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 } } \sim 0.0484 \pm 0.0017 ( Planck 2015 results ) this predicts a nonlocal baryon energy density \Omega _ { \textrm { b,eff } } \sim 0.290 \pm 0.010 , in agreement with observed matter density \Omega _ { \textrm { m } } \sim 0.308 \pm 0.012 .
The effect of nonlocal mass on solar system and galactic scales is considered .