Models of f(Q) gravity with electromagnetic field

Abstract: There are so many ideas that potentially explain the dark energy phenomenon, current research is focusing on a more in-depth analysis of the potential effects of modified gravity on both local and cosmic scales. In this paper we have investigated some cosmic reconstructions in $f (Q)$ cosmology where $Q$ is the non-metricity corresponding to the evolution background in the Friedmann-Lamatre-Robertson-Walker $(FLRW)$ universe. This allows us to determine how any $FLRW$ cosmology can emerge from a particular $f (Q)$ theory. We employ the reconstruction technique to generate explicit formulations of the $f (Q)$ Lagrangian for several types of matter sources like perfect fluid, dust like fluid, stiff fluid and the binary mixture of two fluids. Furthermore, we computed the field equations and equation of state (EoS) parameter $\omega$ for two different reconstructed $f(Q)$ models with the variation of the involved constants, which gives the scenario of accelerating universe, quintessence region and cosmological constant. We also observed that the time dependence of $\omega$ admits cosmic acceleration. These new $f(Q)$ gravity inspired models may have an impact on gravitational phenomena at other cosmological scales.