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according to standard cosmology , neutrinos are probably one of the most abundant particles of the universe . the universe is filled with a sea of relic neutrinos that decoupled from the rest of the matter within the first few seconds after the big bang . it is excessively difficult to measure relic neutrinos since the interactions of their cross sections with matter are tremendously suppressed . besides , it is crucial to detect relic neutrinos in order to test the neutrino aspects of the big bang model of cosmology but it would seem impossible with present methods . however , some indirect evidences of the relic sea may be observed . for example , weiler @xcite have shown that the uhe cosmic neutrinos may interact with relic neutrinos via the following reactions occurring on the z resonance :    @xmath1    in such an event , an uhe cosmic neutrino has energy @xmath2 ev . therefore , the interaction of relic neutrinos and uhe cosmic neutrinos would have significant cross section . the high energy photon - neutrino interactions are very important in astrophysics , high energy cosmic ray physics and cosmology . from yang s theorem @xcite the leading term of the cross section for the @xmath0 process is very small due to the vector - axial vector nature of the weak coupling when the neutrinos are massless . it is shown that @xmath3 , where @xmath4 is the electron mass and @xmath5 is the photon energy in the center of the mass frame where the cross section for the @xmath0 process is in the order of @xmath6 and @xmath7 is the w boson mass @xcite . the dimension-8 effective lagrangian for the photon - neutrino interaction in standard model ( sm ) is as follows @xcite    @xmath8f_{\mu\lambda}f^{\nu\lambda } \label{l1}\end{aligned}\ ] ]    where @xmath9 is the neutrino field , @xmath10 is the electroweak gauge coupling , @xmath11 is the photon field tensor , @xmath12 is the fine structure constant and @xmath13 is the following    @xmath14.\end{aligned}\ ] ]    the equation ( [ l1 ] ) can be rewritten as following format @xcite ,    @xmath15    here @xmath16 and @xmath17 are the stress - energy tensor of the neutrinos and photons which are given below ,    @xmath18,\end{aligned}\ ] ]    @xmath19    for the sm , the photons and neutrinos decouple , i.e. , @xmath0 process at a temperature @xmath20 gev within one micro second after the big bang @xcite . when decoupling temperature is reduced to the qcd phase transition ( @xmath21 mev ) , some remnants of the photons circular polarization can possibly be retained in the cosmic microwave background @xcite which can be considered as an evidence for the relic neutrino background . for reducing the decoupling temperature , the cross section for the @xmath22 process should be increased . this can be done via the models which are beyond the sm . for instance , contribution of large extra dimensions to these process have been calculated in ref . they have shown that the inclusion of the extra dimension effects did not provide large enough high energy neutrinos to scatter from relic neutrinos in this process , but concluded that the photon decoupling temperature can be significantly reduced . also , in ref . @xcite , it has been remarked that unparticle physics can lower decouple temperature below the @xmath23 . the sm has been successful in describing the physics of the electroweak interactions and , it is consistent with experiments . however , some questions are still left unanswered , such as , the number of fermion generation and fermion mass spectrum have not been exhibited by the sm . attractive explanations are provided by models assuming composite quarks and leptons . the existence of excited states of the leptons and quarks is a natural consequence of these models and their discovery would provide convincing evidence of a new scale of matter . in this model , charged and neutral leptons can be considered as a heavy lepton sharing leptonic quantum number with the corresponding sm lepton . they should be regarded as the composite structures which are made up of more fundamental constituents . therefore , excited neutrinos can be considered to spin-@xmath24 bound states or , including three spin-@xmath24 or spin-@xmath24 and spin @xmath25 substructure . all composite models have an underlying substructure which is characterized by a scale @xmath26 . the interaction between spin @xmath24 excited fermions , gauge bosons and the sm fermions can be described by the @xmath27 invariant effective lagrangian as follows @xcite ,    @xmath28    in these expressions , @xmath29 with @xmath30 being the dirac matrices , @xmath31 and @xmath32 are the field strength tensors of the @xmath33 and @xmath34 , @xmath35 and @xmath36 are the generators of the corresponding gauge group , @xmath10 and @xmath37 are standard electroweak and strong gauge couplings . @xmath26 is the scale of the new physics responsible for the existence of excited neutrinos and @xmath38 , @xmath39 scale the @xmath33 and @xmath34 couplings , respectively . the effective lagrangian can be rewritten in the physical basis ,    @xmath40    first term in the above equation is a purely diagonal term with @xmath41 and second term is a non - abelien part , which involves triple as well as quartic vertices with    @xmath42    @xmath43    @xmath44    @xmath45    the chiral @xmath46 ( @xmath47 ) interaction term can be found as follows    @xmath48    where @xmath49 is the momentum of the gauge boson , @xmath50 is the electroweak coupling parameter , @xmath51 is defined for photon by @xmath52 where we have assumed that @xmath53 .    up to now , searches have not found any signal for excited neutrinos at the colliders . the current mass limits on excited neutrinos are @xmath54 gev at the lep @xcite and @xmath55 gev assuming @xmath56 at the hera @xcite . excited neutrinos have been also studied for hadron colliders @xcite and next linear colliders @xcite . in these studies , it has been obtained that excited neutrinos masses up to @xmath57 tev can be detected at the lhc .    in this paper , we examine the effect of the excited neutrinos on the interaction of the uhe cosmic and relic neutrinos for the @xmath0 process . the sm contribution to @xmath0 process have been calculated in refs.@xcite with using equation ( [ l1 ] ) . from this effective lagrangian , the squared amplitude for the sm can be obtained in terms of mandelstam invariants u and t as follows ,    @xmath58 .    the new physics ( np ) contribution comes from t and u channels excited neutrino exchange . the analytical expressions for the polarization summed amplitudes square for np , sm and np interference terms are given below ,    @xmath59    @xmath60    where @xmath61 . therefore , the whole squared amplitude can be calculated as follows ,    @xmath62 . in the limit @xmath63 , the amplitude turns into following formation ,    @xmath64    we have calculated the cross section with / without approximation cross section . we have seen that results are closely for different @xmath65 and @xmath66 . therefore , the differential cross section for @xmath0 process can be obtained by using    @xmath67    then , the total cross section can be found from the equation ( [ dcs ] ) as follows ,    @xmath68    in fig . ( [ fig1 ] ) , we have plotted the total cross sections as a function of the center of mass energy @xmath69 for both the @xmath70 and total cross sections when @xmath71 gev . these cross sections are obtained for the two excited neutrinos , with masses of @xmath72 gev , @xmath73 gev . also , in fig.([fig2 ] ) we have showed the cross sections for @xmath72 gev and three scale of the new physics : @xmath71 gev , @xmath74 gev and @xmath75 gev . this figure shows similar behavior with fig . ( [ fig1 ] ) .    extra contribution to the @xmath76 cross section from excited neutrino exchange influences the decoupling temperature . the temperature at which the this process ceases to take place can be found from the the reaction rate per unit volume ,    @xmath77    the terms in equation ( [ roo ] ) are as following : @xmath78 and @xmath79 are the momentum of the neutrino and antineutrino ; @xmath80 and @xmath81 their energies ; t is the temperature ; @xmath82 is the flux . the @xmath83 can be given in terms of @xmath84 in the center of mass frame by using of invariance of @xmath85    @xmath86    @xmath87    where @xmath88 and @xmath89 is the angle between @xmath78 and @xmath79 . equation ( [ roo ] ) can be found    @xmath90    where @xmath91 and @xmath92 . then the reaction rate per unit volume has been obtained ,    @xmath93^{2}\end{aligned}\ ] ]    where @xmath94 is the riemann zeta function . the interaction rate @xmath95 is obtained by dividing @xmath96 by the neutrino density @xmath97 at temperature @xmath98 . thus we have found ,    @xmath99    multiplying equation ( [ rr ] ) by the age of the universe ,    @xmath100    at least one interaction to occur is @xmath101 . the solution of the following equation gives the decoupling temperature ,    @xmath102    if @xmath103 and @xmath104 are replaced in the above equation , then following equation can be found ,    @xmath105    fig . ( [ fig3 ] ) shows solution of the this equation . we have analyzed the contribution of excited neutrinos on the interaction of relic neutrinos with uhe cosmic neutrinos via the @xmath76 process . it is shown that excited neutrino contribution to total cross section of the @xmath76 process is significant depending on the @xmath106 , @xmath107 . we have seen that for the appropriate values of these parameters , the sm and total cross sections can be distinguished from each other in the specific center of mass energy regions .    for decreasing decoupling temperature , the total cross section of the @xmath76 should be increased . if the @xmath65 or new physics parameter @xmath108 decrease then the total cross section increases . therefore , @xmath109 can be decreased significantly . for different values of @xmath65 , @xmath109 have been shown in fig.([fig3 ] ) as a function of the new physics parameter @xmath108 . as seen from this figure , our obtained values of the decoupling temperature can decrease the value of the sm decoupling temperature ( @xmath110 gev ) .
we examine the effect of excited neutrinos on the annihilation of relic neutrinos with ultra high energy cosmic neutrinos for the @xmath0 process . 
 the contribution of the excited neutrinos to the neutrino - photon decoupling temperature are calculated . 
 we see that photon - neutrino decoupling temperature can be significantly reduced below the obtained value of the standard model with the impact of excited neutrinos .