Comprehensive list of cosmological models and their properties?

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SUMMARY

This discussion centers on the need for a comprehensive list of cosmological models and their properties, specifically mentioning models such as Friedmann-Robertson-Walker (FRW), de Sitter (dS), anti-de Sitter (AdS), and Gödel spacetime. Key mathematical concepts referenced include metrics, Christoffel symbols, Riemann tensors, Ricci tensors, Ricci scalars, and Kretschmann scalars. Tom highlights the lack of a singular resource compiling all these elements, suggesting the paper arXiv:gr-qc/0004016v1 by Bicak and the book "Exact Solutions of Einstein's Field Equations" by Stephani et al. as valuable references. Additionally, he recommends using GrTensor or Maxima for calculating these properties from the metrics.

PREREQUISITES
  • Friedmann-Robertson-Walker (FRW) cosmological model
  • Understanding of de Sitter (dS) and anti-de Sitter (AdS) spaces
  • Familiarity with Riemannian geometry concepts such as metrics and Christoffel symbols
  • Proficiency in using GrTensor or Maxima for tensor calculations
NEXT STEPS
  • Research the paper arXiv:gr-qc/0004016v1 by Bicak for insights on cosmological models
  • Study "Exact Solutions of Einstein's Field Equations" by Stephani et al. for detailed model comparisons
  • Learn how to use GrTensor for calculating cosmological metrics and properties
  • Explore Maxima for symbolic computation of Riemann tensors and Ricci scalars
USEFUL FOR

Astronomers, theoretical physicists, and researchers in cosmology seeking to deepen their understanding of cosmological models and their mathematical properties.

tom.stoer
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Does anybody know about a comprehensive list of cosmological models and their properties? E.g. FRW, dS, AdS, ... Goedelspacetime, ... with metrics g, Christoffel symbols, Riemann tensors, Ricci, Ricci scalar, Kretschmann scalar, ...

Tom
 
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That's a big ask. I've never seen a book or paper that lists all that stuff for every metric. The comparison papers which summarize models tend to focus on symmetries and invariants. There's a good slice of that in this paper arXiv:gr-qc/0004016v1 (Bicak) and in 'the book', "Exact Solutions of Einstein's Field equations", Stephani et al (2nd edition).

You could get GrTensor or Maxima and calculate them yourself from the metrics.
 
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