The phase-space structure of nearby dark matter as constrained by the
  SDSS
  Previous studies using numerical simulations have demonstrated that the shape
of the cosmic web can be described by studying the Lagrangian displacement
field. We extend these analyses, showing that it is now possible to perform a
Lagrangian description of cosmic structure in the nearby Universe based on
large-scale structure observations. Building upon recent Bayesian large-scale
inference of initial conditions, we present a cosmographic analysis of the dark
matter distribution and its evolution, referred to as the dark matter
phase-space sheet, in the nearby universe as probed by the Sloan Digital Sky
Survey main galaxy sample. We consider its stretchings and foldings using a
tetrahedral tessellation of the Lagrangian lattice. The method provides
extremely accurate estimates of nearby density and velocity fields, even in
regions of low galaxy density. It also measures the number of matter streams,
and the deformation and parity reversals of fluid elements, which were
previously thought inaccessible using observations. We illustrate the approach
by showing the phase-space structure of known objects of the nearby Universe
such as the Sloan Great Wall, the Coma cluster and the Bo\"otes void. We
dissect cosmic structures into four distinct components (voids, sheets,
filaments, and clusters), using the Lagrangian classifiers DIVA, ORIGAMI, and a
new scheme which we introduce and call LICH. Because these classifiers use
information other than the sheer local density, identified structures
explicitly carry physical information about their formation history. Accessing
the phase-space structure of dark matter in galaxy surveys opens the way for
new confrontations of observational data and theoretical models. We have made
our data products publicly available.
