de Broglie-Proca and Bopp-Podolsky massive photon gases in cosmology

Abstract

We investigate the influence of massive photons on the evolution of the expanding universe. Two particular models for generalized electrodynamics are considered, namely de Broglie-Proca and Bopp-Podolsky electrodynamics. We obtain the equation of state (EOS) P = P (ε) for each case using dispersion relations derived from both theories. The EOS are inputted into the Friedmann equations of a homogeneous and isotropic space-time to determine the cosmic scale factor a(t). It is shown that the photon non-null mass does not significantly alter the result a ∝ t 1/2 valid for a massless photon gas; this is true either in de Broglie-Proca's case (where the photon mass m is extremely small) or in Bopp-Podolsky theory (for which m is extremely large).

Nonlinear Schrödinger equation in the Bopp–Podolsky electrodynamics: Solutions in the electrostatic case

“…Thus the Bopp-Podolsky parameter a > 0, which has dimension of the inverse of mass, can be interpreted as a cut-off distance or can be linked to an effective radius for the electron. For more physical details we refer the reader to the recent papers [7,10,17,18,20,21] and to references therein.…”

Ground state solutions of the non-autonomous Schrödinger–Bopp–Podolsky system

“…Thus, the Bopp-Podolsky parameter a > 0, which has dimension of the inverse of mass, can be interpreted as a cut-off distance or can be linked to an effective radius for the electron. For more physical details we refer the reader to the recent papers [1,2,9,10,16,17] and to references therein.…”

Second gradient electrodynamics: a non-singular relativistic field theory

“…In the present work, the Lagrangian density of second gradient electrodynamics is given in the covariant form by writing it in the relativistic tensor notation. From this form, applications to general relativity using second gradient electrodynamics in curved spacetime can be constructed as it is done in the case of Bopp-Podolsky electrodynamics in curved spacetime (see [19,20]) or in Bopp-Podolsky cosmology [21]. A relativistic calculation of the self-force is given.…”