The conformal symmetry of the quantized electromagnetic field breaks down in curved space-time .
We point out that this conformal anomaly is able to generate a sizable magnetic field during a phase of slow-roll inflation .
Such primordial magnetism is characterized by the expectation value of the squared of the magnetic field for comoving observers , which at leading order in slow-roll takes the value \langle \vec { B } ^ { 2 } \rangle = \frac { 8 } { 15 ( 4 \pi ) ^ { 2 } } H ^ { 4 } \epsilon , where \epsilon is the standard slow-roll parameter .
This result is insensitive to the intrinsic ambiguities of renormalization in curved space-times .
The information in the quantum state gets diluted during inflation and does not affect the prediction .
A primordial coherent field of this strength may be able to seed the observed cosmic magnetism .