Explaining Phenomenologically Observed Space-time Flatness Requires New Fundamental Scale Physics

The phenomenologically observed flatness - or near flatness - of spacetime cannot be understood as emerging from continuum Planck (or sub-Planck) scales using known physics. Using dimensional arguments it is demonstrated that any immaginable action will lead to Christoffel symbols that are chaotic. We put forward new physics in the form of fundamental fields that spontaneously break translational invariance. Using these new fields as coordinates we define the metric in such a way that the Riemann tensor vanishes identically as a Bianchi identity. Hence the new fundamental fields define a flat space. General relativity with curvature is recovered as an effective theory at larger scales at which crystal defects in the form of disclinations come into play as the sources of curvature.Comment: This article were already in 2011 published as Proceedings of the 14th Bled Conference on "What Comes Beyond the Standard Models" organized by Norma Manko Borstnik, Dragan Lukman, Maxim Khlopov, and H.B. Nielse

Products of Random Matrices

We derive analytic expressions for infinite products of random 2x2 matrices. The determinant of the target matrix is log-normally distributed, whereas the remainder is a surprisingly complicated function of a parameter characterizing the norm of the matrix and a parameter characterizing its skewness. The distribution may have importance as an uncommitted prior in statistical image analysis.Comment: 9 pages, 1 figur

Fermion and Higgs Masses and the AGUT Model

We present two rather differently based predictions for the quark and lepton spectrum: One provides a rather successful fit to the mass suppressions---the well known fermion mass hierarchy---interpreted as due to most mass terms needing to violate approximately conserved quantum numbers corresponding to the AGUT group $SMG^3\times U(1)_f$. This is actually, under certain conditions, the maximal group transforming the known 45 Weyl components of the quark and leptons into each other. From the fit to the fermion spectrum, we get a picture of the series of Higgs fields causing the breakdown (presumably at the Planck scale) of this AGUT to the Standard Model and, thus, providing the small masses of all quarks and leptons except for the top quark. We separately predict the top quark mass to be $173 \pm 5$ GeV and the Higgs mass to be $135 \pm 9$ GeV, from the assumption that there be two degenerate minima in the effective potential for the Weinberg Salam Higgs field with the second one at the Planck field strength.Comment: 6 page LaTeX file plus 1 postscript figure and aipproc style file, uses epsfig.sty; to appear in the Proceedings of Beyond the Standard Model V, Balholm, Norway, 29 April - 4 May 199

Remarkable coincidence for the top Yukawa coupling and an approximately massless bound state

We calculate, with several corrections, the non-relativistic binding by Higgs exchange and gluon exchange between six top and six anti-top quarks (actually replaced by left-handed b quarks from time to time). The remarkable result is that, within our calculational accuracy of the order of 14% in the top quark Yukawa coupling g_t, the experimental running top-quark Yukawa coupling g_t = 0.935 happens to have just that value which gives a perfect cancellation of the unbound mass = 12 top-quark masses by this binding energy. In other words the bound state is massless to the accuracy of our calculation. Our calculation is in disagreement with a similar calculation by Kuchiev et al., but this deviation may be explained by a phase transition. We and Kuchiev et al. compute on different sides of this phase transition.Comment: 68 pages, 3 figures; published version, including a discussion of the results of Ref. (5) and the new Appendix