Mathematics – Logic
Scientific paper
Nov 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006aipc..861..891n&link_type=abstract
ALBERT EINSTEIN CENTURY INTERNATIONAL CONFERENCE. AIP Conference Proceedings, Volume 861, pp. 891-896 (2006).
Mathematics
Logic
Classical General Relativity, Post-Newtonian Approximation, Perturbation Theory, Related Approximations, Relativity And Gravitation, Mathematical And Relativistic Aspects Of Cosmology
Scientific paper
It is known that the Newtonian cosmology (both for the Friedmann background and its linear perturbations) is not purely based on Newton's gravity, but a guided one by Einstein's theory. The action-at-a-distance nature of Newton's gravity requires further verification from Einstein's theory for its use in the large-scale nonlinear simulation. We provide its domain of validity in cosmology by investigating the weakly and fully nonlinear regimes in relativistic cosmology based on Einstein's gravity. In the weakly nonlinear approach the Einstein guided Newtonian cosmology is exactly valid to the second order in perturbation and pure relativistic correction terms start appearing from the third order, and are small in the large-scale near horizon. We also provide fully nonlinear relativistic correction terms in the post-Newtonian approach in cosmological situation. Perturbation approach is valid in weakly nonlinear regime but is applicable in strong gravity (including near and beyond horizon), whereas post-Newtonian approach is valid in fully nonlinear regime but is applicable in the weak gravity (thus far inside horizon). These two approaches provide complementary relativistic correction terms, thus showing the limit and validity of the Newtonian approach in cosmology.
Hwang Jai-chan
Noh Hyerim
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