On the information content of the matter power spectrum
  We discuss an analytical approximation for the matter power spectrum
covariance matrix and its inverse on translinear scales, $k \sim 0.1h -
0.8h/\textrm{Mpc}$ at $z = 0$. We proceed to give an analytical expression for
the Fisher information matrix of the nonlinear density field spectrum, and
derive implications for its cosmological information content. We find that the
spectrum information is characterized by a pair of upper bounds, 'plateaux',
caused by the trispectrum, and a 'knee' in the presence of white noise. The
effective number of Fourier modes, normally growing as a power law, is bounded
from above by these plateaux, explaining naturally earlier findings from
$N$-body simulations. These plateaux limit best possible measurements of the
nonlinear power at the percent level in a $h^{-3}\textrm{Gpc}^3$ volume; the
extraction of model parameters from the spectrum is limited explicitly by their
degeneracy to the nonlinear amplitude. The value of the first, super-survey
(SS) plateau depends on the characteristic survey volume and the large scale
power; the second, intra-survey (IS) plateau is set by the small scale power.
While both have simple interpretations within the hierarchical \textit{Ansatz},
the SS plateau can be predicted and generalized to still smaller scales within
Takada and Hu's spectrum response formalism. Finally, the noise knee is
naturally set by the density of tracers.
