Mathematics – Logic
Scientific paper
May 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008aas...212.2202m&link_type=abstract
American Astronomical Society, AAS Meeting #212, #22.02; Bulletin of the American Astronomical Society, Vol. 40, p.220
Mathematics
Logic
Scientific paper
We present some new results about a systematic approach to higher-order gravity models. These models have recently attracted a lot of attention with nearly 300 papers in the last 3 years. The models are derived from curvature invariants that are more general than the Einstein-Hilbert action. Some of the models exhibit late-time self-acceleration and fit some current observations. The open question is that there are an infinite number of invariants that one could use and many published papers have stressed the need to find a systematic approach that will allow one to study methodically the various possibilities. We present here some new results on a novel systematic approach to these models. We explore a new connection that we made between theorems from the theory of invariants in general relativity and these cosmological models. In summary, the theorems demonstrate that curvature invariants are not all independent from each other and that for a given source fluid and Petrov type (symmetry classification) of the space-time, there exist a complete minimal set of independent invariants (a basis) in terms of which all the other invariants can be expressed. As an immediate consequence of the proposed approach, the number of invariants to consider is dramatically reduced from infinity to four invariants in the worst case and to only two invariants in the cases of interest, including all Friedmann-Lemaitre-Robertson-Walker metrics. We derive models that pass stability and physical acceptability conditions. We present dynamical equations and phase portrait analyses that show the promise of the systematic approach. We also present some preliminary results on comparison between some models built from a basis of invariants and current observations.
Ishak Mustapha
Moldenhauer Jacob
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