Constants and Variations: From Alpha to Omega
John D. Barrow

TL;DR
This paper reviews theories of varying fundamental constants, especially the fine structure constant, and discusses their cosmological implications, observational constraints, and the role of vacuum energy and curvature.
Contribution
It provides a comprehensive overview of varying-constant theories, analyzing their cosmological models and observational consistency, including recent quasar data and black hole thermodynamics.
Findings
Quasar data supports time variation of alpha since redshift 3.5
Vacuum energy and curvature influence the variation of constants
Black hole thermodynamics cannot distinguish variations of different constants
Abstract
We review some of the history and properties of theories for the variation of the gravitation and fine structure 'constants'. We highlight some general features of the cosmological models that exist in these theories with reference to recent quasar data that is consistent with time-variation in alpha since a redshift of 3.5. The behaviour of a simple class of varying-alpha cosmologies is outlined in the light of all the observational constraints. We discuss the key role played by non-zero vacuum energy and curvature in turning off the variation of constants in these theories and the issue of comparing extra-galactic and local observational data. We also show why black hole thermodynamics does not enable us to distinguish between time variations of different constants.
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