Why the cosmological constant goes to zero, and why we see it now

1. Why the cosmological constant goes to zero, and why we see it now

2. Quintessence C.Wetterich A.Hebecker, M.Doran, M.Lilley, J.Schwindt, C.Müller, G.Schäfer, E.Thommes, R.Caldwell, M.Bartelmann, K.Kharwan, G.Robbers, T.Dent, S.Steffen, L.Amendola, M.Baldi , N.Brouzakis , N.Tetradis, D.Mota, V.Pettorino, T.Krüger, M.Neubert

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

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

5. 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 = 7 · 10ˉ¹²¹ matter: ρm/M4= 3 · 10ˉ¹²¹

6. Cosm. Const | Quintessence static | dynamical

7. Cosmological Constant- accident or explanation - • Why so small ? λ/M4 = 10-120 • Why important just today ?

8. 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

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

10. Cosmon • 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 • Time - variable dark energy : ρh(t) decreases with time ! V(φ) =M4 exp( - αφ/M )

11. two key features 1 ) Exponential cosmon potential and scaling solution V(φ) =M4 exp( - αφ/M ) V(φ→ ∞ ) → 0 ! 2 ) Stop of cosmon evolution by cosmological trigger

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

13. Cosmic Attractor Solutions independent of initial conditions V ~ t -2 φ ~ ln ( t ) Ωh ~ const. early cosmology

14. exponential potentialconstant fraction in dark energy can explain order of magnitude of dark energy ! Ωh = 3(4)/α2

15. realistic quintessence fraction in dark energy has to increase in “recent time” !

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

17. coincidence problem What is responsible for increase of Ωh for z < 6 ? Why now ?

18. growing neutrino mass triggers transition to almost static dark energy growing neutrino mass

19. cosmon coupling to neutrinos basic ingredient :

20. Cosmon coupling to neutrinos • can be large ! • interesting effects for cosmology if neutrino mass is growing • growing neutrinos can stop the evolution of the cosmon • transition from early scaling solution to cosmological constant dominated cosmology Fardon,Nelson,Weiner L.Amendola,M.Baldi,…

21. growing neutrinos

22. crossover due to non –relativistic neutrinos growing neutrino mass

23. end of matter domination • growing mass of neutrinos • at some moment energy density of neutrinos becomes more important than energy density of dark matter • end of matter dominated period • similar to transition from radiation domination to matter domination • this transition happens in the recent past • cosmon plays crucial role

24. cosmological selection • present value of dark energy density set by cosmological event ( neutrinos become non – relativistic ) • not given by ground state properties !

25. connection between dark energy and neutrino properties present dark energy density given by neutrino mass present equation of state given by neutrino mass !

26. dark energy fraction determined by neutrino mass constant neutrino - cosmon coupling β variable neutrino - cosmon coupling

27. varying neutrino – cosmon coupling • specific model • can naturally explain why neutrino – cosmon coupling is much larger than atom – cosmon coupling

28. neutrino mass seesaw and cascade mechanism triplet expectation value ~ doublet squared omit generation structure

29. cascade mechanism triplet expectation value ~ M.Magg , … G.Lazarides , Q.Shafi , …

30. varying neutrino mass ε≈ -0.05 triplet mass depends on cosmon field φ neutrino mass depends on φ

31. “singular” neutrino mass triplet mass vanishes for φ → φt neutrino mass diverges for φ → φt

32. strong effective neutrino – cosmon coupling for φ → φt

33. crossover fromearly scaling solution to effective cosmological constant

34. early scaling solution ( tracker solution ) neutrino mass unimportant in early cosmology

35. growing neutrinos change cosmon evolution modification of conservation equation for neutrinos

36. effective stop of cosmon evolution cosmon evolution almost stops once • neutrinos get non –relativistic • ß gets large This always happens for φ → φt !

37. effective cosmological triggerfor stop of cosmon evolution :neutrinos get non-relativistic • this has happened recently ! • sets scales for dark energy !

38. dark energy fraction determined by neutrino mass constant neutrino - cosmon coupling β variable neutrino - cosmon coupling

39. cosmon evolution

40. Hubble parameter as compared to ΛCDM

41. Hubble parameter ( z < zc ) only small difference from ΛCDM !

42. Can time evolution of neutrino mass be observed ? • Experimental determination of neutrino mass may turn out higher than upper bound in model for cosmological constant ( KATRIN, neutrino-less double beta decay ) GERDA

43. neutrino fluctuations • time when neutrinos become non – relativistic • sets free streaming scale • neutrino structures become nonlinear at z~1 for supercluster scales • stable neutrino-cosmon lumps exist D.Mota , G.Robbers , V.Pettorino , … N.Brouzakis , N.Tetradis ,…

44. Conclusions • Cosmic event triggers qualitative change in evolution of cosmon • Cosmon stops changing after neutrinos become non-relativistic • Explains why now • Cosmological selection • Model can be distinguished from cosmological constant

45. two key features 1 ) Exponential cosmon potential and scaling solution V(φ) =M4 exp( - αφ/M ) V(φ→ ∞ ) → 0 ! 2 ) Stop of cosmon evolution by cosmological trigger

46. Why goes the cosmological constant to zero ?

47. 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 …

48. 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

49. Example : Field χ is connected to mass scale of transition from higher dimensional physics to effective four dimensional description

50. theory without explicit mass scale • Lagrange density: