Efectos de las oscilaciones de sabor sobre el desacoplamiento de neutrinos c ó smicos Teguayco Pinto Cejas AHEP - IFIC Teguayco Pinto Cejas AHEP - IFIC Trabajo de investigación hep-ph/

Outline Motivation Basic concepts Early Universe Thermal equilibrium Neutrino decoupling QED corrections Non instantaneous First results Effects of medium Final results Flavour neutrino oscillations

Motivation  Neutrinos are abundant in the Universe  Radiation component  Hot dark matter  Neutrino spectrum depends on decoupling  Decoupling is flavour dependent  Neutrinos are abundant in the Universe  Radiation component  Hot dark matter  Neutrino spectrum depends on decoupling  Decoupling is flavour dependent Hannestad 2003

Early Universe  Primordial Plasma: initial state of high temperature  The plasma is kept in thermal equilibrium by different reactions whose rate is larger than the expansion rate  Primordial Plasma: initial state of high temperature  The plasma is kept in thermal equilibrium by different reactions whose rate is larger than the expansion rate Neutrinos coupled by weak interactions Decoupled neutrinos (CNB) T~MeV t~sec Primordial Nucleosynthesis

Thermal equilibrium  After quark-hadron transition neutrinos are kept in thermal equilibrium by:  Equilibrium implies:  After quark-hadron transition neutrinos are kept in thermal equilibrium by:  Equilibrium implies:

Neutrino decoupling  It occurs in the Radiation Dominated Era, where the radiation component of  is dominant  Since neutrinos have m << MeV they were relativistic at decoupling  Relic neutrinos present a FD distribution with T  At T~m e e  -annihilation processes heat up the  ’s and the temperature ratio is:  It occurs in the Radiation Dominated Era, where the radiation component of  is dominant  Since neutrinos have m << MeV they were relativistic at decoupling  Relic neutrinos present a FD distribution with T  At T~m e e  -annihilation processes heat up the  ’s and the temperature ratio is: m only could be important through oscillations Entropy conservation It depends on momentum because of the smallness of neutrino mass The present day temperatures p and T scale with a

Non-instantaneous decoupling  Below T dec there are residual interactions between and e ± that distort the neutrino spectrum  Non-thermal effect  Below T dec there are residual interactions between and e ± that distort the neutrino spectrum  Non-thermal effect Boltzmann equation I coll is basically proportional to: Statistical factor Weak interaction amplitude I coll is basically proportional to: Statistical factor Weak interaction amplitude Since T dec is close to m e

Non-instantaneous decoupling  Below T dec there are residual interactions between and e ± that distort the neutrino spectrum  Non-thermal effect with the comoving variables  Below T dec there are residual interactions between and e ± that distort the neutrino spectrum  Non-thermal effect with the comoving variables Boltzmann equation

 We also use the energy conservation to set a complete system of integro-differential equations where  The system has no analytical solution  There have been several works dedicated to this problem  We also use the energy conservation to set a complete system of integro-differential equations where  The system has no analytical solution  There have been several works dedicated to this problem Dicus et al 1982 Hannestad & Madsen 1995 Dolgov et al 1997

First results (No oscillations)  The next results have been obtained solving numerically the previous set of integrodifferential equations with a fortran code.  We use a grid on neutrino momenta where i=1,…,100  The next results have been obtained solving numerically the previous set of integrodifferential equations with a fortran code.  We use a grid on neutrino momenta where i=1,…,100

At x < 0.2 ( T~2.5 MeV) there is no decoupling Between 0.2 < x < 4 distortions are effective At low temperatures ( x > 4) the distortions freeze out due to: - decoupling - few e ± Also

The distortion has been Multiplied by 10 to see the effect

z (Temp. ratio)N eff Instant No QED QED Take into account that this definition is only correct when the neutrino are in equilibrium Corrections at finite temperature to the  and e ± plasma equation of state

z (Temp. ratio)N eff Instant No QED QED  Two reasons for the variation of N eff  Distortion on neutrino spectrum  Variation of T   Two reasons for the variation of N eff  Distortion on neutrino spectrum  Variation of T  It is a usual way to parametrize the energy density in function of  

z (Temp. ratio)N eff Instant No QED QED This difference is one of the motivations of this work

Flavour neutrino oscillations  Experimental evidences of neutrino oscillations M. Maltoni et al 2004

Flavour neutrino oscillations  Experimental evidences of neutrino oscillations  They could play a role if they are effective at the epoch of neutrino decoupling  Density matrix  Evolution  Experimental evidences of neutrino oscillations  They could play a role if they are effective at the epoch of neutrino decoupling  Density matrix  Evolution We have to take into account the presence of the medium. It blocks the oscillations and its effect arises later. Remember that it is composed by: e ±,  and spin up signifies e spin down signifies 

Effect of medium (I)  The equation of motion Two different effects induced by the medium Change the axis and speed of precession but not the length Shrinkage of P which destroy the coherence of the evolution MSW effect P z gives the excess of e over  Assuming collisions flavour conserving

Effect of medium (II)  Medium potential V med Modifies the dispersion relation Asymmetry of particle    Neglect neutrino asymmetry N ~0  For e ± background we have to take into account the second order N l ~ N B ~ At high T  N e <<  e At T~1 MeV  N e <<  m 2 /2p

Effect of medium (III) Oscillations start to be effective immediately At high T  V e >  m 2 /2p Oscillations start to be effective around 1MeV Dolgov et al 2002

Final results  Two independent calculations are carried out in the x range from m e /10 to 35 One evaluates the creation of distortions in the neutrino distribution function dividing the evolution in 1000 steps Then the evolution equations involving the components of neutrino matrix are solved dividing each step x 0  x 1 by 100 or more

Oscillations smooth the flavour dependence of the distortion Around T~1 MeV the oscillations start to modify the distortion The variation is larger for e The difference between different flavors is reduced

z fin  e     N eff QED mixing s 2  13 = Bimaximal Small correction The effect on the energy density is higher

Fitting the distorsions  For numerical calculations If neutrino masses are relevant  For numerical calculations If neutrino masses are relevant CMBFAST or CAMB

Some examples  Contribution of neutrinos to total energy density  Neutrino number density  Contribution of neutrinos to total energy density  Neutrino number density Effect of distorsion

Big Bang nucleosynthesis  Production of the primordial abundances of light elements ( 4 He, H…)  The relevant temperature interval is from 1 MeV to 50 keV  Neutrinos have a double influence on nucleosynthesis  Production of the primordial abundances of light elements ( 4 He, H…)  The relevant temperature interval is from 1 MeV to 50 keV  Neutrinos have a double influence on nucleosynthesis As a component of the background radiation The processes n  p are directly affected by neutrino spectrum As a component of the background radiation The processes n  p are directly affected by neutrino spectrum

Big Bang nucleosynthesis As a component of the background radiation The processes n  p are directly affected by neutrino spectrum As a component of the background radiation The processes n  p are directly affected by neutrino spectrum As a component of the background radiation Energy conservation Change in t BBN Energy conservation Change in t BBN

Big Bang nucleosynthesis As a component of the background radiation Energy conservation Change in t BBN As a component of the background radiation Energy conservation Change in t BBN The processes n  p are directly affected by neutrino spectrum

Big Bang nucleosynthesis YpYp QED 1.71  mixing 2.07  s 2  13 =  Bimaximal 2.13  Y p ~ 0.24

Conclusions  We are able to calculate the neutrino spectrum considering the oscillations  We have calculated the frozen values of neutrino distributions  The effects on N eff are not yet detectable but could be measured in future experiments  The effect on BBN is not important over the total correction  We are able to calculate the neutrino spectrum considering the oscillations  We have calculated the frozen values of neutrino distributions  The effects on N eff are not yet detectable but could be measured in future experiments  The effect on BBN is not important over the total correction CMBFAST CAMB not PLANCK maybe CMBPOL

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