1. Growing Neutrinos as a solution of the why now problem of Dark Energy

2. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density given by neutrino mass = 1.27

3. Dark Energy and the Why now problem

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

5. Matter : everything that clumps -------------------- Dark Energy density is the same at every point of space “ homogeneous “ Space between clumps is not empty

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

7. Cosmological Constant - Einstein - 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 ?

8. Cosm. Const | Quintessence static | dynamical

9. Why now problem Why is dark energy important now and not in the past ? Why is dark energy important now and not in the past ?

10. 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

11. connection between dark energy and neutrino properties present dark energy density given by neutrino mass = 1.27 Energy density : ρ 1/4 ~ 2.4×10 -3 eV

12. neutrino masses and dark energy density depend on time !

13. 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

14. 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

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

16. 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 ! V(φ) =M 4 exp( - αφ/M )

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

18. Evolution of cosmon field Field equations Field equations Potential V(φ) determines details of the model Potential V(φ) determines details of the model V(φ) =M 4 exp( - αφ/M ) V(φ) =M 4 exp( - αφ/M ) for increasing φ the potential decreases towards zero ! for increasing φ the potential decreases towards zero !

19. 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

20. exponential potential constant fraction in dark energy can explain order of magnitude of dark energy ! Ω h = 3(4)/α 2

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

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

23. cosmic coincidence

24. coincidence problem What is responsible for increase of Ω h for z < 6 ? Why now ?

25. A new role for neutrinos in cosmology ?

26. growing neutrino mass triggers transition to almost static dark energy growingneutrinomass

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

28. cosmon evolution scaling “stopped”

29. stopped scalar field mimicks a cosmological constant ( almost …) rough approximation for dark energy : before redshift 5-6 : scaling ( dynamical ) before redshift 5-6 : scaling ( dynamical ) after redshift 5-6 : almost static after redshift 5-6 : almost static ( cosmological constant ) ( cosmological constant )

30. cosmon coupling to neutrinos basic ingredient :

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

32. growing neutrinos

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

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

35. connection between dark energy and neutrino properties present equation of state given by neutrino mass ! present dark energy density given by neutrino mass = 1.27

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

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

38. neutrino mass seesaw and cascademechanism omit generation structure triplet expectation value ~ doublet squared

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

40. cascade

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

42. cascade mechanism triplet expectation value ~

43. “singular” neutrino mass triplet mass vanishes for φ → φ t neutrino mass diverges for φ → φ t

44. strong effective neutrino – cosmon coupling for φ → φ t typical present value : β ≈ 50 cosmon mediated attraction between neutrinos is about 50 2 stronger than gravitational attraction

45. crossover from early scaling solution to effective cosmological constant

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

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

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

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

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

51. cosmon evolution scaling “stopped”

52. neutrino fraction remains small m ν = 0.45 eV ΩνΩνΩνΩν z

53. equation of state present equation of state given by neutrino mass !

54. oscillating neutrino mass

55. Hubble parameter as compared to ΛCDM m ν =0.45 eV

56. Hubble parameter ( z < z c ) only small differencefrom ΛCDM ! m ν =0.45 eV

57. bounds on average neutrino mass

58. 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 Experimental determination of neutrino mass may turn out higher than upper bound in model for cosmological constant ( KATRIN, neutrino-less double beta decay ) ( KATRIN, neutrino-less double beta decay ) GERDA

59. neutrino fluctuations neutrino structures become nonlinear at z~1 for supercluster scales stable neutrino-cosmon lumps exist N.Brouzakis, N.Tetradis,… D.Mota, G.Robbers, V.Pettorino, …

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

61. two key features 1 ) Exponential cosmon potential and scaling solution scaling solution V(φ) =M 4 exp( - αφ/M ) V(φ) =M 4 exp( - αφ/M ) V(φ → ∞ ) → 0 ! V(φ → ∞ ) → 0 ! 2 ) Stop of cosmon evolution by cosmological trigger cosmological trigger

62. End

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

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

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

66. effects of early dark energy modifies cosmological evolution (CMB) modifies cosmological evolution (CMB) slows down the growth of structure slows down the growth of structure

67. interpolation of Ω h G.Robbers,M.Doran,…

68. Early quintessence slows down the growth of structure

69. time variation of “fundamental constants” M.Mueller, G.Schaefer, T.Dent, S.Steffen,…

70. 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” C) Apparent violation of equivalence principle D) Possible coupling between Dark Energy and Dark Mater

71. 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,…

72. baryons : the matter of stars and humans Ω b = 0.045

73. primordial abundances for three GUT models T.Dent,S.Stern,… present observations : 1σ He D Li

74. three GUT models unification scale ~ Planck scale unification scale ~ Planck scale 1) All particle physics scales ~Λ QCD 1) All particle physics scales ~Λ QCD 2) Fermi scale and fermion masses ~ unification scale 2) Fermi scale and fermion masses ~ unification scale 3) Fermi scale varies more rapidly than Λ QCD 3) Fermi scale varies more rapidly than Λ QCD Δα/α ≈ 4 10 -4 allowed for GUT 1 and 3, larger for GUT 2 Δln(M n /M P ) ≈40 Δα/α ≈ 0.015 allowed

75. time varying Fermi scale yields triplet expectation value as function of doublet t = insert :

76. time varying electron mass time variation of quantities not related to triplet

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

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

79. End

80. 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)

81. 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, V.Pettorino, D.Mota, M.Neubert, T.Krueger

82. fixed point behavior : apparent tuning

83. Cosmon coupling to atoms Tiny !!! Tiny !!! Substantially weaker than gravity. Substantially weaker than gravity. Non-universal couplings bounded by tests Non-universal couplings bounded by tests of equivalence principle. of equivalence principle. Universal coupling bounded by tests of Brans- Dicke parameter ω in solar system. Universal coupling bounded by tests of Brans- Dicke parameter ω in solar system. Only very small influence on cosmology. Only very small influence on cosmology.

84. Cosmon coupling to Dark Matter Only bounded by cosmology Only bounded by cosmology Substantial coupling possible Substantial coupling possible Can modify scaling solution and late cosmology Can modify scaling solution and late cosmology Role in clustering of extended objects ? Role in clustering of extended objects ? L. Amendola

85. effective cosmological constant realistic value for α φ t / M ≈ 276

86. effective cosmological constant linked to neutrino mass realistic value α φ t / M ≈ 276 : needed for neutrinos to become non-relativistic in recent past - as required for observed mass range of neutrino masses φ t / M : essentially determined by present neutrino mass adjustment of one dimensionless parameter in order to obtain for the present time the correct ratio between dark energy and neutrino energy density no fine tuning ! no fine tuning !

87. crossing time from matching between early solution and late solution

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

89. crossover to dark energy dominated universe starts at time when “neutrino force” becomes important for the evolution of the cosmon field

90. cosmological selection !