1. Pasquale Di Bari (Max Planck, Munich) Neutrino Oscillation Workshop, Conca Specchiulla, September 9-16, 2006 RH neutrinos in cosmology: light vs. heavy

2. 4 ‘PROBLEMS’ from COSMOLOGY: 1.Matter - antimatter asymmetry 2.Dark matter 3.Accelerating Universe 4.Inflation Plus 1 from neutrino physcis: 5. Neutrino Masses

3. Minimal RH implementation 3 limiting cases : pure Dirac: M R = 0 pseudo-Dirac : M R << m D see-saw limit: M R >> m D

4. Option: Advantages Drawbacks pure Dirac Minimal (M R =0) Description of neutrino masses as for all other fermions It can explain current Earth experiment results (except LSND, barring CPT violation that does not work anyway ) Why M R = 0 if not forbidden ? But neutrinos ARE different from all other fermions: neutral and much lighter Not so appealing (today) to solve cosmological problems (exception:Dirac leptogenesis ) Pseudo-Dirac limit Potentially able to explain all Earth experiments including LSND ( Kobayashi,Lim,Nojiri ’91;Giunti,Kim,Lee’92 ) To a closer (and up-to-date) inspection it does not work ! it does not help to understand neutrino lightness See-saw limit elegant way to understand lightness of neutrino masses moreover in line with GUT’s and with experimental results long list of cosmological and astrophysical applications (rest of the talk !) it can be also used to explain LSND depending on the see-saw scale (rest of the talk !) but in any case more attractive than the other cases especially from a cosmological and astrophysical point of view In the rest of the talk we will concentrate on this case ! (Minkowski; Yanagida; Gell Mann,Ramond,Slansky; Glashow; Barbieri,Nanopoulos,Morchio,Strocchi; Mohapatra,Senjanovic; Schechter,Valle)

5. See-saw mechanism 3 light LH neutrinos: 3 light LH neutrinos: N  2 heavy RH neutrinos: N 1, N 2, … N  2 heavy RH neutrinos: N 1, N 2, … m  M SEE-SAW (here we are barring the possibility of a `singular’ see-saw case where M 1 = 0) - considering that m is almost entirely determined by the experiments  2 important quantities for the role of RH neutrinos in cosmology : the `see-saw’ pivot scale  their number N

6. Pivot see-saw scale  * ~ 1 GeV m>  *  high pivot see-saw scale (the usual case: only heavy RH neutrinos are possible) m<  *  low pivot see-saw scale (light RH neutrinos are possible)

7. LSND,BBN and CMB ‘eV’- see-saw can accomodate LSND realizing a ‘3+2’ data fit (De Gouvea’05) If L =0 then the 2 RH neutrinos thermalize: problem for BBN and CMB ! BBN (Helium) Y BBN+CMB = 0.2489 - 0.3 L e +0.014  N Y exp =0.241 ± 0.004 (Steigman ‘05) 2 additional neutrinos (if L e =0) are too many even for a conservative experimental upper bound on Y. CMB  m i <(0.17 – 0.9) eV (only active) (Seljak et al;Lesgourgues &,Pastor;Tegmark et al.;Fogli et al.;Hannestad et al.) m sterile < (0.26-0.55) eV (3+1) (Dodelson,Melchiorri,Slosar;Seljak,Slosar,McDonald) -0.3<  N < 1.6 (95% CL) (no Ly  ) (Hannestad,Raffelt) 0.6<  N < 4.4 (95% CL) (with Ly  ) (Seljak,Slosar,McDonald) Future possible scenarios - MiniBoone disproves LSND and  N =0  no evidence for  ~0.1eV - MiniBoone confirms LSND but  N =0  evidence for  ~eV; an asimmetry L  10 -4 can prevent the thermalization (Foot,Volkas’95;PDB,Lipari,Lusignoli’99;Chu,Cirelli’06) and | L | ~ 10 -2 can also reduce the Helium abundance (Fuller et al;) this could be produced also by RH neutrino decays realizing a late leptogenesis (PDB) -MiniBoone disproves LSND but  N  0; then it can be still interpreted as evidence for for  ~1 eV if RH neutrino are stable or larger if they decay after active neutrino decoupling; -Both MiniBoone confirms LSND and  N  0  very nice interplay between Earth experiments and physics of the early Universe  ~0.1eV

8. Lightest RH neutrino as Dark Matter candidate Even if the active-sterile neutrino mixing is typically very small   s ~ m D /M << 1, the sterile neutrino production is enhanced by matter effects and (Dodelson,Widrow’94;Dolgov,Hansen’01; Abazajian,Fuller,Patel’01) This condition can be fullfilled if m 1 <10 -5 eV and the Dark Matter RH neutrino is the lightest one (i.e. M 1 ~ O(KeV) (Asaka,Blanchet,Shaposhnikov’05) Moroever, the oscillations between the 2 heavier RH neutrinos can be responsible for baryogenesis if M 2  M 3 ~ 10 GeV (Akhmedov,Rubakov,Smirnov’99;Asaka,Shapo shnikov ’05)

9. Good and bad news Bad news: - The same flavor-mixing mechanism describing the prduction, also lead to radiative decay: N 1   +  ”   sin 2 2  M 1 5 >> t 0 - SDSS Ly  : M 1 > (10-14) KeV (Seljak et al. ’06;Lesgourgues et al) - However for L  0 producion is more efficient (resonant) and there is still some allowed region (Abazajian,Fuller,Paterl’01) Production for L =0 : Good news. Also able to explain: - Pulsar kicks (Kusenko,Segrè ‘97 ) - Early reionization and star formation (Kusenko,Biermann ‘05 ) L =0.01 X-Ray Background measurements

10. Heavy RH neutrinos Just 2 but solid motivations: See-saw original philosophy is not spoiled:  ~ M ew, M R ~M GUT : no need to introduce a new third fundamental scale to explain neutrino masses; Leptogenesis from heavy RH neutrino decays: it is simple and it works easily without requiring a particular tuning of parameters (talks by Blanchet,Ma,Petcov,….) Main criticisms : How to prove it ? Can it explain other cosmological problems beyond the matter-antimatter asymmetry (with leptogenesis) ?

11. Cosmological Heavy RH neutrinos beyond leptogenesis models to explain Dark Energy (and LSND) with Mass Varying Neutrinos varying the Universe M R =M R (A) with A a scalar field coupled to matter (Kaplan,Nelson,Weiner ‘04) heavy RH neutrino as candidates of DM (Babu,Eichler,Mohapatra ’89) unified models of leptogenesis and Dark Matter (Cosme et al. ’05;Saju,Urjit,Yajnik’05;Strumia ’06) They all require significant departures from a minimal extension of the SM ! : A point in favor of light RH neutrinos ??

12. Heavy vs. light: which verdict ? Heavy : solid motivations but difficult to test Light : richer phenomenology with many different potential ways to discover them but original see-saw philosophy gets lost

13. Heavy and light together ? Singular see-saw Due some symmetry S  det(M R), det(m D )=0  ‘Taking out’ the zero eigenvalues from M R and m D leads to a see-saw formula just for 2 light neutrinos and 2 heavy neutrinos plus one massless RH neutrino and one massless LH neutrino (Glashow’91,FukugitaYanagida’91,Chun,Kim,Lee’98) Weak breaking of S or loop effects can then lead to a nonzero mass for the RH neutrino that can explain LSND with a 3+1 spectrum (Mohapatra ’01) Double see-saw (Mohapatra,Valle’86;Ellis,Lopez,Nanopoulos 92’) Recently proposed to have both KeV DM and usual leptogenesis at the same time (Kang,Kim’06) Is it possible to have a unified picture joining both virtues of heavy and light neutrinos ?

14. Conclusions Heavy and light RH neutrinos have both attractive, though complementary interest Light RH neutrinos have a rich cosmological phenomenology but (waiting for MiniBoone and more precise measurement of  N ) we do not have today any compelling reason Heavy RH neutrinos have just 2 but solid (and traditional) motivations but difficulty in describing DM ….but maybe it is not impossible ! We are currently considering with A. Anisimov an intriguing possibility: a lightest weakly coupled RH neutrino DM (M 1 ~1 TeV) is produced from the oscillations of a heavier thermalized one while Leptogenesis can proceed from its decays (A.Anisimov,PDB)