violation of equivalence principle violation of equivalence principle

76. ???????????????????????? Why becomes Quintessence dominant in the present cosmological epoch ? Are dark energy and dark matter related ? Can Quintessence be explained in a fundamental unified theory ?

77. End

78. A few references C.Wetterich, Nucl.Phys.B302,668(1988), received 24.9.1987 P.J.E.Peebles,B.Ratra, Astrophys.J.Lett.325,L17(1988), received 20.10.1987 B.Ratra,P.J.E.Peebles, Phys.Rev.D37,3406(1988), received 16.2.1988 J.Frieman,C.T.Hill,A.Stebbins,I.Waga, Phys.Rev.Lett.75,2077(1995) P.Ferreira, M.Joyce, Phys.Rev.Lett.79,4740(1997) C.Wetterich, Astron.Astrophys.301,321(1995) P.Viana, A.Liddle, Phys.Rev.D57,674(1998) E.Copeland,A.Liddle,D.Wands, Phys.Rev.D57,4686(1998) R.Caldwell,R.Dave,P.Steinhardt, Phys.Rev.Lett.80,1582(1998) P.Steinhardt,L.Wang,I.Zlatev, Phys.Rev.Lett.82,896(1999)

79. Dynamics of quintessence Cosmon  : scalar singlet field Cosmon  : scalar singlet field Lagrange density L = V + ½ k(φ)  Lagrange density L = V + ½ k(φ)  (units: reduced Planck mass M=1) (units: reduced Planck mass M=1) Potential : V=exp[-  Potential : V=exp[-  “Natural initial value” in Planck era  “Natural initial value” in Planck era  today:  =276 today:  =276

80. Quintessence models Kinetic function k(φ) : parameterizes the Kinetic function k(φ) : parameterizes the details of the model - “kinetial” details of the model - “kinetial” k(φ) = k=const. Exponential Q. k(φ) = k=const. Exponential Q. k(φ ) = exp ((φ – φ 1 )/α) Inverse power law Q. k(φ ) = exp ((φ – φ 1 )/α) Inverse power law Q. k²(φ )= “1/(2E(φ c – φ))” Crossover Q. k²(φ )= “1/(2E(φ c – φ))” Crossover Q. possible naturalness criterion: possible naturalness criterion: k(φ=0)/ k(φ today ) : not tiny or huge ! k(φ=0)/ k(φ today ) : not tiny or huge ! - else: explanation needed - - else: explanation needed -

81. Simple parameterization of quintessence parameter bnatural “time” variable

82. Early quintessence slows down the growth of structure

83. Growth of density fluctuations Matter dominated universe with constant Ω h : Matter dominated universe with constant Ω h : Dark energy slows down structure formation Dark energy slows down structure formation Ω h < 10% during structure formation Ω h < 10% during structure formation Substantial increase of Ω h (t) since structure has formed! Substantial increase of Ω h (t) since structure has formed! negative w h negative w h Question “why now” is back ( in mild form ) Question “why now” is back ( in mild form ) P.Ferreira,M.Joyce

84. Fluctuation spectrum Caldwell,Doran,Müller,Schäfer,…

85. Anisotropy of cosmic background radiation Caldwell,Doran,Müller,Schäfer,…

86. How to distinguish Q from Λ ? A) Measurement Ω h (z) H(z) i) Ω h (z) at the time of i) Ω h (z) at the time of structure formation, CMB - emission structure formation, CMB - emission or nucleosynthesis or nucleosynthesis ii) equation of state w h ( today ) > -1 ii) equation of state w h ( today ) > -1 B) Time variation of fundamental “constants”

87. Dirac’s hypothesis The very small dimensionless numbers in physics are due to huge age of the universe. The very small dimensionless numbers in physics are due to huge age of the universe. (A) may be true for ratio of dark energy over M 4

90. Cosmon and time variation of couplings small coupling of cosmon to matter due to fixed points behavior small coupling of cosmon to matter due to fixed points behavior close to fixed point : small time evolution of couplings coupling to matter weaker than gravitational strength

91. dependence of fixed point on δ could induce observable effect adjusting b 6 to reproduce results by Webb et al: smaller for Srianand et al !