Europhys. Lett.
Volume 61, Number 2, January 2003
Page(s) 174 - 180
Section General
Published online 01 January 2003
DOI: 10.1209/epl/i2003-00209-3
Europhys. Lett., 61 (2) , pp. 174-180 (2003)

On the cosmological variation of the fine-structure constant

A. F. Rañada

Departamento de Física Aplicada III, Universidad Complutense 28040 Madrid, Spain

(Received 18 April 2002; accepted in final form 31 October 2002)

A phenomenological and Newtonian model is proposed to explain the recent observed cosmological variation of the fine-structure constant as an effect of the quantum vacuum, assuming a flat universe with cosmological constant $\Lambda$ in the cases $(\Omega_M, \Omega_\Lambda)$ equal to (0.3, 0.7) and (1,0). Because of the fourth Heisenberg relation, the lifetime of the virtual pairs of the zero-point radiation must depend on the gravitational potential $\Phi$, so that the quantum vacuum changes its density and acquires a relative permittivity different from one. Since the matter was more concentrated in the past, the gravitational potential of all the universe was stronger and the optical density of the vacuum higher, the electron charge being then more renormalized and smaller than now. The model predicts that $\Delta \alpha/\alpha$ is proportional to $\{\Omega_M[a(t)^{-1}-1]-2\Omega _\Lambda [a(t)^2-1]\}$, a(t) being the scale factor. This agrees with the observations.

06.20.Jr - Determination of fundamental constants.
95.30.Sf - Relativity and gravitation.
98.80.Es - Observational cosmology (including Hubble constant, distance scale, cosmological constant, early Universe, etc).

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