The sign of the induced Newton constant is fixed by the scalar non-minimal coupling

In Sakharov’s induced-gravity mechanism, the sign of the induced Newton constant is set by a heat-kernel number summed over fields. For the Standard Model the gauge and fermion contributions (−48 and +45) nearly cancel, so the Higgs coupling to curvature decides the sign. That coupling is a continuous parameter which no low-energy measurement constrains. The note separates what is scheme independent (the sign) from what depends on the regulator (the size of the coefficient). It then shows that in the Chamseddine–Connes spectral action the Higgs coupling is fixed by the geometry. It is the conformal value for every scalar, inherited from the −R/4 term of the spinor bundle, so the scalar sector contributes exactly zero.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-13
DOI
https://doi.org/10.5281/zenodo.23349825
Primary Topic
Cosmology and Gravitation Theories
Type
preprint
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preprint

The sign of the induced Newton constant is fixed by the scalar non-minimal coupling

Boris Kulangiev
Zenodo (CERN European Organization for Nuclear Research)
Cosmology and Gravitation Theories
preprint

The sign of the induced Newton constant is fixed by the scalar non-minimal coupling

Boris Kulangiev
preprint en

Abstract

In Sakharov’s induced-gravity mechanism, the sign of the induced Newton constant is set by a heat-kernel number summed over fields. For the Standard Model the gauge and fermion contributions (−48 and +45) nearly cancel, so the Higgs coupling to curvature decides the sign. That coupling is a continuous parameter which no low-energy measurement constrains. The note separates what is scheme independent (the sign) from what depends on the regulator (the size of the coefficient). It then shows that in the Chamseddine–Connes spectral action the Higgs coupling is fixed by the geometry. It is the conformal value for every scalar, inherited from the −R/4 term of the spinor bundle, so the scalar sector contributes exactly zero.

Zenodo (CERN European Organization for Nuclear Research)
Cosmology and Gravitation Theories
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