Conformal Fermi Coordinates
  Fermi Normal Coordinates (FNC) are a useful frame for isolating the locally
observable, physical effects of a long-wavelength spacetime perturbation. Their
cosmological application, however, is hampered by the fact that they are only
valid on scales much smaller than the horizon. We introduce a generalization
that we call Conformal Fermi Coordinates (CFC). CFC preserve all the advantages
of FNC, but in addition are valid outside the horizon. They allow us to
calculate the coupling of long- and short-wavelength modes on all scales larger
than the sound horizon of the cosmological fluid, starting from the epoch of
inflation until today, by removing the complications of the second order
Einstein equations to a large extent, and eliminating all gauge ambiguities. As
an application, we present a calculation of the effect of long-wavelength
tensor modes on small scale density fluctuations. We recover previous results,
but clarify the physical content of the individual contributions in terms of
locally measurable effects and "projection" terms.
