On the Self-Consistence of Electrodynamics in the Early Universe

Details On the Self-Consistence of Electrodynamics in the Early Universe On the Self-Consistence of Electrodynamics in the Early Universe

Dec 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002nmgm.meet.1947d&link_type=abstract

"THE NINTH MARCEL GROSSMANN MEETING On Recent Developments in Theoretical and Experimental General Relativity, Gravitation and R

Physics

Scientific paper

Most of the directly measured information of the universe we live come to us in the form of photons. Therefore, there exists a natural bound in the history of spacetime which can be traced back from experimentation; namely, the equilibrium time between matter and radiation. Indirect processes lead us to be confident in the homogeneous and isotropic standard cosmological model of FRW up to scales between the nucleosynthesis and the baryogenesis. Much more speculative are the models which dare to assert what happened at earlier times, since the classical laws of physics dealt with is not likely to hold for large energies. From the weak fields limit of the Euler-Heisenberg Lagrangian5, which describes QED as an effective theory for the electromagnetic field Fμν, we have the Schwinger expression6 L(F,G) = - (1)/(2)F + μ <=ft( {(1)/(4)F2 + (7)/(4)G2 } ; ) where F = Fμν Fμν = 2(E2 - H2) and G = (1)/(2)η {μ ν α β } F{μ ν } F{α β } = - 4ěc E \cdot ěc H. The constant μ = (2)/({45)} α 2 <=ft( {(hbar )/({me c)}} ; )3 (1)/({me c2 )} ≈ 1.67 \cdot 10{ - 31} cm3 /erg accounts for the parameters of the virtual particles (electrons and positrons in this case) being produced. When the gravitational back-reaction of this effect is considered it straightforwardly follows that the resulting spacetime evolves according with a globally regular law of the form A2 = Ho √ {(2)/(3) (κ c2 t2 + 3μ )}, where Ho is the value of the magnetic field when A(t) = 1 and κ = 8πG/c2 is the Einstein gravitational constant. In this way the cosmic singularity is prevented from quantum effects in the level of the matter fields, rather than in the gravitational field itself (for which much higher energies are required).

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