On gravity’s role in the genesis of rest masses of classical fields

  • László B. SzabadosEmail author
Research Article


It is shown that in the Einstein-conformally coupled Higgs–Maxwell system with Friedman–Robertson–Walker symmetries the energy density of the Higgs field has stable local minimum only if the mean curvature of the \(t=\mathrm{const}\) hypersurfaces is less than a finite critical value \(\chi _c\), while for greater mean curvature the energy density is not bounded from below. Therefore, there are extreme gravitational situations in which even quasi-locally defined instantaneous vacuum states of the Higgs sector cannot exist, and hence one cannot at all define the rest mass of all the classical fields. On hypersurfaces with mean curvature less than \(\chi _c\) the energy density has the ‘wine bottle’ (rather than the familiar ‘Mexican hat’) shape, and the gauge field can get rest mass via the Brout–Englert–Higgs mechanism. The spacelike hypersurface with the critical mean curvature represents the moment of ‘genesis’ of rest masses.


General relativity Conformal invariance Rest masses Higgs mechanism 



The author is grateful to Árpád Lukács, Péter Vecsernyés and György Wolf for the numerous and enlightening discussions both on the structure of the Standard Model and on various aspects of the present suggestion. Special thanks to György Wolf for the careful reading of an earlier version of the paper, his suggestions to improve the text at several points and for drawing the figures; and to Helmut Friedrich and Paul Tod for their remarks on both the conformal cyclic cosmological model and the present suggestions. Thanks are due to the ‘Geometry and Relativity’ program at the Erwin Schrödinger International Institute for Mathematics and Physics, Vienna, for the support and hospitality where the final version of the present paper was prepared. Funding was provided by Erwin Schrödinger International Institute for Mathematics and Physics (Grant No. Geometry and Relativity CBS 2017).


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Authors and Affiliations

  1. 1.Wigner Research Centre for PhysicsBudapest 114Hungary

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