1. Neutrino lumps

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

3. 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

4. connection between dark energy and neutrino properties present dark energy density computable in terms of neutrino mass = 1.27 Energy density : ρ 1/4 ~ 2.4×10 -3 eV

5. 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 ?

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

7. 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

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

9. 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 !

10. 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

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

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

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

14. cosmic coincidence

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

16. A new role for neutrinos in cosmology ?

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

18. 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 !

19. cosmon evolution scaling “stopped”

20. 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 )

21. cosmon coupling to neutrinos basic ingredient :

22. 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

23. growing neutrinos

24. 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

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

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

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

28. 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

29. crossover from early scaling solution to effective cosmological constant

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

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

32. 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 !

33. 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 !

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

35. cosmon evolution scaling “stopped”

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

38. How to compute the CMB ?

39. Linear approximation breaks down

40. cosmon attraction much stronger than gravitational attraction much stronger than gravitational attraction neutrino mass changes with time neutrino mass changes with time new methods need to be developed new methods need to be developed non-linear hydro-dynamical equations non-linear hydro-dynamical equations N-body simulations for coupled quintessence N-body simulations for coupled quintessence renormalization group improved resummations renormalization group improved resummations Pettorino, Wintergerst, Mota, Amendola, Baldi, Catena, Schrempp, Nunes, …

41. non-linear fluid equations local scalar potential : 2ß 2 stronger than gravitational potential

42. evolution of single neutrino lump Wintergerst, Pettorino, Mota,…

43. virialization

44. shrinking of radius

45. density profile normalized to 1 in the center of the lump

46. gravitational potential

47. cosmological gravitational potential induced by neutrino lumps

48. time evolution of linear and non-linear gravitational potential

49. backreaction neutrino-mass inside lump different from cosmological neutrino-mass ( smaller ) neutrino-mass inside lump different from cosmological neutrino-mass ( smaller ) effective coupling ß smaller effective coupling ß smaller freezing of growth freezing of growth criterion for backreaction effects : local ß δΦ order one local ß δΦ order one cosmological ß δΦ order 10 -3 cosmological ß δΦ order 10 -3 stop growth of a k-modes with k<k b if k b hits bound stop growth of a k-modes with k<k b if k b hits bound

50. time evolution of linear and non-linear gravitational potential at z = 1.7 backreaction sets in

51. cosmological gravitational potential induced by neutrino lumps

52. Linear approximation breaks down

53. enhanced peculiar velocities in bulk flow modification of ISW correlations chances for observation

54. bounds on average neutrino mass

55. 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

56. 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

57. End

58. 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

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

60. 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 )

61. 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

62. 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 !

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

64. cascade mechanism triplet expectation value ~

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

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

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

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

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

70. 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

71. 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

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

73. Early quintessence slows down the growth of structure

74. 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.

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

76. 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

77. 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,…

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

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

80. 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

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

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

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

84. 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)

85. 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 !