Abstract
We summarize the status of the theory of resummed quantum gravity. In the context of the Planck scale cosmology formulation of Bonanno and Reuter, we review the use of our resummed quantum gravity approach to Einstein’s general theory of relativity to estimate the value of the cosmological constant as ρΛ = (0.0024 eV)4. Constraints on susy GUT models that follow from the closeness of the estimate to experiment are noted. Various consistency checks on the calculation are discussed. In particular, we use the Heisenberg uncertainty principle to remove a large part of the remaining uncertainty in our estimate of ρΛ.
Highlights
We use the well-known elementary example of “summation”: ∞= ∑ xn, 1−x n =0Citation: Ward, B.F.L
If we accept loop quantum gravity [4,5,6,7] we find that the answer is no, the fundamental theory entails a space-time foam with a Planck scale loop structure
Weinberg [11] suggests that quantum gravity may be asymptotically safe, with an S-matrix that depends only on a finite number of observable parameters, due to the presence of a non-trivial UV fixed point, with a finite dimensional critical surface; this is equivalent to an answer of yes
Summary
We use the well-known elementary example of “summation”:. Applications. If we accept loop quantum gravity [4,5,6,7] we find that the answer is no, the fundamental theory entails a space-time foam with a Planck scale loop structure. Weinberg [11] suggests that quantum gravity may be asymptotically safe, with an S-matrix that depends only on a finite number of observable parameters, due to the presence of a non-trivial UV fixed point, with a finite dimensional critical surface; this is equivalent to an answer of yes. In conformity with the example in Equation (1), the resultant resummed theory, resummed quantum gravity (RQG), is very much better behaved in the UV compared to what one would estimate from that Feynman series.
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