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Zur kosmologischen Testung des Machschen Prinzips
Author(s) -
Treder H.J.
Publication year - 1982
Publication title -
astronomische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.394
H-Index - 63
eISSN - 1521-3994
pISSN - 0004-6337
DOI - 10.1002/asna.2103030602
Subject(s) - physics , cosmology , isotropy , gravitational constant , mathematical physics , cosmological constant , acceleration , gravitation , dark energy , classical mechanics , inertia , newtonian fluid , modified newtonian dynamics , theoretical physics , astrophysics , quantum mechanics , galaxy rotation curve , galaxy , halo
The Machian models of isotropic expanding universes according to the “inertia‐free” gravo‐dynamics imply the equations\documentclass{article}\pagestyle{empty}\begin{document}$$ \[H_0^2 \, = \,\frac{E}{{R_0^2 }}\, + \,\frac{{C^2 }}{{{}_3R_0^2 }}\,and\,q_0 \, = \, ‐ \,\frac{E}{{{}_3f_0 MR_0 }}H_0^{ ‐ 2} \, = \,\frac{{4\pi }}{3}f_0 \ell _0 H_0^{ ‐ 2} \, ‐ \,\frac{1}{2}\] $$\end{document}between the instantan values H 0 and q 0 of the H UBBLE parameter H , the acceleration q , and the matter density o. Therefore, in Machian universes with linear expansion q 0 = 0 the energy integral E = ‐1/2ϵ c 2 is zero and the matter density becomes (with H 0 2 R 0 2 = c 2 /3)\documentclass{article}\pagestyle{empty}\begin{document}$$ \[\,\ell _0 \, = \,\,\frac{3}{{8\pi f_0 }}H_0^2\] $$\end{document}( f 0 the Newtonian gravitational constant). This is the critical density in general relativistic cosmology.