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This is a thesis which contributes to research in two different fields: theoretical physics and physics education research. The common link between these two research areas is that both involve explorations of abstract physics and mathematical representations, but from different perspectives.

The first part of this thesis is situated in theoretical physics. Here a cosmological scenario is explored where a de Sitter phase is replaced with a phase described with a scale factor a(t) ~ tq, where 1/3<1. This scenario could be viewed as an inflationary toy model, and is shown to open up the possibility of an information paradox. This potential paradox is resolved even in the worst case scenario by showing that the time scales involved for such a paradox to occur is of the order of magnitude of the recurrence time for the de Sitter space.

The second part of this thesis is situated in physics education research. A number of learning situations that are experienced as abstract by students are explored: probability in one dimensional quantum tunnelling; the mindsets that students adopt towards understanding physics equations used in typical teaching scenarios; and what students focus on when presented with physics equations. The results for the quantum scattering study are four phenomenographic categories of description, for the mind sets study, six epistemological components of mindsets and for the focus on physics equations study, three foci creating five levels of increasing complexity of ways of experiencing physics equations.  Pedagogical implications of these results are discussed.