Eletrodinâmica de Podolsky aplicada à cosmologia

Abstract

The same procedure established by the classical field theory which leads us to Maxwell's equations also leads to Podolsky's electrodynamics provided that the Lagrangian contains derivatives of the field strength. With Podolsky's field equations in hand, which has a coupling constant a associated to the photon mass, it's possible to derive an equation of state for Podolsky's radiation. The equation of state is of the type P=w(a,T)ε, where P is the pressure of the photon gas; ε is its energy density and w is the barotropic parameter depending on the temperature T and the photon mass. If we use the equation of state in the fluid equation and afterwards in Friedmann's equation, it's possible to solve the cosmic dynamics for a universe filled with Podolsky radiation. We show that the cosmic dynamics is not affected in a significant way by the massive photons, once 0,282< wPodolsky<wMaxwell=1/3 for any value of T, or equivalently of the cosmic time t. Podolsky correction to the Stefan-Boltzmann law is obtained for every T; it potentially describes the whole cosmic history. This correction is significant in the interval 0≲ξ≲8 for the dimensionless parameter ξ=βm. The maximum influence of the photon mass takes place at ξref=2,899. Out the above interval for ξ, Podolsky cosmic dynamics tends to the Maxwell's one: the scale factor behaves as √t in the limits corresponding to the primeval universe (ξ≪1) and present-day universe (ξ≫1), when wPodolsky →wMaxwell.