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Effective theory framework based on symmetry has recently gained widespreadinterest in the field of cosmology. In this paper, we apply the same idea onthe genesis of the primordial magnetic field and its evolution throughout thecosmological universe. Given the broken time-diffeomorphism symmetry by thecosmological background, we considered the most general Lagrangian ofelectromagnetic and metric fluctuation up to second order, which naturallybreaks conformal symmetry in the electromagnetic (EM) sector. We also includeparity violation in the electromagnetic sector with the motivation that haspotential observational significance. In such a set-up, we explore theevolution of EM, scalar, and tensor perturbations considering differentobservational constraints. In our analysis we emphasize the role played by theintermediate reheating phase which has got limited interest in all the previousstudies. Assuming the vanishing electrical conductivity during the entireperiod of reheating, the well-known Faraday electromagnetic induction has beenshown to play a crucial role in enhancing the strength of the present-daymagnetic field. We show how such physical effects combined with the PLANCK andthe large scale magnetic field observation makes a large class of models viableand severely restricts the reheating equation of state parameter within a verynarrow range of $0.01 < \omega_\mathrm{eff} < 0.27$, which is nearlyindependent of reheating scenarios we have considered.

Effective Theory of Inflationary Magnetogenesis and Constraints on Reheating