Quintessence - a fifth force from variation of the fundamental scale

1. Quintessence - a fifth force from variation of the fundamental scale

2. Ωm + X = 1 Ωm : 25% Ωh : 75% Dark Energy ?

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

4. Dark Energy dominates the Universe Energy - density in the Universe = Matter + Dark Energy 25 % + 75 %

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

6. Ωm= 0.25 gravitational lens , HST

7. Ωtot=1

8. Dark Energy Ωm + X = 1 Ωm : 25% Ωh : 75% 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 “ Ωh

11. Predictions for dark energy cosmologies The expansion of the Universe accelerates today !

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

13. 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 ?

14. Cosm. Const. | Quintessence static | dynamical

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

16. 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

17. 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 ?

18. 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 …

19. Quintessence from time evolution of fundamental mass scale

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

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 cosmology

34. 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

35. 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 )

36. 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 !

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

38. 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

39. 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 -

40. 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 !

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

42. 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 )

43. Cosmological equations

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

45. Quintessence becomes important “today”

46. 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

47. 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 :

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

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

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