Voyage through the Hidden Physics of the Cosmic Web
  The majority of the ordinary matter in the local Universe has been heated by
strong structure formation shocks and resides in a largely unexplored hot,
diffuse, X-ray emitting plasma that permeates the halos of galaxies, galaxy
groups and clusters, and the cosmic web. We propose a next-generation "Cosmic
Web Explorer" that will permit a complete and exhaustive understanding of these
unseen baryons. This will be the first mission capable to reach the accretion
shocks located several times farther than the virial radii of galaxy clusters,
and reveal the out-of-equilibrium parts of the intra-cluster medium which are
live witnesses to the physics of cosmic accretion. It will also enable a view
of the thermodynamics, kinematics, and chemical composition of the
circumgalactic medium in galaxies with masses similar to the Milky Way, at the
same level of detail that $Athena$ will unravel for the virialized regions of
massive galaxy clusters, delivering a transformative understanding of the
evolution of those galaxies in which most of the stars and metals in the
Universe were formed. Finally, the proposed X-ray satellite will connect the
dots of the large-scale structure by mapping, at high spectral resolution, as
much as 100% of the diffuse gas hotter than $10^6$ K that fills the filaments
of the cosmic web at low redshifts, down to an over-density of 1, both in
emission and in absorption against the ubiquitous cosmic X-ray background,
surveying at least 1600 square degrees over 5 years in orbit. This requires a
large effective area (~10 m$^2$ at 1 keV) over a large field of view ($\sim1$
deg$^2$), a megapixel cryogenic microcalorimeter array providing integral field
spectroscopy with a resolving power $E/\Delta E$ = 2000 at 0.6 keV and a
spatial resolution of 5 arcsec in the soft X-ray band, and a low and stable
instrumental background ensuring high sensitivity to faint, extended emission.
