Quintessence from time evolution of fundamental mass scale

1. Quintessence from time evolution of fundamental mass scale

2. Ωm + X = 1 Ωm : 30% Ωh : 70% Dark Energy ?

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

4. Dark Energy dominates the Universe Energy - density in the Universe = Matter + Dark Energy 30 % + 70 %

5. Matter : Everything that clumps Abell 2255 Cluster ~300 Mpc

6. Ωm= 0.3 gravitational lens , HST

7. Ωtot=1

8. Dark Energy Ωm + X = 1 Ωm : 30% Ωh : 70% Dark Energy h : homogenous , often ΩΛ instead of Ωh

9. Space between clumps is not empty :Dark Energy !

10. Dark Energy density isthe same at every point of space “ homogeneous “

11. Two important predictions The expansion of the Universe accelerates today ! Structure formation : One primordial fluctuation- spectrum

12. consistent cosmological model !

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

14. Cosmological Constant- Einstein - • Constant λ compatible with all symmetries • No time variation in contribution to energy density • Why so small ? λ/M4 = 10-120 • Why important just today ?

15. Cosm. Const. | Quintessence static | dynamical

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

17. Energy density ρ ~ ( 2.4×10 -3 eV )- 4 Reduced Planck mass M=2.44×1018GeV Newton’s constant GN=(8πM²) Cosmological mass scales Only ratios of mass scales are observable ! homogeneous dark energy: ρh/M4 = 6.5 10ˉ¹²¹ matter: ρm/M4= 3.5 10ˉ¹²¹

18. Time evolution tˉ² matter dominated universe tˉ3/2 radiation dominated universe • ρm/M4 ~ aˉ³ ~ • ρr/M4 ~ aˉ4~ t -2radiation dominated universe Huge age small ratio Same explanation for small dark energy ?

19. Time dependent Dark Energy :Quintessence • What changes in time ? • Only dimensionless ratios of mass scales are observable ! • V : potential energy of scalar field or cosmological constant • V/M4 is observable • Imagine the Planck mass M increases …

20. Quintessence from time evolution of fundamental mass scale

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

22. Cosmon and fundamental mass scale • Assume all mass parameters are proportional to scalar field χ (GUTs, superstrings,…) • Mp~ χ , mproton~ χ , ΛQCD~ χ , MW~ χ ,… • χ may evolve with time : cosmon • mn/M : ( almost ) constant - observation! Only ratios of mass scales are observable

23. 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…)

24. Dilatation symmetry • Lagrange density: • Dilatation symmetry for • Conformal symmetry for δ=0

25. Dilatation anomaly • Quantum fluctuations responsible for dilatation anomaly • Running couplings: hypothesis • Renormalization scale μ: ( momentum scale ) • λ~(χ/μ) –A • E > 0 : crossover Quintessence

26. Dilatation anomaly and quantum fluctuations • Computation of running couplings ( beta functions ) needs unified theory ! • 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 !

27. Cosmology Cosmology : χ increases with time ! ( due to coupling of χ to curvature scalar ) for large χ the ratio V/M4 decreases to zero Effective cosmological constant vanishes asymptotically for large t !

28. Asymptotically vanishing effective “cosmological constant” • Effective cosmological constant ~ V/M4 • λ ~ (χ/μ) –A • V ~ (χ/μ) –A χ4 • M = χ V/M4 ~(χ/μ) –A

29. Weyl scaling Weyl scaling : gμν→ (M/χ)2 gμν , φ/M = ln (χ4/V(χ)) Exponential potential : V = M4 exp(-φ/M) No additional constant !

30. Without dilatation – anomaly : V= const. Massless Goldstone boson = dilaton Dilatation – anomaly : V (φ ) Scalar with tiny time dependent mass : cosmon

31. Crossover Quintessence ( 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(φc – φ)/M)” ifj c≈ 276/M ( tuning ! ) This will be responsible for relative increase of dark energy in present cosmological epoch

32. Realistic cosmology Hypothesis on running couplings yields realistic cosmology for suitable values of A , E , φc

33. Quintessence Dynamical dark energy , generated by scalar field (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

34. Prediction : homogeneous dark energyinfluences recent cosmology- of same order as dark matter - Original models do not fit the present observations …. Modifications ( i.e. E > 0 )

35. Quintessence Cosmon – Field φ(x,y,z,t) Homogeneous und isotropic Universe : φ(x,y,z,t)=φ(t) Potential und kinetic energy of the cosmon -field contribute to a dynamical energy density of the Universe !

36. “Fundamental” Interactions Strong, electromagnetic, weak interactions On astronomical length scales: graviton + cosmon gravitation cosmodynamics

37. Dynamics of quintessence • Cosmonj: scalar singlet field • Lagrange density L = V + ½ k(φ)¶j ¶j (units: reduced Planck mass M=1) • Potential : V=exp[-j] • “Natural initial value” in Planck era j=0 • today: j=276

38. Quintessencemodels • Kinetic function k(φ) : parameterizes the details of the model - “kinetial” • k(φ) = k=const. Exponential Q. • k(φ ) = exp ((φ – φ1)/α) Inverse power law Q. • k²(φ )= “1/(2E(φc – φ))” Crossover Q. • possible naturalness criterion: k(φ=0)/ k(φtoday) : not tiny or huge ! - else: explanation needed -

39. Cosmon • Scalar field changes its value even in the presentcosmological epoch • Potential und kinetic energy of cosmon contribute to the energy density of the Universe • Time - variable dark energy : ρh(t) decreases with time !

40. Cosmon • Tiny mass • mc ~ H • New long - range interaction

41. cosmon mass changes with time ! for standard kinetic term • mc2 = V” for standard exponential potential , k ≈ const. • mc2 = V”/ k2 = V/( k2 M2 ) = 3 Ωh (1 - wh ) H2 /( 2 k2 )

42. Realistic model :Crossover Quintessence ( 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(φc – φ)/M)” ifj c≈ 276/M ( tuning ! ) Relative increase of dark energy in present cosmological epoch

43. Quintessence becomes important “today”

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

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

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

47. Quintessence becomes important “today” No reason why w should be constant in time !

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

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

50. Measure Ωh(z) !