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Qualitative Analysis of Universes with Varying Alpha

John D. Barrow·David F. Mota
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Abstract

Assuming a Friedmann universe which evolves with a power-law scale factor, $a=t^{n}$, we analyse the phase space of the system of equations that describes a time-varying fine structure 'constant', $α$, in the Bekenstein-Sandvik-Barrow-Magueijo generalisation of general relativity. We have classified all the possible behaviours of $α(t)$ in ever-expanding universes with different $n$ and find new exact solutions for $α(t)$. We find the attractors points in the phase space for all $n$. In general, $α$ will be a non-decreasing function of time that increases logarithmically in time during a period when the expansion is dust dominated ($n=2/3$), but becomes constant when $n>2/3$. This includes the case of negative-curvature domination ($n=1$). $α$ also tends rapidly to a constant when the expansion scale factor increases exponentially. A general set of conditions is established for $α$ to become asymptotically constant at late times in an expanding universe.

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John D. Barrow, David F. Mota. 2002-07-02. Qualitative Analysis of Universes with Varying Alpha. https://doi.org/10.1088/0264-9381%2F19%2F23%2F317

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