Bias-Limited Extraction of Cosmological Parameters
  It is known that modeling uncertainties and astrophysical foregrounds can
potentially introduce appreciable bias in the deduced values of cosmological
parameters. While it is commonly assumed that these uncertainties will be
accounted for to a sufficient level of precision, the level of bias has not
been properly quantified in most cases of interest. We show that the
requirement that the bias in derived values of cosmological parameters does not
surpass nominal statistical error, translates into a maximal level of overall
error $O(N^{-1/2})$ on $|\Delta P(k)|/P(k)$ and $|\Delta C_{l}|/C_{l}$, where
$P(k)$, $C_{l}$, and $N$ are the matter power spectrum, angular power spectrum,
and number of (independent Fourier) modes at a given scale $l$ or $k$ probed by
the cosmological survey, respectively. This required level has important
consequences on the precision with which cosmological parameters are hoped to
be determined by future surveys: In virtually all ongoing and near future
surveys $N$ typically falls in the range $10^{6}-10^{9}$, implying that the
required overall theoretical modeling and numerical precision is already very
high. Future redshifted-21-cm observations, projected to sample $\sim 10^{14}$
modes, will require knowledge of the matter power spectrum to a fantastic
$10^{-7}$ precision level. We conclude that realizing the expected potential of
future cosmological surveys, which aim at detecting $10^{6}-10^{14}$ modes,
sets the formidable challenge of reducing the overall level of uncertainty to
$10^{-3}-10^{-7}$.
