  We consider a novel mechanism to account for the observed distance-redshift
relation. This is done by presenting a toy model for the large-scale matter
distribution in a static Universe. Our model mainly concerns particles with
masses far below those in the Standard Model of Particle Physics. The model is
founded on three main assumptions: (1) a mass spectrum dN$_{\rm i}$/dm$_{\rm
i}$ $=$ $\beta$m$_{\rm i}^{-\alpha}$ (where $\alpha$ and $\beta$ are both
positive constants) for low-mass particles with m$_{\rm i}$ $\ll$ 10$^{-22}$ eV
$\ll$ M$_{\rm P}$, where M$_{\rm P}$ is the Planck mass; (2) a particle
mass-wavelength relation of the form $\lambda_{\rm i} =$ $\hbar$/$\delta_{\rm
i}$m$_{\rm i}$c, where $\delta_{\rm i} =$ $\eta$m$_{\rm i}^{\gamma}$ and $\eta$
and $\gamma$ are both constants; and (3) For such low-mass particles, locality
can only be defined on large spatial scales, comparable to or exceeding the
particle wavelengths.
  We use our model to derive the cosmological redshift characteristic of the
Standard Model of Cosmology, which becomes a gravitational redshift in our
model. We compare the results of our model to empirical data and show that, in
order to reproduce the sub-linear form of the observed distance-redshift
relation, our model requires $\alpha$ + $\gamma$ $<$ 0. We further place our
toy model in the context of the Friedmann Universe via a superposition of
Einstein Universes, each with its own scale factor a$_{\rm i}$. Given the
overwhelming evidence supporting an expanding Universe, we then address
possible modifications to our base model that would be required to account for
the available empirical constraints, including the addition of some initial
expansion. Finally, we consider potentially observable distinctions between the
cosmological redshift and our proposed mechanism to account for the observed
distance-redshift relation.
