Cosmic kinematic dynamos in non-singular anisotropic universe

A marginally excited cosmic kinematic dynamo is found in the background of a non-singular anisotropic Kasner cosmological metric solution of Einstein field equation of general relativity. The magnetic field is not amplified but is frozen inside the universe. Since a finite resistivity is assumed, a nonsingular flow velocity is orthogonal to the magnetic field plane. The model presents an inflationary phase. Magnetic field components are stretched along the orthogonal planar directions while the flow is orthogonal to this magnetic sheet. The self-induction magnetohydrodynamic field equation in Kasner universe may be written in the form of a polynomial in the time coordinate which yields a periodic flow.