The observed large scale structure of the Universe is thought to be due to the gravitational growth of density fluctuations in the post-inflation era. In this model, the evolving cosmic web is governed by non-linear gravitational growth of the initially weak density fluctuations in the dark energy dominated cosmology. The web is traced by a tiny fraction of luminous baryonic matter. Cosmological shock waves are an essential and often the only way to power the luminous matter by converting a fraction of gravitational power to thermal and non-thermal emissions of baryonic/leptonic matter.
At high redshifts (z > 1100) the pre-galactic medium was hot, relatively dense, ionised, with a substantial pressure of radiation. The cosmic microwave background (CMB) observations constrain the amplitudes of density inhomogeneities to be very small at the last scattering redshift z ~ 1000. Strong non-linear shocks are therefore unlikely at that stage. The universe expands, the matter cools, and eventually recombines, being mostly in neutral phase during the "dark ages" of the universe. At some redshift, 6 < z < 14, hydrogen in the universe is reionised, likely due to UV radiation from the first luminous objects, leaving the intergalactic medium (IGM) highly reionised (see e.g. Fan et al. 2006 for a recent review). The reionisation indicates the formation of the first luminous objects at the end of the "dark ages", either star-forming galaxies or Active Galactic Nuclei (AGN). The compact luminous objects with an enormous energy release would have launched strong (in some cases, relativistic) shock waves in the local vicinity of the energetic sources. At the same evolution stage, formation of strong density inhomogeneities in the cosmic structure occurs. Since then the non-linear dynamical flows in the vicinity of density inhomogeneities would have created large scale cosmic structure shocks of modest strength, thus heating the baryonic matter and simultaneously producing highly non-equilibrium energetic particle distributions, magnetic fields and electromagnetic emission.
Most of the diffuse X-ray emitting matter was likely heated by
cosmological shocks of different scales. Accretion and merging
processes produce large-scale gas shocks. Simulations of structure
formation in the Universe predict that in the present epoch about
40% of the normal baryonic matter is in the Warm-Hot Intergalactic
Medium (WHIM) at overdensities
~ 5-10 (e.g.
Cen & Ostriker
1999,
Davé et
al. 2001).
The WHIM is likely shock-heated
to temperatures of 105 - 107 K during the continuous
non-linear structure evolution and star-formation processes.
The statistics of cosmological shocks in the large-scale structure
of the Universe were simulated in the context of the
CDM-cosmology
using PM / Eulerian adiabatic hydrodynamic codes (e.g.
Miniati et
al. 2000,
Ryu et al. 2003,
Kang et al. 2007)
and more recently with a smoothed particle hydrodynamic code by
Pfrommer et
al. (2006).
They identified two main populations of
cosmological shocks: (i) high Mach number "external" shocks due to
accretion of cold gas on gravitationally attracting nodes, and
(ii) moderate Mach number (2
s
4)
"internal" shocks. The shocks are due to supersonic flows induced by
relaxing dark matter substructures in relatively hot, already
shocked, gas. The internal shocks were found by
Ryu et al. (2003)
to be most important in energy dissipation providing intercluster
medium (ICM) heating, and they were suggested by
Bykov et
al. (2000)
to be the likely sources of non-thermal emission in clusters of galaxies.
Hydrodynamical codes deal with N-body CDM and single-fluid gas dynamics. However, if a strong accretion shock is multi-fluid, providing reduced post-shock ion temperature and entropy, then the internal shocks could have systematically higher Mach numbers.
Space plasma shocks are expected to be collisionless.
Cosmological shocks, being the main gas-heating agent, generate
turbulent magnetic fields and accelerate energetic particles via
collisionless multi-fluid plasma relaxation processes thus producing
non-thermal components. The presence of these non-thermal components
may affect the global dynamics of clusters of galaxies
Ostriker et
al. (2005)
and the 
v -
T, M - T,
LX - T scaling relations
Bykov (2005).
Detailed discussion of
the cosmological simulations of the scaling relations with account
of only thermal components can be found in
Borgani et
al. 2008
- Chapter 13, this volume.
In Sect. 2 we discuss the basic features of the standard collisional shocks. The main part of the review is devoted to physical properties of cosmological shocks with an accent on collisionless shocks and associated non-thermal components. In Sect. 5 we discuss the most important features of multi-fluid collisionless shocks in the cosmological context including the effects of reduced entropy production, energetic particle acceleration and magnetic field amplification in the shocks.