Mass in cosmological perspective

Abstract

We consider the total nonlocal energy associated with a particle at rest in the Hubble flow, i.e., the relational energy between this particle and all connected particles within the causal horizon. The particle, even while at rest, partakes in relative recessional and peculiar motion of connected particles in three dimensions. A geometrical argument due to Berkeley suggests that the nonlocal mass of recessional energy associated with the particle is 3 times its Newtonian mass. It follows that nonlocal recessional and peculiar energy of the Universe are equal, and match Misner-Sharp energy within the apparent horizon. Contributions of recessional and peculiar nonlocal energy are thus shown to generate a 6 times higher level of matter energy than expected from the Newtonian mass. Accordingly, the nonlocal energy density of baryons is expected to be 6 times the standard local energy density of baryons, i.e., ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{b},\mathrm{eff}}=6{\mathrm{\ensuremath{\Omega}}}_{\mathrm{b}}$. At ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{b}}\ensuremath{\sim}0.0484\ifmmode\pm\else\textpm\fi{}0.0017$ [P. A. R. Ade et al. (Planck Collaboration), Astron. Astrophys. 594, A13 (2016) ] this predicts a nonlocal baryon energy density ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{b},\mathrm{eff}}\ensuremath{\sim}\phantom{\rule{0ex}{0ex}}0.290\ifmmode\pm\else\textpm\fi{}0.010$, in agreement with observed matter density ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{m}}\ensuremath{\sim}0.308\ifmmode\pm\else\textpm\fi{}0.012$. The effect of nonlocal mass on solar system and galactic scales is considered.