Bimetric Gravity Theory, Varying Speed of Light and the Dimming of Supernovae

TL;DR

This paper explores a bimetric scalar-tensor gravity theory where the speed of light varies with time, affecting supernova observations and potentially explaining cosmic acceleration without dark energy.

Contribution

It introduces a novel bimetric framework linking two metrics via a scalar field, showing how varying light speed impacts supernova dimming and cosmic acceleration interpretations.

Findings

Varying speed of light causes supernova dimming without dark energy.

Different metric choices lead to apparent cosmic acceleration or deceleration.

The gravitational constant G can vary, but the fine-structure constant remains constant.

Abstract

In the bimetric scalar-tensor gravitational theory there are two frames associated with the two metrics {\hat g}_{\mu\nu} and g_{\mu\nu}, which are linked by the gradients of a scalar field \phi. The choice of a comoving frame for the metric {\hat g}_{\mu\nu} or g_{\mu\nu} has fundamental consequences for local observers in either metric spacetimes, while maintaining diffeomorphism invariance. When the metric g_{\mu\nu} is chosen to be associated with comoving coordinates, then the speed of light varies in the frame with the metric {\hat g}_{\mu\nu}. Observers in this frame see the dimming of supernovae because of the increase of the luminosity distance versus red shift, due to an increasing speed of light in the early universe. Moreover, in this frame the scalar field \phi describes a dark energy component in the Friedmann equation for the cosmic scale without acceleration. If we choose {\hat g}_{\mu\nu} to be associated with comoving coordinates, then an observer in the g_{\mu\nu} metric frame will observe the universe to be accelerating and the supernovae will appear to be farther away. The theory predicts that the gravitational constant G can vary in spacetime, while the fine-structure constant \alpha=e^2/\hbar c does not vary. The problem of cosmological horizons as viewed in the two frames is discussed.