Let $(M, g)$ denote a cosmological spacetime describing the evolution of a
universe which is isotropic and homogeneous on large scales, but highly
inhomogeneous on smaller scales. We consider two past lightcones, the first,
$\mathcal{C}^-_L(p, g)$, is associated with the physical observer $p\in\,M$ who
describes the actual physical spacetime geometry of $(M, g)$, whereas the
second, $\mathcal{C}^-_L(p, \hat{g})$, is associated with an idealized version
of the observer $p$ who, notwithstanding the presence of local inhomogeneities,
wish to model $(M, g)$ with a member $(M, \hat{g})$ of the family of
Friedmann-Lemaitre-Robertson-Walker spacetimes. In such a framework, we discuss
a number of mathematical results that allows a rigorous comparison between the
two lightcones $\mathcal{C}^-_L(p, g)$ and $\mathcal{C}^-_L(p, \hat{g})$. In
particular, we introduce a scale-dependent lightcone-comparison functional,
defined by a harmonic type energy, associated with a natural map between the
physical $\mathcal{C}^-_L(p, g)$ and the FLRW reference lightcone
$\mathcal{C}^-_L(p, \hat{g})$. This functional has a number of remarkable
properties, in particular it vanishes iff, at the given length-scale, the
corresponding lightcone surface sections (the celestial spheres) are isometric.
We discuss in detail its variational analysis and prove the existence of a
minimum that characterizes a natural scale-dependent distance functional
between the two lightcones. We also indicate how it is possible to extend our
results to the case when caustics develop on the physical past lightcone
$\mathcal{C}^-_L(p, g)$. Finally, we show how the distance functional is
related to spacetime scalar curvature in the causal past of the two lightcones,
and briefly illustrate a number of its possible applications.