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Neutrino lumps

Neutrino lumps. connection between dark energy and neutrino properties. = 1.27. present dark energy density computable in terms of neutrino mass. present equation of state given by neutrino mass !. Energy density ρ ~ ( 2.4×10 -3 eV ) - 4. Reduced Planck mass M=2.44 ×10 18 GeV

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Neutrino lumps

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  1. Neutrino lumps

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

  3. 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

  4. connection between dark energy and neutrino properties = 1.27 present dark energy density computable in terms of neutrino mass Energy density : ρ1/4 ~ 2.4×10 -3 eV

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

  6. neutrino masses anddark energy densitydepend on time !

  7. 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

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

  9. 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 !

  10. 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

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

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

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

  14. cosmic coincidence

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

  16. A new role forneutrinos in cosmology ?

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

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

  19. cosmon evolution “stopped” scaling

  20. stopped scalar fieldmimicks acosmological constant( almost …) rough approximation for dark energy : • before redshift 5-6 : scaling ( dynamical ) • after redshift 5-6 : almost static ( cosmological constant )

  21. cosmon coupling to neutrinos basic ingredient :

  22. 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,…

  23. growing neutrinos

  24. varying neutrino – cosmon coupling • specific model • 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 ε≈ -0.05 triplet mass depends on cosmon field φ neutrino mass depends on φ

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

  28. strong effective neutrino – cosmon coupling for φ → φt typical present value : β≈ 50 cosmon mediated attraction between neutrinos is about 502 stronger than gravitational attraction

  29. crossover fromearly 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 • neutrinos get non –relativistic • ß gets large This always happens for φ → φt !

  33. effective cosmological triggerfor stop of cosmon evolution :neutrinos get non-relativistic • this has happened recently ! • 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 “stopped” scaling

  36. neutrino fluctuations 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 ,…Bertolami

  37. How to compute the CMB ?

  38. Linear approximation breaks down

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

  40. non-linear fluid equations local scalar potential : 2ß2 stronger than gravitational potential

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

  42. virialization

  43. shrinking of radius

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

  45. gravitational potential

  46. cosmological gravitational potentialinduced by neutrino lumps

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

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

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

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