Gravitational-wave implications for structure formation: A second-order
  approach
  Gravitational waves are propagating undulations in the spacetime fabric,
which interact very weakly with their environment. In cosmology,
gravitational-wave distortions are produced by most of the inflationary
scenarios and their anticipated detection should open a new window to the early
universe. Motivated by the relative lack of studies on the potential
implications of gravitational radiation for the large-scale structure of the
universe, we consider its coupling to density perturbations during the
post-recombination era. We do so by assuming an Einstein-de Sitter background
cosmology and by employing a second-order perturbation study. At this
perturbative level and on superhorizon scales, we find that gravitational
radiation adds a distinct and faster growing mode to the standard linear
solution for the density contrast. Given the expected weakness of cosmological
gravitational waves, however, the effect of the new mode is currently
subdominant and it could start becoming noticeable only in the far future.
Nevertheless, this still raises the intriguing possibility that the late-time
evolution of large-scale density perturbations may be dictated by the
long-range (the Weyl), rather than the local (the Ricci) component of the
gravitational field.
