Effects of the Higgs Scalar on Gravity

Abstract

Let us consider a role of the Higgs scalar in the present elementary particle physics. The Higgs scalar has been used to generate particle masses through the spontaneous symmetry breakdown and couples to almost all fields. There is also a gravitational field which couples to all fields. These facts naturally lead us to the question Is there any role of the Higgs scalar played in gravity? or Is there any effect of the spontaneous symmetry breakdown on gravity? In this paper, we shall find how the Higgs scalar affects gravity. There have already been many papers in which a scalar field is incorporated with a Lagrangian for gravity. A heuristic method was used to construct a scalar­ tensor gravity by Brans and Dicken and others.) There have also appeared pa­ pers3l,4l in which a scalar field is combined with a scalar curvature so that a theory is conformally invariant. The latter theory has a severe defect that a scalar field becomes a ghost when an action for a gravitational field has a minimum. 4l There is another way in which one can determine an effective Lagrangian for any field. It is a nonlinear spinor theory of the Nambu-Jona-Lasinio type 5l which has recently revived and produced many interesting results one after another. 6l~sl In this paper, we shall incorporate the Higgs scalar with a gravitational Lagrangian, using a nonlinear spinor theory of the Nambu-Jona-Lasinio type. A gravitational field is taken as a weak field in our model. This is shown in § 2. Section 3 is devoted to discussion of main results of our model. Summary and discussion are given in § 4.