Seminal magnetic fields from Inflato-electromagnetic Inflation

We extend some previous attempts to explain the origin and evolution of primordial magnetic fields during inflation induced from a 5D vacuum. We show that the usual quantum fluctuations of a generalized 5D electromagnetic field cannot provide us with the desired magnetic seeds. We show that special fields without propagation on the extra non-compact dimension are needed to arrive to appreciable magnetic strengths. We also identify a new magnetic tensor field $B_{ij}$ in this kind of extra dimensional theories. Our results are in very good agreement with observational requirements, in particular from TeV Blazars and CMB radiation limits we obtain that primordial cosmological magnetic fields should be close scale invariance.

💡 Research Summary

The paper investigates the origin and evolution of primordial magnetic fields within a five‑dimensional (5D) vacuum framework, specifically through a model termed “inflato‑electromagnetic inflation.” The authors begin by reviewing earlier attempts that treat the 5D electromagnetic field as a straightforward extension of the usual four‑dimensional (4D) Maxwell theory. By quantizing the generalized 5D field on an inflating de Sitter background (scale factor (a(t)=e^{Ht})), they find that the resulting magnetic power spectrum is far too weak to serve as the seed required by observations. The suppression originates from the extra non‑compact dimension: modes with non‑zero momentum along this dimension ((k_{5}\neq0)) are heavily damped during inflation, and even the zero‑mode contribution does not generate a magnetic field strength larger than (10^{-15}) G.

To overcome this limitation, the authors propose a special class of fields that do not propagate along the extra dimension. They decompose the 5D vector potential (A_{A}) into the usual 4D components (A_{\mu}(x^{\nu})) and an extra‑dimensional component (A_{5}(x^{\nu})). By imposing the condition that the wavefunction of (A_{5}) is static in the fifth direction ((k_{5}=0)), the dynamics reduce to a set of 4D equations for both (A_{\mu}) and a newly identified antisymmetric tensor field \