Abstract
The polarizations of the tensor modes of the geometry evolving in cosmological backgrounds are treated as the components of a bispinor whose dynamics follows from an appropriate gauge-invariant action. This novel framework bears a close analogy with the (optical) Jones calculus and leads to a compact classification of the various interactions able to polarize the relic gravitons.
Highlights
The stochastic backgrounds of gravitational radiation may be formed by relic gravitons parametrically amplified in the early Universe, as suggested long ago by Grishchuk [1]
The evolution of the relic gravitons is affected by various anisotropic stresses whose transverse and traceless modes could induce a certain degree of polarization
The polarization of the graviton background induced by the anisotropic stresses typically involves a limited interval of frequencies reflecting the physical properties of the source
Summary
The stochastic backgrounds of gravitational radiation may be formed by relic gravitons parametrically amplified in the early Universe, as suggested long ago by Grishchuk [1]. The main purpose of this paper is to scrutinize and classify the mutual interactions of the tensor polarizations in cosmological backgrounds by expressing their gauge-invariant action in terms of appropriate bispinors whose components coincide with the polarized amplitudes. In this context, the parity-violating interactions mentioned in the previous paragraph as well as other possible contributions will be parametrized in terms of an effective action reducing to the Ford-Parker action in the unpolarized case [2].
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