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Larry Abbott, by the way, also reaches the same result  [30], p. 96:
“All measurements are in agreement that, unto the largest distances accessible to astronomers – about 10 billions of light years or 10 ²³ kilometers   - no indications exist for any distortions of the space-time due to a not disappearing cosmological constant. From this follows that the amount of the cosmological constant must be smaller than
1/(10 ²³ kilometers)² = 10 ^-52 m^-2.”
Arthur Eddington, who once said [14]:
“I am a detective on search for a criminal – the cosmological constant. I know that he exists, but I don’t know what he looks like”, certainly would have been surprised about the “search result” presented here.
The example of the cosmological constant, by the way, shows which false tracks physics can enter if it rests upon purely mathematical formalisms only. Einstein had once introduced the cosmological constant L, as it seemed necessary for the stabilization of the static universe he postulated and as it was not forbidden from the view of the GTR. A physical necessity based on a fundamental principle did not exist for this.
After it was found, the universe is not static, but expanding by publications of Friedmann and the discovery of the red shift by Hubble, Einstein abandoned his ad-hoc decision again, as it led to a complication of his theory,  [10], p. 110:
" which considerably lessened its logical simplicity."
Besides, his opinion was [10], p. 126:
“If the Hubble expansion had already been discovered at the establishment of the General Theory of Relativity, it would never have come to the introduction of a cosmological term.
“À posteriori, it seems now all the more unjustified to introduce such a term into the field equations, as the introduction has lost its only original right of existence – to lead to a natural solution of the cosmological problem.”
In spite of this, the cosmological constant survived, in its original formulation, as a measure for the vacuum density. This formal “clinging” to a term born by Einstein’s emergency situation in my opinion has contributed to the fact, the vacuum energy density is regarded as a constant value until today, for which there exists no plausible physical reason.
Obviously, only  the detour via a new physical principle – the CTH – is able  to overcome the “stuck” situation which the discussion about the cosmological constant is facing.
According to the CTH, a cosmological constant as once demanded by Einstein and later by other scientists as well, namely a „fifth natural force“ accelerating the expansion of the universe, does not exist!
The vacuum energy supplies only – same as matter and radiation, a contribution to the total gravity force field in the universe.
Larry Abbott also supports this opinion [30], p. 92/93:
“In the General Theory of Relativity, the energy density of the vacuum has an absolute importance;
one can define it by measurement of that gravity force field which is not created by matter, but by the vacuum itself.”
 

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