1. Dunkle Energie – Ein kosmisches Raetsel Quintessence

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

3. What is our Universe made of ?

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

5. Dark Energy : homogeneously distributed

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

7. 209 SN Ia and medians Tonry et al. 2003 Ω h =0.7 Ω m =0.3

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

9. consistent cosmological model !

10. 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

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

12. 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 ?

13. Cosm. Const. | Quintessence static | dynamical

14. 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

15. 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

16. 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

17. 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 !

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

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

20. 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 !

21. 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

22. 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

23. 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 -

24. Quintessence becomes important “today”

25. 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

26. 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 :

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

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

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

30. Early quintessence slows down the growth of structure

31. 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

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

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

34. 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”

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

36. “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)

37. 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,…

38. Variation of fine structure constant Observation of (molecular absorption lines Observation of (molecular absorption lines in the light of quasars ) in the light of quasars ) 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

39. 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 !

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

41. 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 !

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

43. 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

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

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

46. Link between time variation of α and violation of equivalence principle typically : η = 10 -14

47. 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

48. ???????????????????????? 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 ?

49. Cosmon and fundamental mass scales 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 χ may evolve with time m n /M : ( almost ) constant - observation ! m n /M : ( almost ) constant - observation ! Only ratios of mass scales are observable

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

51. Dilatation anomaly Quantum fluctuations responsible for Quantum fluctuations responsible for dilatation anomaly dilatation anomaly Running couplings: Running couplings: V~χ 4-A, M p (χ )~ χ V~χ 4-A, M p (χ )~ χ V/M p 4 ~ χ -A : decreases for increasing χ !! V/M p 4 ~ χ -A : decreases for increasing χ !! E>0 : crossover quintessence E>0 : crossover quintessence

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

53. 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 !

54. Crossover Quintessence ( like QCD gauge coupling) ( like QCD gauge coupling) critical χ where δ grows large critical φ where k grows large 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

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

56. End

57. 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)

58. Supernova Ia Hubble-diagram redshift z Filippenko