Friedmann-Robertson-Walker spacetimes from the perspective of geometric algebra
arxiv(2024)
摘要
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.
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