This licentiate thesis gives an overview of modified gravity and primordial magnetic fields, bridged by gravitational waves (GWs) as a phenomenological probe of both sectors. First we derive the GW equation in a homogeneous and isotropic background from general relativity. This is followed by a brief review of modified gravity – its motivations and some common approaches. Within the vast theory space of modified gravity, however, only a handful of parameters enter at the level of the GW equation, in a relatively model- independent manner.
We then discuss a range of possible mechanisms giving rise to GWs in the early universe – from inflation to the early radiation era – and note, in particular, that magnetically-driven turbulence could be present regardless of the orders of the phase transitions. Therefore, the anisotropic stress due to primordial magnetic fields could be an ubiquitous category of production mechanisms for GWs, whose present-day relic spectrum could then be used to constrain the parameters of modified gravity, in addition to inferring the nature of the primordial magnetic sources themselves.