Propagation of information by electromagnetic and gravitational waves in cosmology

Abstract

The propagation of arbitrary information by electromagnetic and gravitational waves in spatially homogeneous and isotropic cosmological models is examined. The test Maxwellian fields and the gravitational perturbations we study depend upon arbitrary functions in the spirit of Trautman's pioneering analysis. We use the covariant and gauge-invariant approach developed by Ellis and Bruni to study cosmological perturbations under this assumption.

Shear-free gravitational waves in an anisotropic universe

“…Finally we see from (2.23) that the null hypersurfaces φ = constant in the anisotropic background have null geodesic generators with shear provided σ (2) = σ (3) . It is informative to carry out an analysis in parallel with that of section IV in this case.…”

“…This idea of introducing arbitrary functions into solutions of Einsteins equations describing gravitational waves goes back to work by Trautman [7]. Its use in the context of gauge-invariant perturbations of cosmological models was initiated by Hogan and Ellis [3] and further developed by Hogan and O'Shea [1]. We note that all of the quantities in (4.1) are orthogonal to u a and B ab , C ab and Π ab are trace-free with respect to the background metric g ab (i.e.…”

“…For the remainder of this section we seek to construct perturbations of the anisotropic background cosmological model which describe shear-free gravitational waves having the null hypersurfaces φ(x a ) = constant as the histories of their wave fronts in the background space-time. For the function φ(x a ) in (4.32) we shall take φ(x, t) given by (2.20) and in order to have these null hypersurfaces shear-free we see from (2.23) that we must have σ (2) = σ (3) . This is a relationship between the (non-vanishing) principal shears of the background matter distribution.…”

“…is now a gauge-invariant variable which vanishes in the background spacetime in which σ (2) = σ (3) . When σ ab is the perturbed shear m a is given its background value which, for our case, is given implicitly in (2.22 We shall consider pure pure gravity wave perturbations of the anisotropic background.…”

“…We note from (2.23) that the null hypersurfaces φ = constant have null geodesic generators with shear provided σ (2) = σ (3) . We briefly describe in this appendix the perturbations analogous to those of Section IV in this case.…”