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We discuss tensor metric perturbations in a magnetic field around thehomogeneous Juttner equilibrium of massless particles in an expanding universe.We solve the Liouville equation and derive the energy-momentum tensor up tolinear terms in the metric and in the magnetic field.The term linear in themagnetic field is different from zero if the total charge of the primordialplasma is non-zero. We obtain an analytic formula for temperature fluctuationstreating the tensor metric perturbations and the magnetic field as independentrandom variables. Assuming a cutoff on large momenta of the magnetic spectralfunction we show that the presence of the magnetic field can discriminate onlylow multipoles in the multipole expansion of temperature fluctuations. In sucha case the term linear in the magnetic field can be more important than thequadratic one (corresponding to the fluctuations of the pure magnetic field).

Linear metric and temperature fluctuations of a charged plasma in a primordial magnetic field