Seminal Electromagnetic fields from preinflation

Abstract: We investigate the geometric dynamics of the primordial electric and magnetic fields during the early stages of the universe by extending a recently introduced quantum algebra \cite{BMM,BMAS}. We work on an extended model of gravity that considers the boundary terms from the Einstein-Hilbert action as geometric quantum fluctuations of the spacetime. We propose that the extended Riemann manifold is generated by a new connection ${\hat{\delta\Gamma}}^{\mu}_{\alpha\beta}$. This connection contains geometric information about the fluctuations of gravitational and electromagnetic fields in the vacuum, which could have been crucial during the primordial stages of the universe's evolution. We revisit a preinflationary cosmological model \cite{mb} with a variable time scale and negative spatial curvature, such that the universe begins with a null initial background energy density. We observed the emergence of large scale magnetic fields starting from small values during the early phases of the universe's evolution. Subsequently, these fields decrease to reach present day values on the order of $\left<\hat{\delta B}\right> \simeq 10^{-12}\,{\rm G}$ on cosmological scales (between $10^{24}$ and $10^{26}$ meters). This significant deviation from inflationary models eliminates the need to impose excessively large initial values on these fields.