Unruh effect in a real scalar field with the Higgs potential on a dynamically variable background space-time

It is predicted that an accelerating electron performs a Brownian motion in the inertial frame. This Brownian motion in the inertial frame has its roots in the interaction with the thermal excitation given by the Unruh effect in the accelerating frame. If such a prediction is possible, correspondingly we propose a prediction in this study that the thermal radiation is emitted in the inertial frame from an electron heated due to the Unruh effect in the accelerating frame. The point in our prediction is, although the Unruh effect is limited in the accelerating frame, as well as that the Brownian motion rooted in the Unruh effect appears in the inertial frame, the heat of the particle appears in the inertial frame. Based on such a prediction in this paper, we investigate phenomena in the neighborhood of an accelerating electron in the inertial frame. The model we consider is the four-dimensional Klein–Gordon real scalar field model with the Higgs potential term at the finite temperature identified with the Unruh temperature on the de Sitter space-time. We calculate the one-loop effective potential in the inertial frame with the corrections by the thermal radiation rooted in the Unruh effect in the accelerating frame. In this calculation, we take into account that the background space-time is deformed due to the field theory’s corrected one-loop effective potential. Based on such an analysis, we illustrate the restoration of the spontaneous symmetry breaking and the dynamical variation of the background space-time, and we examine the accelerating particle’s world-line and the amount of the energy corresponding to the change of the acceleration