Energy production in varying α theories

¹ Grupo de Gravitación, Astrofísica y Cosmología, Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata, Paseo del Bosque S/N, cp 1900 La Plata, Argentina
e-mail: lkrai@fcaglp.fcaglp.unlp.edu.ar; vucetich@fcaglp.fcaglp.unlp.edu.ar
² Instituto de Astrofísica La Plata, Argentina
³ Grupo de Evolución estelar y pulsaciones, Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata, Paseo del Bosque S/N cp 1900 La Plata, Argentina
e-mail: mmiller@fcaglp.fcaglp.unlp.edu.ar
⁴ Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, cp 7600 Mar del Plata, Argentina
e-mail: sisterna@mdp.edu.ar

Received: 21 October 2010
Accepted: 23 February 2011

Abstract

Aims. On the basis of the theoretical model proposed by Bekenstein for α’s variation, we analyze the equations that describe the energy exchange between matter and both the electromagnetic and the scalar fields.

Methods. We determine how the energy flow of the material is modified by the presence of a scalar field. We estimate the total magnetic energy of matter from the “sum rules techniques”. We compare the results with data obtained from the thermal evolution of the Earth and other planets.

Results. We obtain stringent upper limits to the variations in α that are comparable with those obtained from atomic clock frequency variations.

Conclusions. Our constraints imply that the fundamental length scale of Bekenstein’s theory “ℓ_B” cannot be larger than Planck’s length “ℓ_P”.