Thanks for the reference to the recent arXiv paper by Rainer Beck. I find his work exceedingly interesting, and this one is no different. One section is relevant here: The Intergalactic Magnetic Field, introducing which subject he writes:
Magnetic fields in the intergalactic medium (IGM) are of fundamental importance for cosmology [146]. Their role as the likely seed field for galaxies and clusters and their possible relation to structure formation in the early Universe place considerable importance on its discovery. Various generation mechanisms have been suggested. The field could be produced via the Weibel instability at structure formation shocks [97].
One can learn a lot from Beck — not only the methodologies in use to detect and quantify magnetic fields at large distances, but some of his own views and discssions on their importance, plus a peek at the future using new radio telescope arrays, such as the Square Kilometre Array.
Beck has also collaborated with another outstanding radio astronomer at the University of Sydney, Brian Gaensler. See his references in the above paper for that.
Gravitational potential energy is an interesting subject, too, especially out in the intergalactic parts of the map. Ian Sefton notes that if you lift a brick in Earth's gravity field, you do not increase the brick's potential energy; you increase the potential energy of the system that consists of the Earth and the brick.
PE is not stored in either Earth or the brick nor is it possible to apportion the PE between the two interacting objects. The first step to enlightenment is to learn not to think of gravitational or electrical PR of electrons (or of any kind of particle) and think instead of energy as a property of the whole system.
This makes the conceptualization or modeling of the gravitational as well as magnetic or electromagnetic potential energy out in a fairly remote region of space among the galaxies a very difficult exercise in taking all the interacting objects into account. Summing all the vectors, in other words.
Here is a simple example: What is the gravitational attraction (the net direction and amount of acceleration in gees (Earth gravities) at some point between the Sun and its nearest neighbor (which would be the center of gravity or barycenter of the binary pair Alpha Centauri A and B). Assume that the Sun and Alpha Cen have no relative motion, for simplicity. If you take a test mass, a 1 kg sphere, say, and release it with no relative motion to either star system, on the straight line between the two systems at the point where each pulls the mass with the same force toward its own center, the mass will be in a zero-g or nano-g condition and acceleration will be nil. If the test mass were the Sun itself, the acceleration on the Sun due to Alpha Cen is only about 1.5 x 10^-14 gee.
If the 1 kg test mass is released in similar fashion someplace else, it will feel a net acceleration. The imaginary field of gravity acceleration vectors between two star systems varies smoothly everywhere in space around those two. The revolution of the binary pair about its barycenter adds a further complication - dynamics - to the gravity vectors. Add in all the other stars and bodies in the galaxy, each of which exerts a finite, if small, force on the test mass, and the situation, while "real", becomes mathematically intractable. Even "numerical methods" to solve an n-body problem won't be much help, and certain simplifications have to be applied. "Ignore all vectors coming from things on the "other half" of the galaxy". " Ignore masses less than 1 Jupiter mass." Once upon the simplification road, the mathematician is on a bifurcated manifold branch, the non-reality side.
So it is difficult, at the very least, to define how much energy from this or that set of attractions or repulsions exists at random points in intergalactic space. That Beck and Gaensler and others have learned how to infer the strengths of galactic fields from Faraday rotation and line-splitting and other sophistries is quite amazing. And as important as the magnetic fields in IG space may be according to Beck's studies, the really important stuff is where the electrodynamics and complex, chaotic trajectories of plasma physics conspire to increase the fields, drawing in ionized matter in great electromagnetic Bennett pinches which increase the mass density along with the charged particle density and the overall combined field densities in ways to form stars and galaxies, at the nodes of the thin wispy soup of filaments of partially ionized matter and charged dusty grains lurking between the stars and galaxies.