Grøn has conducted research within the areas of general relativity, cosmology and classical electromagnetism.
[6] Together with Erik Eriksen at the University of Oslo he has also studied properties of the electromagnetic field produced by accelerated electric charges.
He has, among other things, shown that it is possible to interpret observations from cosmos so that the concept of dark energy is unnecessary.
[11] Grøn (together with Matthew Aadne) have found solutions to the field equations without a cosmological constant for empty space in the theory of gravitation developed by John Nash.
[12] They correspond to the solutions of the field equations with a cosmological constant in the gravitational theory developed by Einstein.