Abstract
The main task of this review is to discuss quantum cosmology minisuperspace models based on the Wheeler–DeWitt equation, which apart from the standard matter and 3-geometry configuration degrees of freedom, allow those related to the variability of physical constants—varying speed of light (VSL) c and varying gravitational constant G. The tunneling probability of the universe “from nothing” to the Friedmann phase will be given for such varying constants minisuperspace models.
Highlights
Some physicists often express their doubts about the statement that constants—which are considered to be fundamental in physics—may vary
If we consider them as fields which are influenced by some unknown physical interaction, this statement is just a consequence
The variability of the speed of light and the gravitational constant have been included by using the ansätze (14) and (15)
Summary
Some physicists often express their doubts about the statement that constants—which are considered to be fundamental in physics—may vary. We could look for the first epochs of the evolution of the Universe, near the Planck scale of 1019 GeV, at which quantum effects cannot be described classically. Another problem which arises when we go back in time to the moment of the birth of the Universe is the initial singularity—a state for which our gravity theory fails. The theories with varying speed of light can provide a solution to some well-known cosmological problems, such as the flatness problem, the horizon problem, the Λ-problem, and the singularity problem [8]. According to the current data [11,12], one should consider both possibilities—a decreasing as well as an increasing value of c
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