Abstract
H.A. Wilson, then R.H. Dicke, proposed to describe gravitation by a spatial change of the refractive index of the vacuum around a gravitational mass. Dicke extended this formalism in order to describe the apparent expansion of the universe by a cosmological time dependence of the global vacuum index. In this paper, we develop Dicke’s formalism. The metric expansion in standard cosmology (the time-dependent scale factor of the Friedmann–Lemaître curved spacetime metric) is replaced by a flat and static Euclidean metric with a change with time of the vacuum index. We show that a vacuum index increasing with time produces both the cosmological redshift and time dilation, and that the predicted evolution of the energy density of the cosmological microwave background is consistent with the standard cosmology. We then show that the type Ia supernovæ data, from the joint SDSS-II and SNLS SNe-Ia samples, are well modeled by a vacuum index varying exponentially as n(t)=exp(t/tau _0), where tau _0=8.0^{+0.2}_{-0.8} Gyr. The main consequence of this formalism is that the cosmological redshift should affect any atom, with a relative decrease of the energy levels of about -2 10^{-18} mathrm {s}^{-1}. Possibilities for an experimental investigation of this prediction are discussed.
Highlights
At the end of his above-mentioned paper, Dicke proposed to extend this formalism by introducing a cosmological time dependence of the vacuum index in order to describe the apparent expansion of the universe in a static Euclidean metric
This approach is radically different from the standard cosmology, where the cosmological redshift is modeled by the expansion of the Friedmann–Lemaître metric, through a time-dependent scale factor which is mainly driven at the present epoch by a cosmological constant Λ
As initially proposed by Wilson and Dicke, the curved spacetime in a stationary gravitational field can be equivalently interpreted as being due to a spatial change of the vacuum refractive index and the inertial masses in a Euclidean metric
Summary
At the end of his above-mentioned paper, Dicke proposed to extend this formalism by introducing a cosmological time dependence of the vacuum index in order to describe the apparent expansion of the universe in a static Euclidean metric. It is important to note that the formalism proposed in this paper is different from the class of models commonly named tired light (TL) theories (see [10] and references inside), where, in order to produce the cosmological redshift, an energy loss of photons is assumed but vacuum properties are kept constant. 3 the extension of that model to a vacuum refractive index varying with time and show how it can produce both the observed cosmological redshift and the time stretching of SNe-Ia light curves. As detailed for instance in [7] or in [8], predictions of General Relativity in the weak field approximation such as the deflection of light, the gravitational redshift, or the advance of the perihelion of Mercury, can be calculated in a static and flat metric using the following relations of physical parameters with the vacuum index c(r ) = n−1(r ) × c∞.
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