Friedmann-Robertson-Walker spacetimes from the perspective of geometric algebra
The intention of our paper is to provide a pedagogical application of geometric algebra to a particularly well-investigated system: We formulate the geometric and dynamical properties of Friedmann-Robertson-Walker spacetimes within the language of geometric algebra and re-derive the Friedmann-equations as the central cosmological equations. Through the geometric algebra-variant of the Raychaudhuri equations, we comment on the evolution of spacetime volumes, before illustrating conformal flatness as a central property of Friedmann-cosmologies. An important aspect of spacetime symmetries are the associated conservation laws, for which we provide a geometric algebra formulation of the Lie-derivatives, of the Killing equation and of conserved quantities in Friedmann-Robertson-Walker spacetimes. Finally, we discuss the gravitational dynamics of scalar fields, with their particular relevance in cosmology, for cosmic inflation, and for dark energy.