  There is an observational indication of extragalactic magnetic fields. No
known astrophysical process can explain the origin of such large scale magnetic
fields, which motivates us to look for their origin in primordial inflation. By
solving the linearized Einstein equations, we study metric perturbations
sourced by magnetic fields that are produced during inflation. This leads to a
simple but robust bound on the inflation models by requiring that the induced
metric perturbation should not exceed the observed value 10^-5. In case of the
standard single field inflation model, the bound can be converted into a lower
bound on the Hubble parameter during inflation.
