Title: Isocurvatures at second order and Magnetogenesis

Abstract: Observations have offered strong support for the theory of Inflation, but many details of the physics of the early Universe are still unknown. An observation of primordial isocurvature modes would change our view of the early Universe and point towards multi-field inflation. In this talk, I will describe some recent work towards the calculation of second-order effects from isocurvature modes, in which all possible growing mode initial conditions have been calculated for second-order Boltzmann solvers. I then apply these results to the second-order Boltzmann code SONG and compute the magnetic field generated by vortical currents in the presence of isocurvature modes. A mild enhancement of the generated magnetic field is found in the presence of general isocurvature modes, when compared to the adiabatic case. A particularly interesting case is that of compensated isocurvature modes, for which the enhancement increases by several orders of magnitude due to the allowed large amplitude of those modes. We show in this particular case how these compensated modes can influence observables at second order and produce interesting effects which may be used to constrain these modes in the future.