BBN, CMB and CNB probes of nonequilibrium neutrino

1
BBN, CMB and CNB probes of nonequilibrium
neutrino
CTSCMB Aug08

• Daniela Kirilova
• Institute of Astronomy
• Bulgarian Academy of Sciences
• Sofia, Bulgaria

2
OUTLINE

• Neutrinos in the standard cosmological model and
  in reality
• Deviations from the equilibrium Fermi-Dirac
  neutrino spectrum caused by different processes
• Cosmological influence of nonequilibrium
  processes involving neutrino during neutrino
  decoupling, BBN and CMB epoch and on CNB
• The effect of active-sterile oscillations on the
  Universe dynamics and on the nucleon kinetics
  during BBN
• The effect of particle decays on BBN
• Cosmological constraints on the basis of
  primordial abundance measurements, BBN and CMB
  results

3
Neutrino in the standard cosmological model

• According to SCM our Universe is filled with
  massless non-oscillating neutrinos (an
  assumption).
• There exist three neutrino flavours - ?e, ?m ?t
  , (confirmed for weakly interacting species
  lighter than MZ / 2 by LEP , however sterile
  neutrino is allowed).
• The lepton asymmetry is zero (an assumption).
• Neutrino spectra have the equilibrium
  Fermi-Dirac distribution (an assumption).

4
Relic Neutrino Background
At high temperatures neutrinos are in equilibrium
due to weak interactions with the particle of
the high temperature plasma. Around 3 MeV muon
and tau and at 2 MeV electron neutrino decouple
and since then they are free streaming, i.e.
cosmological neutrino background.

• After the electron-positron annihilation neutrino
  temperature becomes lower than the temperature of
  the photons Tn(4/11)1/3 Tcmb. The cosmological
  neutrino background (CNB) today is expected with
  an extremely low temperature 1.9 K, i.e. less
  than the temperature of the CMB Tcmb2.7 K.
• Precise calculation of decoupling accounts
  for partial heating of neutrinos. Pastor et al,
  2008
• Dolgov, Hansen Semikoz, NPB 503 (1997)
  426 Mangano et al, PLB 534 (2002) 8
• Today relic neutrino (CNB) is expected to be the
  most numerous particle after the CMB photons.
• n n 3/11 ncmb n
  n112 cm-3 ncmb 411 cm-3
• 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 weak interactions and
  second, because cosmological neutrinos are
  expected to have today extremely low energy
  density Tn4.

5
Neutrino from experimental and observational data

• Standard model description does not match
  reality
• Flavour neutrino oscillations exist (solar,
  atmospheric, terrestrial expts data).
• Not all neutrino species are
  massless!
• Lepton flavor is violated.
• Mixing in the lepton sector
  exists.
• CPV?
• Sterile neutrino is allowed (not constrained by
  LEP, predicted by GUT models, wellcomed by
  cosmology LSS, DM, baryogenesis, astrophysics)
• LA may be non-zero L lt 0.1 in all neutrino
  sectors
• Neutrino spectra n(E) may differ from the
  equilibrium ones

6
Neutrino Oscillations
Positive 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.

• 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 evidence for ? oscillations
• Solar neutrino anomaly Homestake, Kamiokande,
  SuperKamioKa, Gallex, SAGE, SNO experiments
• ?? ? ?? LMA ?m2? 7.2-9.2 .10-5 eV2
  sin22? 0.3
• Atmospheric neutrino anomaly SuperKamioKa,
  Macro, Soudan 2, IMB
• ?? ? ??, ?m2? 2.6.10-3eV2 maximal ?
• Terrestrial experiments KamLAND, MINOS, K2K,
  LSND ?? ? ?e, ?m2? O(1eV2) ? sin22?O(0.003)
• alternative models with ?s give better agreement
  with Homestake and explain the variation of the
  flux with B.
• Though neutrino anomalies are well described in
  terms of flavor neutrino oscillations,
• sub-leading sterile oscillations may provide
  better fit (3 plus 2 schemes).

7
Neutrino Oscillations in the early Universe

• Cosmological influence of oscillations
• Active sterile oscillations corresponding to the
  regions favored by the atmospheric and solar
• neutrino data establish an equilibrium between
  active neutrino species before BBN epoch.
• No considerable influence on BBN, CMB, CNB.
• Neutrino active-sterile oscillations may excite
  additional light particles into
• equilibrium, i.e change the expantion rate
• distort the neutrino energy spectrum from the
  equilibrium FD form
• affect neutrino-antineutrino asymmetry of the
  medium (suppress / enhance).
• All these may play crucial role for neutrino
  involved processes in the
• early Universe during BBN, CMB, LSS, CNB.
• Cosmological constraints on oscillations
• From the allowed range of the observables of the
  early Universe, like

8
Neutrino from experimental and observational data

• Standard model description does not match
  reality
• Flavour neutrino oscillations exist (solar,
  atmospheric, terrestrial expts data).
• Not all neutrino species are
  massless!
• Lepton flavor is violated.
• Mixing in the lepton sector
  exists.
• CPV?
• Sterile neutrino is allowed (not constrained by
  LEP, predicted by GUT models, wellcomed by
  cosmology LSS, DM, baryogenesis, astrophysics)
• LA may be non-zero L lt 0.07 in all neutrino
  sectors
• Neutrino spectra n(E) may differ from the
  equilibrium ones

9
Sterile Neutrinos

• Sterile neutrino is not constrained by LEP
• Required for producing non-zero neutrino masses
  by most models
• Predicted by GUT models
• Welcomed by oscillations data for better fit
  (subdominant sterile oscillations channel
  required by Homestake data, Holanda, Smirnov,
  2004), Chauhan, Pulido, 2004, variation of the
  flux with B, Caldwell D, Sturrock P.,2005
• required for explanation of LSND in combination
  with other expts
• Wellcomed by cosmology
• may be the particle accounting for all
  DM (mlt3.5 KeV if MSM produced)
• may play subdominant role as DM
  component (eV, KeV)
• Fast moving neutrinos do not play
  major role in the evolution of structure in the
  universe.
• may play a role in LSS formation
  (when constituting few of the DM it suppresses
  small scale power in the matter power spectrum
  and better fits the observational data from SDSS,
  cluster abundance, weak lensing, Lyman Alpha
  forest, CMB) Tegmark et al., 2004
• plays major role in natural
  baryogenesis through leptogenesis
• Wellcomed by astrophysics
• may explain pulser kicks Kusenko 2006
• explain r-process nucleosynthesis
• explain supermasive black holes

10
Sterile Neutrinos

• The X ray photons from sterile neutrino decays
  may catalize the production of molecular H and
  speed up the star formation, causing earlier
  reionization Kusenko 2007
• X ray photons from sterile neutrino
  decays observational feature
• Lyman alpha bound mgt10 KeV (of MSM
  Dodelson-Widrow mechanism of production)
• CMB feels the increase in the density due to
  additional particles
• Sterile neutrino is constrained by BBN, because
  it increases the expansion rate and hence
  dynamically influences He production, in case it
  is brought into equilibrium Dolgov, 1981
• In case of oscillations with active neutrino it
  exerts major effect on nucleons kinetics during
  pre-BBN and its mixing parameters are constrained
  by BBNCMB Dolgov, Villante.
• In case of radiative decays its decay products
  may distort CMB
• In case of non-raditive decays, the decay poducts
  may influence
• nucleons kinetics and hence BBN
  constraints on its decay time, mass and number
  densities hold Dolgov, DK, 1986
• Et cetera..

11
Neutrino from experimental and observational data

• Standard model description does not match
  reality
• Flavor neutrino oscillations exist (solar,
  atmospheric, terrestrial expts data).
• Not all neutrino species are
  massless!
• Lepton flavor is violated.
• Mixing in the lepton sector
  exists.
• CPV?
• Sterile neutrino is allowed (not constrained by
  LEP, predicted by GUT models, wellcomed by
  cosmology LSS, DM, baryogenesis, astrophysics)
• LA may be non-zero L lt 0.1 in all neutrino
  sectors
• Neutrino spectra n(E) may differ from the
  equilibrium ones

12
Different processes leading to neutrino spectrum
distortion

• Electron-positron annihilation negligible
  effect Dolgov et al. 1997
• The equivalent number of neutrino species
  3.046 instead of 3.
• Account for flavour oscillations Mangano
  et al, 2005
• Number density of one neutrino species
  113 per cubic cm instead 112 in SCM.
• Neutrino-antineutrino asymmetry strongly
  constrained
• by BBN in all sectors because of flavour
  oscillations
• Active-sterile oscillations before neutrino
  decoupling slightly influence active neutrino
  disrbutions, because the active neutrino states
  are refilled due to interactions with the plasma.
  Barbieri,Dolgov, 1991
• Active-sterile oscillations proceeding after
  decoupling may strongly distort neutrino energy
  spectrum DK, 1986
• Particles decay into neutrinos

13

• Deviations from the equilibrium FD caused by
  different processes
• Nonequilibrium neutrino spectrum caused by
  oscillations
• Nonequilibrium neutrinos due to particle
  decays

14
Neutrino Oscillations Cosmological Influence

• Mixing b/n active neutrinos influence neutrino
  spectra and BBN negligibly.
• Oscillations b/n active and sterile neutrinos ?a
  ? ?s
• and ?Nslt1 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 (?Nslt1), 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

15
Oscillations effects

• Dynamical effect production of additional
  neutrino species.
• Additional degree of freedom enhances the energy
  density
• and drives expansion faster.
• Tf geff1/6 ? 4?? overproduction
• 
  Shvartsman, 1969
  
• 
  BBN constraints on ?Ns
  
• ?Yd 0.013 ?Ns
  Dolgov ,1981
• ( 1 additional ? ? ?Yp/Yp 5 )
  oscillations dynamical effect

16
Effects of nonequilibrium ?a ? ?s

• Kinetic effect ? ?a
  energy spectrum distortion,
  
• ? ?e depletion,
  D.K.,1988
  Barbieri,Dolgov, 1990
• 
  
  Enqvist et.al., 92 DK M.Chizhov, PLB
  ,1997
• ? energy threshold effect
  ? pre-BBN kinetics
• ? neutrino-antineutrino asymmetry growth
  Foot, Volkas,1996 DK M.Chizhov,1996
• 
  
  Dolgov et al., 2002
• In case of oscillations effective after ?
  decoupling and
• provided that the sterile state is not in
  equilibrium (?Nslt1),
• the spectrum distortion effect is the major one.
• Expressed in terms of effective number of
  neutrinos
• ?Nk,0 ?6 for resonant oscillations
• ?Nk,0 ?3 for non-resonant oscillations
  DK , Astrop.Phys.,2003

17
Oscillations medium influence

• Medium suppresses the oscillations amplitude
• Medium may enhance them
• Negligible spectrum distortion ?
• (work with particle densities and T shift one
  momentum approximations.)

• -Fast oscillations equilize pre-existing
  asymmetries
• - Oscillations cause great spectrum
  distortion, asymmetry growth
• Persists, and is often the leading effect ,
  hence it
• should be precisely described !

18
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
mediumsimultaneously DK 1988,
Chizhov, DK, 1997
Analytical solution for vacuum
neutrino oscillations (post BBN epoch)
DK 1988,
19
The evolution of spectrum distortion
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 FD form.
• The non-equilibrium initial condition
• leads to considerable and continuous
• deviations from the equilibrium.

20
Evolution of the distortionThe spectrum
distortion of the active neutrino for a wide
range of oscillation parameters persists during
the nucleons freezing period.
21
Energy spectrum distortion evolution
22
Spectrum distortion for non zero initial
popuation of ?s
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 ?Ns0, 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. ?Ns0 the lowest curve,
?Ns0,5 and ?Ns0,8 the upper curve. The dashed
curve shows the equilibrium spectrum.
23
Distortion evolution for non zero ?Ns
Spectrum distortion for different initial
population of ?s. ?Ns0 the lowest curve,
?Ns0,5 and ?Ns0,8 the upper curve. The
dashed curve shows the equilibrium spectrum. DK
, IJMPD2004,2007
24
The depletion of active neutrinos(an integral
effect of the distortion) DK,
Chizhov 1997, 2004
25
Role of flavor mixing

• Sterile state is filled for the sake of ?e
• CNB neutrinos may have the equilibrium
  number density or be depleted depending on the
  type of oscillations and their parameters.
• 0.5 Neq lt Ne lt Neq
• Energy spectum strongly distorted from the
  equilibrium Fermi-Dirac one.
• Sterile state filles from ?e , while ?e
  is partially refilled for the sake of muon and
  tau neutrino
• Flavor oscillations reestablish the
  equilibrium between the
• different neutrino flavors.
• Then CNB electron neutrinos will have
  slightly depleted
• number densities, at most 3/4 of the SCM
  value, i.e 1123/484 per cubic cm.
• Flavor mixing decreases the depletion and
  spectrum
• distortion

• 2 neutrino mixing
• 4 neutrino mixing
• ?Nk,4 lt ?Nk,2

26
BBN - one of the most precision probes of
new neutrino physics

• BBN provides a unique information about the
  physical conditions of our
• Universe at the very early epoch (t 1 sec) and
  thus allow to constrain
• physics beyond the standard cosmological model
  and the standard electroweak
• model.
• We explored a modification of the standard
  Big Bang Nucleosynthesis with neutrino
  oscillations ne ? ns
• effective after electron neutrino
  decoupling.

27
BBN with oscillations

• He-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 ? 4?? is
  overproduced
• BBN with fast ?a ? ?s
  increase
• effective before ?a decoupling
  Dolgov ,1981
• BBN with ?a ? ?s ?e
  spectrum
• effective after ?a decoupling and ?Nslt1
  distortions

28
Evolution of nucleons in the presence of ?? ?
?sthe numerical approach
29
The interplay b/n effects
?Nk,0 gt1
?N ?Nk,0- ?Nk,0 ?Ns ?Ns
?Nk,0 ?Ns gt?Ns
?m2 10-7 eV2 sin22? 1
30
The role of additional light ?s
?Nk,0 lt 1
?N ?Nk,0- ?Nk,0 ?Ns ?Ns
?Nk,0 ?Ns lt ?Ns
31
Maximum He-4 overproduction in BBN with
oscillations due to spectrum distortion

• Dependence of maximum
• overproduction on the mixing
• 0??Y/Y ?32 for resonant case
• 0??Y/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

32
Maximum He-4 overproduction in BBN with
oscillations due to spectrum distortion

• Maximal overproduction
• dependence on mass difference
• BBN is very sensitive to neutrino
• spectrum distortion
• BBN constraints do exist
• if He-4 uncertainty is over 5 but
• for non-equilibrium oscillations.
• BBN with nonequilibrium ?e??s
• allows to constrain ? oscillation
• parameters for He-4 uncertainty
• up to32 (14) in resonant
• (non-resonant) case.
• DK , Astrop.Phys.,2003

33
4?? the preferred element

• BBN - 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 ??? low metalicity regions of dwarf
  galaxies
• Extrapolated towards zero metalicity
• Yp0,2421? 0,0021 Izotov, Thuan 2000
• Yp0,2429? 0,009 Izotov, Thuan 2004
• Yp0,2472? 0,0012 Izotov, Thuan 20007
  (93 spectra of 86 low-metalicity HII regions)
• 
  dispersion of the
  determinations
• Yp0,245? 0,013 Olive, Skillman 2004
• Yp0,2491? 0,0091 Olive, Skillman 2004
• Yp0,2384? 0,0025 Peimbert et al 2002
• Yp0,2474? 0,0028 Peimbert, Luridiana.
  Peimbert 2007, new atomic data
• Determinations indicate 3-5 uncertainty
  (systematic errors). Sasselov, 95
• Possibly it is related with the evaluation of
  ionization level, stellar absorption, ..
  Luridiana, 2002

34
BBN constraints on oscillationsBBN with
neutrino oscillations between initially empty
ns and ne
Observational data on primordial He- 4 was
used to put stringent limits on the allowed
oscillation parameters. BBN constraints on ?? ?
?s Barbieri, Dolgov 91 depletion
account Dolgov 2000 dashed curve DK, Enqvist
et al. 92 one p approx. DK.,Chizhov 2001
distortion and asymmetry growth account Dolgov,
Villante, 2003 - spectrum distortion
35
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.

?Ns0
36
Role of the initial population of ?s BBN
constraints relaxed or strengthened?Additional
?s population may lead to stonger or weaker
BBN constraints on oscillation parameters.
There exist an interplay b/n the effects of
non-zero initial population of ?s on BBN in
case the dynamical effect dominates, He-4
overproduction is enhanced and BBN constraints
strengthen, in case the kinetic effect
dominates He-4 overproduction decreases and BBN
constraints relax. The dotted blue (red) contour
presents ?Yp/Yp3 (?Yp/Yp5.2 ) for ?Ns0,
the solid blue (red) contour presents ?Yp/Yp3
(?Yp/Yp5) for ?Ns0,5.
DK, Panayotova, 2006, DK, 2007
37
Spectrum distortion and BBN constraintsFor
nonequilibrium oscillations the constraints are
strengthened by orders of magnitude
Dolgov A., F.Villante ,2003 ?m2gt10-6 eV2, i.e.
kinetic equilibrium constraints for non-resonant
case
At smaller ?m2 re-population of active neutrino
becomes slow, spectrum distortion is
considerable. Chizhov M., DK, 2001 D.K.
2007 BBN is a very sensitive probe of
neutrino spectrum distortion caused by
oscillations
38
LSS, CMB, BBN

• In case neutrino masses are in the eV range they
  can constitute several of the DM, they can
  influence matter clustering (suppressing
  small-scale power of the matter power spectrum)
  providing better correspondence between models
  and observational data (from SDSS, cluster
  abundance, weak lensing, Lyman Alpha forest,
  CMB). Tegmark et al., 2004
• CMB anisotropy spectrum feels energy density
  increase caused by additional
• particles, hence it may constrain the fast
  active-sterile oscillations before decouling.
• For the oscillations effective after active
  neutrino decoupling the total energy density of
  neutrinos remains unchanged.
• BBN is a sensitive probe both to additional
  species and to distortions
• in the energy distribution of neutrinos.

39
BBN - one of the most precision probes of
new neutrino physics

• BBN with decaying particles
• We explored a modification of the standard
  Big Bang with decaying particles X during or
  before n-p feezing. The presence of such
  particles increases the expansion rate and their
  decay products change nucleons kinetics.
• Depending on its mass, density and life
  time, n-p ratio may be shifted in either
  direction. This allows relaxation of the BBN
  bounds on the number of relativistic species.

40
At high E (big X masses)
increase of n density, while
at low E (small masses) n
decreases The precise analysis of BBN with
decaying X reveals the possibility to achieve
either overproduction or underproduction of
primordial He-4
41
Evolution equations of decaying X and its decay
products
42
Evolution of neutrons
BBN may provide a sensitive probe to additional
non-radiatively decaying particles, due to the
kinetic effect of the decay products on n/p
freezing, and hence on He production.
43
For m lt 7 MeV and in case
He underproduction is
possible The possibility for a considerable
underproduction allows to weaken the BBN bounds
on neutrino species BBN with decaying MeV
particles may resolve the discrepancy b/n LSSCMB
constraints on N (based on WMAP3 power spectrum
and galaxy clustering power spectrum of SDSS, L
alpha data, 2dF, HST, SN, etc.) pointing to a
higher than 3 value of N (in case it persists).
Seljak et al., JCAP, 2006 In a non-standard BBN
with more than 3 neutrino species, the dynamical
effect of these may be compensated by the effect
of the decay products on nucleons kinetics during
BBN.
44
CNB, BBN and CMB constraints

• For oscillations parameters corresponding to the
  regions favored by the atmospheric and solar
  neutrino data flavor equilibrium between active
  neutrino species is established before BBN epoch.
  
• In case of fast active-sterile oscillations
  before decoupling of active neutrinos, leading to
  additional species into equilibrium, CBM and BBN
  constraints hold.
• Due to oscillations the sterile state is
  filled for the sake of the electron neutrino,
  which
• is refilled by the plasma. Thus the total
  energy density in neutrino sector increases,
  hence
• CMB constraints (sensitive to the total
  energy density) can be obtained.
• Stringent BBN constraints on oscillation
  prameters exist.
• In case of active-sterile oscillations after
  decoupling of active neutrinos only BBN
  constraints hold.
• Due to oscillations the sterile state is
  filled for the sake of the electron neutrino,
  which
• is not refilled by the plasma. Thus the
  total energy density in neutrino sector does not
  change
• hence CMB constraints cannot be obtained.
• Stringent BBN constraints on oscillation
  prameters exist.
• The number densities of CNB neutrinos are
  reduced, the spectrum differs from FD.
• CNB neutrinos may have the equilibrium number
  density or be depleted
• depending on the type of oscillations and
  their parameters.
• 0.5 lt
  ?Ns lt 1

45

• In 2 neutrino oscillation case CNB is
  considerably influenced
• relic electron neutrino can be expected in
  the extreme about twice less numerous than in
  SCM, and considerably less energetic with an
  energy spectum strongly distorted from the
  equilibrium Fermi-Dirac one.
• In 4 neutrino case it should be expected that
  when flavor oscillations are taking
• place they will tend to reestablish the
  equilibrium between the different neutrino
  flavors.
• Then CNB electron neutrinos will have
  slightly depleted number densities,
• around 3/4 of the SCM value, i.e 1123/484
  per cubic cm.
• The depletion of the electron neutrino and,
  correspondingly, the kinetic effect of
  oscillations is
• reduced. Hence, the cosmological constraints
  on oscillation parameters, corresponding
• to 4-neutrino mixing case will be less
  stringent than the ones calculated for 2-neutrino
  case.
• BBN provides stringent constraints on
  nonequilibrium decays of additional particles,
  leading to deviations of the electron neutrino
  spectrum, which reflects in changes in the
  kinetics of nucleons.

46
????????? ?? ??????????!Thanks for the
attention!
47

•        D. Kirilova, More General BBN Constraints
  on Neutrino Oscillations
• Parameters Relaxed or Strengthened, IJMPD
  16 (2007) 7, 1-14.
•  
• D.K.,M.Panayotova, Relaxed constraints on
  neutrino oscillation parameters,
• JCAP 2006, 12, 014 astro-ph/0608103
• D.K., astro-ph/0511231 I.J.M.P.D 2004,13,831
• Kirilova D.,Overproduction of helium-4 in the
  presence of neutrino oscillations,
• Astropart. Phys. v.19, pp. 409-417, 2003
  astro-ph/0109105
• Kirilova D., Chizhov M., Neutrino Degeneracy
  Effect on Neutrino
• Oscillations and Primordial Helium Yield,
  preprint ICTP IC/98/61,
• Trieste 1998, pp.17 hep-ph/9806441 Nucl.
  Phys. B 534, p. 447-463,
• 1998.
• Dolgov A.,Kirilova D.,Nonequilibrium Decays of
  Light Particles
• and Primordial Nucleosynthesis,
  Int.J.Mod.Phys.A3, p.267-277, 1988
• Preprint JINR E2-87-32, Dubna, 1987
• Kirilova D., Baryon Density in alternative BBN,
  ICTP preprint

48

• Universe Constituents
• WMAP measured the density of baryonic
• and non-baryonic matter to an accuracy
• of better than 5.
• WMAP determined that the universe is flat
• the mean energy density is equal to the
• critical density (within a 2 margin of error),
  9.9 x 1030 g/cm-3 (5.9 protons per cubic
• meter). It consists of 4 Atoms, 23 Cold Dark
  Matter, 73 Dark Energy.
• Fast moving neutrinos do not play any major role
  in the evolution of structure in the
• universe, massive neutrinos are less than 5 .
  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.

49
Constraints on neutrino oscillations
BBN with electron-sterile neutrino oscillations
4?? depends on the nucleon kinetic, which
depends on ?e characteristics ?e decrease ?
n/p freezes earlier ? 4?? is overproduced .
DK, 88 Chizhov, DK, 97,00 4?? depends
on the dynamics of the Universe g increase ? n/p
freezes earlier ? 4?? is overproduced .
Dolgov 81, Barbieri, Dolgov 90
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