Cosmological perturbation theory in 1+1 dimensions
  Many recent studies have highlighted certain failures of the standard
Eulerian-space cosmological perturbation theory (SPT). Its problems include (1)
not capturing large-scale bulk flows [leading to an O(1) error in the 1-loop
SPT prediction for the baryon acoustic peak in the correlation function], (2)
assuming that the Universe behaves as a pressureless, inviscid fluid, and (3)
treating fluctuations on scales that are non-perturbative as if they were.
Recent studies have highlighted the successes of perturbation theory in
Lagrangian space or theories that solve equations for the effective dynamics of
smoothed fields. Both approaches mitigate some or all of the aforementioned
issues with SPT. We discuss these physical developments by specializing to the
simplified 1D case of gravitationally interacting sheets, which allows us to
substantially reduces the analytic overhead and still (as we show) maintain
many of the same behaviors as in 3D. In 1D, linear-order Lagrangian
perturbation theory ("the Zeldovich approximation") is exact up to shell
crossing, and we prove that n^{th}-order Eulerian perturbation theory converges
to the Zeldovich approximation as n goes to infinity. In no 1D cosmology that
we consider (including a CDM-like case and power-law models) do these theories
describe accurately the matter power spectrum on any mildly nonlinear scale. We
find that theories based on effective equations are much more successful at
describing the dynamics. Finally, we discuss many topics that have recently
appeared in the perturbation theory literature such as beat coupling, the shift
and smearing of the baryon acoustic oscillation feature, and the advantages of
Fourier versus configuration space. Our simplified 1D case serves as an
intuitive review of these perturbation theory results.
