Mass in cosmological perspective
  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 3 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.,
$\Omega_{\textrm{b,eff}}=6\Omega_{\textrm{b}}$. At
$\Omega_{\textrm{b}}\sim0.0484\pm0.0017$ (Planck 2015 results) this predicts a
nonlocal baryon energy density $\Omega_{\textrm{b,eff}}\sim0.290\pm0.010$, in
agreement with observed matter density $\Omega_{\textrm{m}}\sim0.308\pm0.012$.
The effect of nonlocal mass on solar system and galactic scales is considered.
