Energy dependent growth of the nucleon and hydrodynamic initial conditions

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Due to gluon saturation, the growth of the inelastic nucleon-nucleon cross section with increasing collision energy $\sqrt{s}$ results in a broadening of the nucleon's density distribution in position space. This leads to a natural smoothing of the initial energy density distribution in the transverse plane of the matter created near midrapidity in heavy-ion collisions. We study this effect for fluctuating initial conditions generated with the Monte Carlo Kharzeev-Levin-Nardi model for $\mathrm{Au}+\mathrm{Au}$ collisions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). We argue that at the LHC, viscous hydrodynamics is applicable at earlier times than at the RHIC, not only because of the higher temperature but also since the length scale over which the initial pressure fluctuates increases with collision energy.