Primordial magnetic fields generated in the very early universe are one of the candidates for the origin of magnetic fields observed in galaxy clusters .
After recombination , the Lorentz force acts on the residual ions and electrons to generate density fluctuations of baryons .
Accordingly these fluctuations induce the early formation of dark halos which cause the Sunyaev-Zel ’ dovich ( S-Z ) effect in cosmic microwave background radiation .
This additional S-Z effect due to primordial magnetic fields amplifies the angular power spectrum of cosmic microwave temperature anisotropies on small scales .
This amplification depends on the comoving amplitude and the power law index of the primordial magnetic fields spectrum .
Comparing with the small scale CMB observations , we obtained the constraints on the primordial magnetic fields , i.e. , B \la 2.0 nGauss for n = -2.9 or B \la 1.0 nGauss for n = -2.6 , where B is the comoving amplitude of magnetic fields at h ^ { -1 } Mpc and n is the power law index .
Future S-Z measurements have the potential to give constraints tighter than those from temperature anisotropies and polarization of cosmic microwave background induced by the magnetic fields at the recombination epoch .