Among primordial magnetogenesis models , inflation is a prime candidate to explain the current existence of cosmological magnetic fields .
Assuming conformal invariance to be restored after inflation , their energy density decreases as radiation during the decelerating eras of the universe , and in particular during reheating .
Without making any assumptions on inflation , on the magnetogenesis mechanism and on how the reheating proceeded , we show that requiring large scale magnetic fields to remain subdominant after inflation gives non-trivial constraints on both the reheating equation of state parameter and the reheating energy scale .
In terms of the so-called reheating parameter , we find that \ln R _ { \mathrm { rad } } > -10.1 for large scale magnetic fields of the order 5 \times 10 ^ { -15 } Gauss today .
This bound is then compared to those already derived from Cosmic Microwave Background ( CMB ) data by assuming a specific inflationary model .
Avoiding magnetic field backreaction is always complementary to CMB and can give more stringent limits on reheating for all high energy models of inflation .
For instance , a large field matter dominated reheating can not take place at an energy scale lower than typically 500 \mbox { GeV } if the magnetic field strength today is B _ { 0 } = 5 \times 10 ^ { -15 } \mathrm { G } , this scale going up to 10 ^ { 10 } \mbox { GeV } if B _ { 0 } = 10 ^ { -9 } \mathrm { G } .