Neutrino Oscillations in the Universe

Universe Constituents from CMB Results

WMAP measures the density of baryonic and non-baryonic matter to an accuracy of better than 5%. It is able to determine some of the properties of the non-baryonic matter: the interactions of the non-baryonic matter with itself, its mass and its interactions with ordinary matter all affect the details of the cosmic microwave background fluctuation spectrum.

WMAP determined that the universe is flat: the mean energy density is equal to the critical density (within a 2% margin of error), equivalent to a 9.9 x 10-30 g/cm3 (5.9 protons per cubic meter).

4% Atoms, 23% Cold Dark Matter, 73% Dark Energy. Thus 96% of the energy density in the universe is in a form that has never been directly detected in the laboratory. Fast moving neutrinos do not play any major role in the evolution of structure in the universe. They would have prevented the early clumping of gas in the universe, delaying the emergence of the first stars, in conflict with the new WMAP data.

The data places new constraints on the Dark Energy. It seems more like a "cosmological constant" than a negative-pressure energy field called "quintessence". But quintessence is not ruled out.

• According to the standard cosmological model (SCM) our Universe is filled with massless non-oscillating neutrinos (an assumption);

• There exist three neutrino flavours- e, confirmed for weakly interacting species by LEP, however sterile neutrino may exist)

• The lepton asymmetry is zero (an assumption); ;

• Neutrino spectra are the equilibrium ones (an assumption); :

• After the electron-positron annihilation neutrino temperature becomes lower than the temperature of the photons T=(4/11)1/3 Tcmb. The cosmological neutrino phone today is expected with an extremely low temperature ~ 1.9 K, i.e. less than the temperature of the CMB Tcmb~2.7 K.

• Today neutrino is the most numerous particle after the CMB photons. Still in contrast to CMB observations the detection of the cosmological neutrino is very difficult: first, because it is an extremely elusive particle due to its very weak interactions and second, because cosmological neutrinos are expected to have today extremely low energy ~ T

4.

However, it has been observationally and experimentally proved that neutrinos oscillate: i.e. not all neutrino species are massless. LA may be non-zero, and n(E) may differ from the equilibrium ones.

A cosmological model accounting for ν oscillations is needed!

Neutrino in the standard cosmological model

exp( / ) /(1 exp( / ))eqn E T E T

neutrino oscillationsPositive indications for oscillations of neutrino were obtained at the greatest neutrino experiments. Solar neutrino problem, atmospheric neutrino anomaly and the positive results of terrestrial experiments can be resolved by the phenomenon of neutrino oscillations.

We explored a modification of the standard Big Bang Nucleosynthesis with neutrino oscillations e <-> s. Oscillations effect both expansion rateand the weak interactions rate, leading to He-4 overproduction.

Neutrino oscillations: Mass eigenstates are distinct from the flavor eigenstates.

m = Umf f, (f = e, , )

Transitions b/n different flavors are possible - flavor composition changes with time. Neutrino

oscillations imply non-zero mass differences and mixing: m2 0, at least 2 neutrino have mn 0.

observational evidences for oscillations:

Solar neutrino anomaly: Homestake, Kamiokande, SuperKamioKa, Gallex, SAGE, SNO experiments

е LMA: m2 7.9.10-5eV2 sin22 =0.31

Atmospheric neutrino anomaly: Super-KamioKa, Macro, Soudan 2, IMB

, m2 2.6.10-3eV2 maximal

Terrestrial experiments: KamLAND, K2K, LSND e, m2 O(1eV2) и sin22=O(0.003)

alternative models with s give better agreement with Homestake and explain the

variation of the flux with B.

Possible cosmological influence of e s:

Oscillations a s effective after a decoupling < and Ns<1 may distort e energy spectrum,

causing e depletion, neutrino-antineutrino asymmetry and influences the neutrino involved processes in the Universe, like BBN Kinetics, CMB, etc.

In case of oscillations effective after decoupling provided that the sterile state is not in equilibrium (Ns<1), the spectrum distortion effect is the major one.

Cosmological constraints on oscillations may be derived:From the allowed range of the observables of the early Universe, like

baryonic density, light elements abundances, expansion rate, CMB spectrum, structure characteristics of

the Universe, etc., it is possible to constrain the parameters of neutrino oscillations.

2 2~ F EГ NG 2~ TGgH eff

710.75 3

4eff ssg N N N

Evolution of neutrinos in the presence of oscillations

Approach: follow the evolution of neutrino for each momentum;

account for oscillations, expansion and interactions with the medium simultaneously

20 2

( ) ( ), ( ) 2 , ( )F F

W

t t QHp i t i G L N t O G

t p M

H

*

3

, ,

~ ~ 2 ~ /

1 0exp / 1 exp /

0 0

e e

ie je i il l

LL LL

in eq in eqLL

U U U l e s

is free neutrino Hamiltonian

Q E T L L L L L d p N

n E T E T n

0H

2 2 2 2 3 30

20

1 2 2 cos / ,

where 0.1 / and =3 MeV.

e e

eqLL v

Pl eff

n c s c s BT E T T n

B M m g T

Analytical solution for vacuum neutrino oscillations (post BBN epoch):

Numerical solutions for matter neutrino oscillations

• The distortion concerns first the low energetic part of the spectrum because the oscillations become effective first to low energy neutrinos.

• Soon after, the whole spectrum is distorted from its equilibrium

Fermi-Dirac form. The non-equilibrium initial condition leads to considerable and continuous deviations from the equilibrium The spectrum distortion of the active neutrino for a wide range of oscillation parameters persists during BBN

Sterile neutrinos may be present at the onset of BBN epoch -- may be produced in GUT models, in models with large extra dimensions, Manyfold Universe models, mirror matter models, or by oscillations in 4-neutrino mixing schemes, etc. The degree of population may be different depending on the production model. The distortion of the neutrino spectrum due to active-sterile oscillations and the kinetic effect caused

Nk depends on the degree of initial population of s.

The biggest effect is Nk,0 at Ns=0, the effect decreases with Ns . DK,Int.J.M.P.D,2004, 2007

Nk ~ Nk,0- Nk,0 Ns

Spectrum distortion for different initial population of s.: Ns=0 – the lowest curve, Ns=0,5 and Ns=0,8 – the upper

curve. The dashed curve shows the equilibrium spectrum.

Dependence of neutrino evolution on the initial popuation of s

Ns

BBN with oscillationsHe-4 mass fraction is a strong function of the effective

number of light stable particles at BBN epoch

It depends also on the e characteristics decrease n/p freezes earlier 4Не is overproduced

BBN with fast a s : increaseeffective before a decoupling

BBN with a s e spectrum effective after a decoupling and Ns<1 distortions

2~ TGgH eff

710.75 3

4eff ssg N N N

2 2~ F EГ NG

sN

2 4 7sin 2 10m

Evolution of nucleons in the presence of е s

the numerical approach

)()(),,(2

LLnpen

nn

p nnnnpeApedp

nHp

t

n

)()~()~,,(2

LLpnennnpneAped

2 7 210 0 1

2 0.3sm eV all mixing angles N

MeV T MeV

The interplay b/n effects

dynamic effect increases

kinetic effect decreases

total effect decreases

N= Nk,0- Nk,0 Ns +NsNk,0 >1

Nk,0 Ns >Ns

m2 = 10-7 eV2 sin22 = 1

The interplay b/n effects

dynamic effect increases

kinetic effect decreases

total effect decreases

N= Nk,0- Nk,0 Ns +NsNk,0 >1

Nk,0 Ns >Ns

m2 = 10-7 eV2 sin22 = 1

Dependence of maximum overproduction on the mixing

0Y/Y 32% for resonant case

0Y/Y 14 % for non-resonant

Expressed in terms of effective number of neutrinos the kinetic effect due to e spectrum distortion: Nk,0 6 for resonant osc Nk,0 3 for non-resonant osc

DK , Astrop.Phys.,2003

2 7 210m eV

2 8 210m eV

Maximum He-4 overproduction in BBN with oscillations due to spectrum distortion

Maximal overproduction dependence on mass difference

BBN constraints do exist if He-4 uncertainty is over 5% but

for non-equilibrium oscillations.

BBN with nonequilibrium es

allows to constrain oscillation parameters for He-4 uncertainty up to32% (14%) in resonant (non-resonant) case.

DK , Astrop.Phys.,2003

Maximum He-4 overproduction in BBN with oscillations due to spectrum distortion

4Не – the preferred elementBBN - the most early and precision probe for physical conditions in the early

Universe, and for constraining new physics, relevant at this E.For a precise analysis of the oscillations effect on BBN, He-4 is used because the most reliable and abundant data now available are for that element.- Observed in НІІ low metalicity regions of dwarf galaxies- Extrapolated towards zero metalicityYp=0,2421 0,0021 Izotov, Thuan 2000

Yp=0,2429 0,009 Izotov, Thuan 2004

dispersion of the determinationsYp=0,245 0,013 Olive, Skillman 2004

Yp=0,2491 0,0091 Olive, Skillman 2004

Determinations indicate 3-5% uncertainty (systematic errors). Sasselov, 95Possibly it is related with the evaluation of ionization level, stellar absorption, .. Luridiana, 2002

For a precise analysis of the oscillations effect on BBN, He-4 is used because the most reliable and abundant data now available are for that element.

The primordial abundance Yp, predicted from SBBN, is calculated withgreat precision: the theoretical uncertainty is less than 0.1% within a widerange of baryon density.

Constraints on neutrino oscillation parameters

BBN with electron-sterile neutrino oscillations:

4Не depends on the e characteristics : e decrease n/p freezes earlier 4Не is overproduced . DK, 88; Chizhov, DK, ‘97,’00

4Не depends on the dynamics of the Universe: g increase n/p freezes earlier 4Не is overproduced . Dolgov ’81, Barbieri, Dolgov 90

BBN constraints on oscillations

BBN with neutrino oscillations between initially empty s

and e

Observational data on primordial He- 4 was used to put stringent limits on the allowed oscillation parameters.

BBN constraints on е s :

Barbieri, Dolgov 91 – depletion accountDolgov 2000 – dashed curve; DK, Enqvist et al. 92 – one p approx. DK.,Chizhov 2001 – distortion and asymmetry growth accountDolgov, Villante, 2003 - spectrum distortion

Spectrum distortion reflected in neutrino oscillations constraints from BBN

The distortion leads to a decrease of the

weak rates to an increase of the n/p

freezing T and He overproduction.

Correspondingly the account of spectrum

distortion leads to strengthening of BBN

constraints at large mixings.

The account of the neutrino-antineutrino

asymmetry growth caused by resonant

oscillations leads to relaxation of the

constraints for small mixings.

42 2 9 2 2

2 10 2 2

sin 2 1.5 10 0

8.2 10 large , 0

m eV m

m eV m

Ns=0

Spectrum distortion and BBN constraints

For nonequilibrium oscillations the constraints are strengthened by orders of magnitude:

Dolgov A., F.Villante ,2003m2>10-6 eV2, i.e. kinetic equilibrium constraints for non-resonant case:

42 2 9 2 2

2 10 2 2

sin 2 1.5 10 0

8.2 10 large , 0

m eV m

m eV m

At smaller m2 re-population of active neutrino becomes slow, spectrum distortion is considerable.

Chizhov M., DK, 2001; D.K. 2005

22 4 5 2

22 4 5 2

sin 2 3.16 10

sin 2 1.74 10

es es

s s

m eV N

m eV N

Antimatter in the UniverseBaryogenesis

Antimatter in the UniverseMissions for search of cosmic/galactic antimatter: PAMELA, BESS, AMS, AMS-2(2009),PEBS(2010), etc• The cosmic ray results from search of antiprotons, positrons and antinuclei indicate that there is not significant quantity ofantimatter objects within a radius 1 Mpc.

BESS 98

AMS 01• Gama ray flux measurements exclude significant amounts of antimatter up to the distance of galaxy cluster scales ~ 10 -20 Mpc.

Steigman 79, Stecker 85, Dolgov 99Cosmic ray and gama ray data do not rule out large antimatter domains on scales larger than 10 -20 Mpc, or small ratios of antimatter/matter objects on small scales (stars, globular clusters). Large but subdominant domains of antimatter allowed within the Galaxy as well.Both ‘natural’ theory and observations allow the presence of antimatter in astronomically significant quantities.

Antimatter signatures

We have analyzed all experimental data, available from experiments on balloons and on spacecraft , for antinuclei and antiprotons in cosmic rays. The figure presents the antiproton data from BESS, MASS and CAPRICE experiments compared with different models predictions for secondary antiprotons. The comparison with theoretical predictions for secondary antiprotons does not exclude the possibility for a small fraction of primordial antiprotons. Kirilova,Panayotova, 2002

B Asymmetric Universe

General conditions for successful BA generation

Due to considerations based on the existance of an inflationary period:

BA may not be postulated as an initial condition

BA should be generated in the Early Universe before BBN epoch

Sacharov's conditions for BA generation:• Baryon number violation (BV).• C and CP violation.• Departure from thermal equilibrium.

AD Baryogenesis

• We analyzed numerically a baryogenesis model, based on the Afleck-Dine baryogenesis scenario.

Dolgov, DK 89; DK, Chizhov 95;

• We have provided more precise account for the particle creation processes, which were proved to play an essential role for baryogenesis.

2000DK, Valchanov, Panayotova 2005,2007

The model allows natural production of large antimatter domains in the Universe.

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