Astronomy and Astrophysics – Astrophysics – Cosmology and Extragalactic Astrophysics
Scientific paper
2011-09-02
Astronomy and Astrophysics
Astrophysics
Cosmology and Extragalactic Astrophysics
20 pages, 4 figures, 2 table
Scientific paper
Although this is well known that variations of fundamental constants should be restricted to their dimensionless combinations, the literature on variations of G is entirely dimensionful, and in some cases this had led to inconsistent results. The issue that appears to have been missed in many studies is that in cosmology the strength of gravity is bound up in the cosmological equations, and the epoch at which we live is a crucial part of the model. We argue that it is useful to consider the hypothetical situation of communicating with another civilization (with entirely different units), comparing only dimensionless constants, in order to decide if we live in a Universe governed by precisely the same physical laws. In this thought experiment, we would also have to compare epochs, which can be defined by giving the value of any one of the evolving cosmological parameters. By setting things up carefully in this way one can avoid inconsistent results for when considering variable constants, caused by effectively fixing more than one parameter today. We show examples of this effect by considering in some detail the physics of Big Bang nucleosynthesis, recombination and microwave background anisotropies, being careful to maintain dimensionlessness throughout. We present Fisher matrix calculations to estimate how well the fine structure constants for electromagnetism and gravity can be determined with future microwave background experiments. We highlight how one can be misled by simply adding G to the usual cosmological parameters. We also explicitly give a dimensionless version of the parameters of the standard cosmological model. Rigorously determining how to talk about the model in a way which avoids physical dimensions is a requirement for proceeding with a calculation to constrain time-varying fundamental constants.
Moss Adam
Narimani Ali
Scott Douglas
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