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Isotropy theorem for cosmological vector fields · Around

2012

Isotropy theorem for cosmological vector fields

Cembranos, J. A. R., Hallabrin, C., Maroto, A. L. et al.

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We consider homogeneous abelian vector fields in an expanding universe.

We find a mechanical analogy in which the system behaves as a particle moving in three dimensions under the action of a central potential.
In the case of bounded and rapid evolution compared to the rate of expansion, we show by making use of the virial theorem that for arbitrary potential and polarization pattern, the average energy-momentum tensor is always diagonal and isotropic despite the intrinsic anisotropic evolution of the vector field.
For simple power-law potentials of the form V=\lambda (A^\mu A_\mu)^n, the average equation of state is found to be w=(n-1)/(n+1).

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2011
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