How much cosmological information can be measured?
  It has become common to call this the "era of precision cosmology," and hence
one rarely hears about the finiteness of the amount of information that is
available for constraining cosmological parameters. Under the assumption that
the perturbations are purely Gaussian, the amount of extractable information
(in terms of total signal-to-noise ratio for power spectrum measurements) is
the same (up to a small numerical factor) as an accounting of the number of
observable modes. For studies of the microwave sky, we are probably within a
factor of a few of the amount of accessible information. To dramatically reduce
the uncertainties on parameters will require three-dimensional probes, such as
ambitious future redshifted 21-cm surveys. However, even there the available
information is still finite, with the total effective signal-to-noise ratio on
parameters probably not exceeding $10^7$. The amount of observable information
will increase with time (but very slowly) into the extremely distant future.
