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Gravitational Waves in Bianchi Type-I Universes I: The Classical Theory
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The propagation of classical gravitational waves in Bianchi Type-I universes is studied. We find that gravitational waves in Bianchi Type-I universes are not equivalent to two minimally coupled massless scalar fields as it is for the Robertson-Walker universe. Due to its tensorial nature, the gravitational wave is much more sensitive to the anisotropy of the spacetime than the scalar field is and it gains an effective mass term. Moreover, we find a coupling between the two polarization states of the gravitational wave which is also not present in the Robertson-Walker universe.
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Propagation of Gravitational Waves in Anisotropic Universe
In a toy anisotropic universe, gravitational waves acquire direction-dependent dispersion relations and anisotropy-dependent tidal acceleration, but the background equations contain a sign error that undermines the model.
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