  We develop a theoretical framework to describe the cosmological observables
on the past light cone such as the luminosity distance, weak lensing, galaxy
clustering, and the cosmic microwave background anisotropies. We consider that
all the cosmological observables include not only the background quantity, but
also the perturbation quantity, and they are subject to cosmic variance, which
sets the fundamental limits on the cosmological information that can be derived
from such observables, even in an idealized survey with an infinite number of
observations. To quantify the maximum cosmological information content, we
apply the Fisher information matrix formalism and spherical harmonic analysis
to cosmological observations, in which the angular and the radial positions of
the observables on the light cone carry different information. We discuss the
maximum cosmological information that can be derived from five different
observables: (1) type Ia supernovae, (2) cosmic microwave background
anisotropies, (3) weak gravitational lensing, (4) local baryon density, and (5)
galaxy clustering. We compare our results with the cosmic variance obtained in
the standard approaches, which treat the light cone volume as a cubic box of
simultaneity. We discuss implications of our formalism and ways to overcome the
fundamental limit.
