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Cosmological Constant Problem Solution Valid for Both Planck's and Cosmological Scales

As it is well-known Einstain himself set his cosmological constant to zero, Lambda = 0, in 1931 “ for reason of logical economy” , because he thought that no hope of measuring this quantity experimentally at the time. Meanwhile, the relation between Lambda and the energy density of the vacuum has led to a big problem in more recent times (Feynman, Magic Without Magic, 1972 ; Weinberg, Reviews of Modern Physics 61, 1989). Thus, modern quantum field theories such as quantum chromodynamics (QCD), electroweak (EW) and grand unified theories (GUTs) predicted vary large values for vacuum density ro-lambda and its dimensionless form Omega-lambda, o at the present time (GUTs: ro-lambda=10exp.93 gcm-3, Omega-lambda, o = (10exp.122)ho exp(-2), where ho is a present Hubble parameter). On the other side some cosmologists have preferred that Lambda should be close to zero. But, setting Lambda to zero is not in accordance with the present observations indicating that Omega-lambda, o is in fact of order unity. Now, the main problem is to find out a cancellation mechanism which may cancel at precisely the 123 decimal places. This “ cosmological-constant problem” has been reviewed by many people, but there is no consensus on how to solve it (Overduin and Wesson, Physics Reports 402, 2004). In order to solve this “ cosmological-constant problem” in this paper a new nondiagonal form of the Riemann’ s type line element is employed. In that context, the static vacuum solution of the related Einstein’ s field equations, including Lambda, for a spherically symmetric non-rotating body, predicts the following: (i) the so-called cosmological constant Lambda can not be equal to zero, (ii) Lambda can not be a constant, and (iii) Lambda is in fact a function of a gravitational radius (Lambda = f (r)). This solution of Lambda et the Planck’ s scale is of order 10exp.70 and gives values for ro-lambda and Omega-lambda, o exactly equal to predictions of GUTs. On the other side, the same solution of Lambda at the cosmological scale is of order 10 exp(-53) and gives values for Omega-lambda, o of order unity. Thus, one can conclude that this solution of Lambda is valid for both Planck’ s and cosmological scales. This solution of Lambda can be applied, among the others, to cosmology for determination of the repulsive acceleration that gives rise to accelerating expansion of the universe at the present time. In that context, the solution Lambda = f (r) can be connected with the solution of the dark energy problem. The very important property of the solution of the nondiagonal Riemann’ s type line element is the nonsingularity for all gravitational radius r, except for r = 0.

Riemann's Geometry; Nondiagonal Line Element; Cosmological Constant Problem; Vacuum Energy; Attractive and Repulsive Gravity

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