Power spectra in the eikonal approximation with adiabatic and
  non-adiabatic modes
  We use the so-called eikonal approximation, recently introduced in the
context of cosmological perturbation theory, to compute power spectra for
multi-component fluids. We demonstrate that, at any given order in standard
perturbation theory, multipoint power spectra do not depend on the large-scale
adiabatic modes. Moreover, we employ perturbation theories to decipher how
nonadiabatic modes, such as a relative velocity between two different
components, damp the small-scale matter power spectrum, a mechanism recently
described in the literature. In particular, we do an explicit calculation at
1-loop order of this effect. While the 1-loop result eventually breaks down, we
show how the damping effect can be fully captured by the help of the eikonal
approximation. A relative velocity not only induces mode damping but also
creates large-scale anisotropic modulations of the matter power spectrum
amplitude. We illustrate this for the Local Group environment.
