Non-comoving Cosmology
  One of the fundamental assumptions of the standard $\Lambda$CDM cosmology is
that, on large scales, all the matter-energy components of the Universe share a
common rest frame. This seems natural for the visible sector, that has been in
thermal contact and tightly coupled in the primeval Universe. The dark sector,
on the other hand, does not have any non-gravitational interaction known to
date and therefore, there is no a priori reason to impose that it is comoving
with ordinary matter. In this work we explore the consequences of relaxing this
assumption and study the cosmology of non-comoving fluids. We show that it is
possible to construct a homogeneous and isotropic cosmology with a collection
of fluids moving with non-relativistic velocities. Our model extends
$\Lambda$CDM with the addition of a single free parameter $\beta_0$, the
initial velocity of the visible sector with respect to the frame that observes
a homogeneous and isotropic universe. This modification gives rise to a rich
phenomenology, while being consistent with current observations for
$\beta_0<1.6\times 10^{-3} \text{(95% CL)}$. This work establishes the general
framework to describe a non-comoving cosmology and extracts its first
observational consequences for large-scale structure. Among the observable
effects, we find sizeable modifications in the density-velocity and
density-lensing potential cross-correlation spectra. These corrections give
rise to deviations from statistical isotropy with a dipolar structure. The
relative motion between the different fluids also couples the vector and scalar
modes, the latter acting as sources for metric vector modes and vorticity for
all the species.
