Unraveling the Enigma of Dark Energy in Our Universe

1. Early Dark Energy Dunkle Energie – Ein kosmisches Raetsel

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

3. What is our universe made of ? fire , air, water, soil ! quintessence !

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

5. What is Dark Energy ?

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

7. Dark Matter Ωm = 0.25 total “matter” Most matter is dark ! So far tested only through gravity Every local mass concentration gravitational potential Orbits and velocities of stars and galaxies measurement of gravitational potential and therefore of local matter distribution

8. Ωm= 0.25 gravitational lens , HST

9. Ωtot=1

10. WMAP 2006 Polarization

11. Dark Energy Ωm + X = 1 Ωm : 25% Ωh : 75% Dark Energy h : homogenous , often ΩΛ instead of Ωh

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

13. Dark Energy density isthe same at every point of space “ homogeneous “ No force in absence of matter –“ In what direction should it draw ? “

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

15. Power spectrum Baryon - Peak galaxy – correlation – function Structure formation : One primordial fluctuation- spectrum SDSS

16. consistent cosmological model !

17. Composition of the Universe Ωb = 0.045 visible clumping Ωdm= 0.2 invisibleclumping Ωh = 0.75 invisiblehomogeneous

18. Dark Energy- a cosmic mystery Dunkle Energie – Ein kosmisches Raetsel

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

20. 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 ?

21. Cosm. Const. | Quintessence static | dynamical

22. 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

23. 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?

24. Quintessence Dynamical dark energy , generated by scalarfield (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

25. Prediction : homogeneous dark energyinfluences recent cosmology- of same order as dark matter - Original models do not fit the present observations …. modifications

26. Quintessence Cosmon – Field φ(x,y,z,t) similar to electric field , but no direction ( scalar field ) 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 !

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

28. Evolution of cosmon field Field equations Potential V(φ) determines details of the model e.g. V(φ) =M4 exp( - φ/M ) for increasing φ the potential decreases towards zero !

29. 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 !

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

31. Cosmological equations

32. 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

33. 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

34. kinetial Small almost constant k : • Small almost constant Ωh This can explain tiny value of Dark Energy ! Large k : • Cosmon dominated universe ( like inflation )

35. 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 )

36. Quintessence models • 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 -

37. More models … • Phantom energy( Caldwell ) negative kinetic term ( w < -1 ) consistent quantum theory ? • K – essence( Amendariz-Picon, Mukhanov, Steinhardt ) higher derivative kinetic terms why derivative expansion not valid ? • Coupling cosmon / (dark ) matter( C.W., Amendola ) why substantial coupling to dark matter and not to ordinary matter ? • Non-minimal coupling to curvature scalar – f(φ) R - can be brought to standard form by Weyl scaling !

38. observation will decide !

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

40. Quintessence becomes important “today”

41. 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

42. 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 :

43. 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

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

45. coincidence problem What is responsible for increase of Ωh for z < 10 ?

46. Early quintessence Ωh changes only modestly w changes in time transition special feature in cosmon potential or kinetic term becomes important “now” tuning at ‰ level Late quintessence w close to -1 Ωh negligible in early cosmology needs tiny parameter, similar to cosmological constant a) Properties of cosmon potential or kinetic term

47. Transition to cosmon dominated universe • Large value k >> 1 : universe is dominated by scalar field • k increases rapidly : evolution of scalar fied essentially stops • Realistic and natural quintessence: k changes from small to large values after structure formation

48. crossover quintessence k(φ) increase strongly for φ corresponding to present epoch Example (LKT) : exponential quintessence:

49. Onset of matter dominance K- essence Amendariz-Picon, Mukhanov, Steinhardt needs higher derivative kinetic term Appearance of non-linear structure Back-reaction effect needs coupling between Dark Matter and Dark Energy b) Quintessence reacts to some special event in cosmology

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