1. Search for the Cosmic Neutrino Background and the Nuclear Beta Decay (KATRIN). Amand Faessler, Rastislav Hodak, Sergey Kovalenko, Fedor Simkovic; Bad Honnef 24. April 2014 Publication: arXiv: 1304.5632 [nucl-th] 11. Dec. 2013 and accepted by EPJ Web of Conferences vol. 71.

2. Cosmic Microwave Background Radiation (Photons in the Maximum 2 mm) Decoupling of the photons from matter about 380 000 years after the Big Bang, when the electrons are captured by the protons and He4 nuclei and the universe gets neutral. Photons move freely.

3. Penzias and Wilson; BellTelephon Nobel Price 1978 Radiation follows exactly the Planck Black Body formula with T = 2.7255(6) Kelvin in all directions. Microwave Background Radiation

4. 4 (2002) Temperature-Fluctuations of the Cosmic Microw.-Background: 1/100 000 COBE  WMAP COBE = Cosmic Background Explorer 1989-90 WMAP = Wilkinson Microwave Anisotropy Probe 2001

5. Planck Satellite Temperature Fluctuations Comic Microwave Background (Release March 21. 2013) One sees the „hot“ spots as large as they have to be. Thus Universe flat: WMAP: 2%; Planck Satellite: ~ 0.1 %.

6. 6 Curvature of the Univers flat xxx We know the size of the hot spots.

7. Fingerprint of the Gravitational Waves of the Inflationary Expansion of the Big Bang in the Cosmic Background Radiation. Gravitational Waves at Photon Decoupling 380 000 Years after Big Bang lead to Fluctuations at 1.5 to 3 angular Degrees. On 18. March 2014 the BICEP2 Collaboration published in the arXiv: 1403.3985v2 [astro-ph.CO] Gravitational Waves are Quadrupole Oscillations of Space not in Space.

9. What are gravitational Waves? Prolate to oblate oscillations of space ; not in space. Hulse and Taylor 1974 Nobel-P 1993

11. The Universe is flat. The density has the critical value:  = 1.00+-0.02 We can only see till the sphere of the the last photon- electron scattering: ~14 x10 12 light years

12. Black body radiation. Temperature adjusted (pdg 2012): T=2.7255(6) K Experiment Microwave Background Radiation T = 2.7255(6) Kelvin

13. The relative number abundance of the light nuclei formed in the big bang allows to determine the absolute baryon density and relative to the critical density (flat universe).  Baryon =  Baryon /  critical = 0.02h -2 = 0.04 n B = 0.22 m -3 e B = 210 MeV/m -3 h = 0.71 h 2 = 0.5 Hubble-Konstant= H = 100 h [km/(sec Mpc)]  B h 2 = 0.02 h = 0.71

14. Planck‘s Black Body Radiation

16. Neutrino Decoupling and Cosmic Neutrino Background For massless  massive Neutrinos:  90 eV

18. Neutrino Density/Critical Density For one type of neutrino + antineutrino

19. Estimate of Neutrino Decoupling Universe Expansion rate: H=(da/dt)/a  Interaction rate:  n e-e+ Stefan- Boltzmann

20. Neutrino Decoupling   /H = ( k B T/ 1MeV) 3 ~ 1 T(Neutrinos) decoupl ~ 1MeV ~ 10 10 Kelvin; today: 1.95 K Time after Big Bang: 1 Second T(Photons) decoupling = 3000 Kelvin; today: 2.7255 K Time(Photons) decoupling = 380 000 years Below T = 1 MeV:

22. (Energy=Mass)-Density of the Universe log  a(t)~1/T Matter dominated:  ~ 1/a 3 ~ T 3 Dark Energy 1/Temp 1 MeV ~1sec  dec. 1 eV 5x10 4 y today 3000 K 380 000 y  dec. 8x10 9 y  2.7255 K 1.95 K

23. Hamburg, March 3. 2008. (Bild) Results from Oscillations: No Hierarchy, no absolute Mass Scale Fogli, Lisi, Marrone, Palazzo: Phys. Rev. D86 (2012) 013012

24. 1. The Neutrino Mass from  -Decay: Tranformation from Mass to Flavor Eigenstates

25. Mass of the Electron Neutrino? Tritium decay (Mainz + Troitsk) With:

26. Upper Limit of the Neutrino Mass in Mainz+Troitsk: m < 2.2 eV 95% C.L. Kurie-Plot Q = 18.562 keV m 2 >0 m 2 <0 Electron Energy Eur. Phys. J. C40 (2005) 447

27. 2. Neutrino Mass from Astrophysics: Density Distribution of Matter in the Universe (Power Spectrum of Matter Distribution) H = 100 x h [km/(sec x Mpc)]; Planck Sat: h = 0.67

28. Fourier Transform of Distance Distribution of Galaxies

29.  0 = 1.0   = 0.66  b = 0.04 h = 72 n s = 0.94  = 0 0.01 Cosmic Background Radiation n S = power index for fluctuations k**n S after inflationary expansion.

30.  0 = 1.0   = 0.66  b = 0.04 h = 72 n s = 0.94  = 0.05 0.01

31. BAO = Baryon Acoustic Ocscillations

32. How can one detect the Cosmic Neutrino Background? 1.Anihilation of extreme high energy neutrinos with low energy relic neutrinos into Z 0 burst above the Greisen-Zatsepin-Kuzmin cut-off. 2. Free magnetic floating divided cylinder with neutrino absorber and neutrino non-absorbing material. 3. Electron-Neutrino capture on Tritium (KATRIN).

33. relic 1.95 Kelvin D GZK =50Mpc 1.Anihilation of Relic Neutrinos with extreme High Energy Neutrinos > 10 22 eV Z0Z0 Above GZK Anihilation below Greisen-Zatsepin-Kuzmin Distance of 50 Mpc m  = 1.0 and 0.1 eV Antineutrino E = 4x(10 21 to 10 22 ) eV m = 1 eV m = 0.1 eV

34. Cosmic Radiation from Z-Burst expected at 10 21 -10 22 eV Above GZK

35. 2. Free magnetic floating cylinder with half  absorbing material Permanent Magnet Superconducting Magnet Cylinder shaped One half  absorbing, the other sterile. Balanced. The system rotates into the neutrino wind. Thomas Müller pointed this out to me (Rujula). A. Ringwald: arXiv:hep- ph/031157v1; 2003.

36. 3. Search for Cosmic Neutrino Background C B by Beta decay: Tritium Kurie-Plot of Beta and induced Beta Decay: (CB ) + 3 H(1/2 + )  3 He (1/2 + ) + e - Electron Energy 2xNeutrino Masses Emitted electron Q = 18.562 keV Infinite good resolution Resolution Mainz: 4 eV  m < 2.3 eV Resolution KATRIN: 0.93 eV  m < 0.2 eV 90% C. L. Fit parameters: m 2 and Q value meV Additional fit: only intensity of C B

37. Tritium Beta Decay: 3 H  3 He+e - + c e

38. Neutrino Capture: (relic) + 3 H  3 He + e - 20  g(eff) of Tritium  2x10 18 T 2 -Molecules: N capture(KATRIN) = 1.7x10 -6 n e / [year -1 ] Every 590 000 years a count! for = 56 cm -3

39. Number of Events with average Electron-Neutrino Density of n e   Electron-Neutrinos/cm 3 ] KATRIN: 1 Count in 590 000 Years Gravitational Clustering of Cosmic Background Neutrinos in our Galaxy. Problem:

40. Gravitational Clustering of Neutrinos R.Lazauskas,P. Vogel and C.Volpe, J. Phys.G. 35 (2008) 025001; Light neutrinos: Gravitate only on 50 Mpc (Galaxy Cluster) scale: n / ~ n b / ~ 10 3 – 10 4 ; = 0.22 10 -6 cm -3 N capture(KATRIN) = 1.7x10 -6 n / (year -1 )= 1.7 [counts per year] Effective Tritium Source: 20 microgram  2 milligram N capture(KATRIN*) = 1.7x10 -4 n / (year -1 )= 170 [counts/year];

41. 20 microgram  2 milligram Tritium Such an Increase of the Tritium Source Intensity is with a KATRIN Type Spectrometer is difficult, if not impossible!

42. Three important Requirements: 1)The Tritium Decay Electrons are not allowed to scatter with the Tritium Gas. 2) The Magnetic Flux must be conserved in the whole Detection System. 3) The Energy resolution must be of the Order of 1 eV.

43. Source 1)The decay electrons should not scatter by the Tritium gas. Beam Column length d Base 1 cm 2 Tritium Gas Number of Tritium-Atoms in Column d = Column-Density Magnetic Field 3.6 Tesla Optimal Column Density slightly below  *d free /2 Troitsk: 30%; Mainz: 40%; KATRIN: 90% Only 36% have not scattered

44. How many electrons come out without scattering from a gaseous Tritium source? Mean free path of e:  = 1/(  *  ) = d free KATRIN Design Report After only 36% of e - have not scattered.

45. 2) Conservation of Magnetic Flux If one cant increase the intensity per area, increase the area by factor 100 from 53 cm 2 to 5000 cm 2. Magnetic Flux: (A i =5000 cm 2 ) x (B i =3.6 Tesla) = 18 000 Tesla cm 2 = A f x (3 Gauss); A f = 6 000 m 2  spectrometer-diam. = 97 meters

46. KATRIN Spectrometer tank on the way from the Rhine to the FZ Karslsruhe A giant on trip

48. Compress the electron cyclotron beam of diameter 80 cm to the diameter = 8 cm of the transport channel by an increase 0.036  3.6 Tesla magnetic field Beat the magnetic mirror by accelerating the electrons by a positive Voltage of the transport channel. In the start of the spectrometer one must be back to earth potential.

49. Lorentz-Force = Centrifugal Force

50. 3) Energy resolution of  E~ 1 eV Energy resolution: E f (perpend.) = E fp =  E

51. 3 H-Source, Spectrometer and Detector Magnetic Flux Conservation: Area*Magnetic Field; Electron Momentum p e ; Resolution:  E = E f perpendicular B(Source) = 3.6*10 4 Gauss Area(Source)~ 50 cm 2 B(Spectro) = 3 Gauss Area(Spectro) = 63.6 m 2 KATRIN Design Report

52. Angular Momentum of the Spiraling Electrons must be conserved  = 0.005 = 0.5 % Beam direction  max (electrons) = 5.7° p parallel P perpendicular

54. 20 microgram  2 milligram Tritium Such an Increase of the Tritium Source Intensity with a KATRIN Type Spectrometer is difficult, if not impossible.

56. Cyclotron Radiation Detection of Tritium Decay Electrons. Phys. Rev. D80 (2009) 051301

57. Summary 1 The Cosmic Microwave Background allows to study the Universe 380 000 years after the BB. The Cosmic Neutrino Background 1 sec after the Big Bang (BB).

58. 2xNeutrino Masses Emitted electron Kurie-Plot Electron Energy Summary 2 1.Average Density: n e = 56 [ Electron-Neutrinos/cm -3 ] Katrin: 1 Count in 590 000 Years Gravitational Clustering of Neutrinos n / < 10 6 and 20 micrograms Tritium  1.7 counts per year. (  2 milligram 3 H  170 counts per year. Impossible ?) 2. Measure only an upper limit of n ENDE