The thermal and gravitational energy densities in the large-scale
  structure of the Universe
  As cosmic structures form, matter density fluctuations collapse
gravitationally and baryonic matter is shock-heated and thermalized. We
therefore expect a connection between the mean gravitational potential energy
density of collapsed halos, $\Omega_{W}^{\rm halo}$, and the mean thermal
energy density of baryons, $\Omega_{\rm th}$. These quantities can be obtained
using two fundamentally different estimates: we compute $\Omega_{W}^{\rm halo}$
using the theoretical framework of the halo model which is driven by dark
matter statistics, and measure $\Omega_{\rm th}$ using the Sunyaev-Zeldovich
(SZ) effect which probes the mean thermal pressure of baryons. First, we derive
that, at the present time, about 90% of $\Omega_{W}^{\rm halo}$ originates from
massive halos with $M>10^{13}\,M_\odot$. Then, using our measurements of the SZ
background, we find that $\Omega_{\rm th}$ accounts for about 80% of the
kinetic energy of the baryons available for pressure in halos at $z\lesssim
0.5$. This constrains the amount of non-thermal pressure, e.g., due to bulk and
turbulent gas motion sourced by mass accretion, to be about $\Omega_{\rm
non-th}\simeq 0.4\times 10^{-8}$ at $z=0$.
