Effective theory framework based on symmetry has recently gained widespread interest in the field of cosmology. In this paper, we apply the same idea on the genesis of the primordial magnetic field and its evolution throughout the cosmological universe. Given the broken time-diffeomorphism symmetry by the cosmological background, we considered the most general Lagrangian of electromagnetic and metric fluctuation up to second order, which naturally breaks conformal symmetry in the electromagnetic (EM) sector. We also include parity violation in the electromagnetic sector with the motivation that has potential observational significance. In such a set-up, we explore the evolution of EM, scalar, and tensor perturbations considering different observational constraints. In our analysis we emphasize the role played by the intermediate reheating phase which has got limited interest in all the previous studies. Assuming the vanishing electrical conductivity during the entire period of reheating, the well-known Faraday electromagnetic induction has been shown to play a crucial role in enhancing the strength of the present-day magnetic field. We show how such physical effects combined with the PLANCK and the large scale magnetic field observation makes a large class of models viable and severely restricts the reheating equation of state parameter within a very narrow range of 0.01 < ω_eff < 0.27, which is nearly independent of reheating scenarios we haveconsidered.

基于对称性的有效理论框架最近在宇宙学领域引起了广泛的兴趣。在本文中，我们将相同的想法应用于原始磁场的起源及其在整个宇宙学宇宙中的演化。鉴于宇宙学背景破坏了时间微分同胚对称性，我们考虑了最一般的电磁和度量涨落的二阶拉格朗日量，这自然会破坏电磁 (EM) 扇区中的共形对称性。我们还将电磁领域的奇偶破坏包括在内，其动机具有潜在的观察意义。在这样的设置中，我们探讨了考虑不同观察约束的 EM、标量和张量扰动的演变。在我们的分析中，我们强调了中间再加热阶段所起的作用，这在之前的所有研究中都受到了有限的关注。假设在整个重新加热期间电导率消失，众所周知的法拉第电磁感应已被证明在增强当今磁场强度方面起着至关重要的作用。我们展示了这种物理效应与 PLANCK 和大规模磁场观测相结合如何使一大类模型可行，并将状态参数的再加热方程严格限制在 0.01 < ω 的非常窄的范围内 众所周知的法拉第电磁感应已被证明在增强当今磁场的强度方面起着至关重要的作用。我们展示了这种物理效应与 PLANCK 和大规模磁场观测相结合如何使一大类模型可行，并将状态参数的再加热方程严格限制在 0.01 < ω 的非常窄的范围内 众所周知的法拉第电磁感应已被证明在增强当今磁场的强度方面起着至关重要的作用。我们展示了这种物理效应与 PLANCK 和大规模磁场观测相结合如何使一大类模型可行，并将状态参数的再加热方程严格限制在 0.01 < ω 的非常窄的范围内_eff < 0.27，这几乎与我们考虑的再加热方案无关。