BBN bounds on active-sterile neutrino oscillations F.L. Villante – Università di Ferrara and INFN NOW 2006 – 10 September 2006 Based on work done in collaboration with A.D. Dolgov

The Physics of BBN GW / H = 1 Baryon density Bh2 ≈ 3.7 10 7 η The abundances of 4He, D, 3He, 7Li produced by BBN depends on the following quantities: Deuterium bottleneck Baryon density Bh2 ≈ 3.7 10 7 η Hubble expansion rate GW = Weak rate (ne +n  p+e) Weak interaction freeze-out GW / H = 1 Non standard neutrinos may affect BBN via modifications of: - Expansion rate of the universe (extra neutrinos, nm or nt degeneracy …) Weak interaction rates (ne degeneracy, distorsion of ne spectrum …) ……

Active-sterile n-oscillations Kinetic + chemical equilibrium Ann./creat. neutrino reactions nn  l l Kinetic equilibrium Elastic scattering n l  n l nmt ne act - s oscillations before chemical decoupling  ns brought into equilibrium  boost the Universe exp. rate Kinetic + Chemical eq. Kinetic eq. e - s oscillations after chemical decoupling  e number density reduction  affect n/p interconversion rate. e - s oscillations after kinetic decoupling  e spectral distorsion Energy density increase ne depletion

n-oscillations in the early universe: the basic equations Neutrino oscillations in the early universe are described by kinetic equations: Coherence breaking terms due to: - Annihilation nn  l l ni ni  nh nh - Elastic scattering n l  n l Generally dominant term in potential U = neutrino mixing matrix Among all the references: Dolgov,Barbieri 1990

Neutrino oscillations: 1 active + 1 sterile x = m T y E Analytic estimates are possible: H = n e u t r i o h a m l H x @ ½ a = i s ( ¡ ) I c o l [ ° ] + ° = n e u t r i o a c : s For dm2 > 10-6 eV2, sterile neutrino production occurs at “high” temperatures: T p r o d ' 1 M e V ( ± m 2 = ) 6 Neutrino interaction rates (gas) are large compared to hubble expansion rate (H)  Quasi stationary approximation for off-diagonal components: ½ a s = H ( ¡ ) i ° In presence of “late” resonance (Haa – Hss =0) the behaviour of ras through resonace can be obtained by saddle-point integration. Dolgov and Villante 2004

Non-resonance case Gs = ( Gact / 4 ) sin2(2 matter) Energy density + e depletion ms > ma in the small mixing angle limit The rate of ns production is: Gs = ( Gact / 4 ) sin2(2 matter) Log(dm2/eV2) nmt- ns This gives:  - s mixing (m2 / eV2) sin4(2) < 1.7 * 10-5 (N)2 e - s mixing Log(dm2/eV2) ne-ns (m2 / eV2) sin4(2) < 3.2 * 10-5 (N)2 Dolgov 2001 e number density reduction. Relevant effect for small mass differences. Log(sin2(2Q))

Resonance Case (m2 / eV2) sin4(2) < 1.9 * 10-9 (N)2 Energy density + e depletion ms < ma in the small mixing angle limit Our anlytic results coincide (in the proper limit) with the Landau-Zener description of resonance crossing: nmt- ns Log(dm2/eV2)  - s mixing (m2 / eV2) sin4(2) < 1.9 * 10-9 (N)2 e - s mixing (m2 / eV2) sin4(2) < 5.9 * 10-10 (N)2 Dolgov and FLV 2004 ne-ns Our calculations show larger effects respect to previous estimates (e.g. Enqvist et a. 1992, Shi et al. 1993) Log(dm2/eV2) ne depl. effect included in numerical and analyt. est. Log(sin2(2Q))

Neutrino oscillations: 3 active + 1 sterile Active neutrinos are now known to be mixed. Their mixing should be taken into account together with nact - ns mixing: 4 (dm2)14 = variable 3 (dm2)23 = (dm2)atmo 2 (dm2)12 = (dm2)solar 1 ns mixing with one flavour eigenstate (e.g. h1 ≠ 0, h2,h3 = 0)  three different dm2 (e1,e2,e3 ≠ 0), new resonances …. ns mixing with one mass eigenstate (e.g. e1 ≠ 0, e2,e3 = 0)  one dm2, oscillation into mixed flavours (h1,h2,h3 ≠ 0) N.B. Mixing among active neutrinos cannot be rotated away, because BBN is flavour sensitive.

Neutrino oscillations: 3 active + 1 sterile Problem partially simplificated considering that early universe does not distinguish nm and nt Complete numerical calculation “ne-ns mixing” Analytic estimates: h3’ Log(dm2/eV2) Analytic estimates: h1’ and h2’ Log(dm2/eV2) All results in Dolgov and Villante 2004 See also: Cirelli, Marandella, Strumia, Vissani 2004 Dolgov and Villante 2003 Log((2h1) 2)

Comparing with observations … Main messagge of the previous slides: BBN can rule-out large regions of nact-ns mass-mixing parameter space ... if a robust bound DNn << 1 is obtained from observations However: Systematic errors and evolutionary effects makes difficult the interpretation of the observational results. Focusing on 4He  Note that ΔYp  0.012 ΔNn To obtain ΔNn < 1.0 at 2, we need ΔYp < 0.006 or better At present (ΔYp)syst > 0.005 (or larger: PDG2006  (ΔYp)syst = 0.009)

In conclusion, … We performed a complete analysis of active-sterile neutrino oscillations in early universe, providing: Analytical understanding (resonant and non resonant oscillations); Accurate and complete numerical description; 3 active + 1 sterile scenario. At this point … we need better observational data. N.B. An accurate verification of BBN is important not only for n-sterile (e.g. CMB/LSS - BBN consistency).