Fisher Matrix Decomposition for Dark Energy Prediction
  Within the context of constraining an expansion of the dark energy equation
of state w(z) we show that the eigendecomposition of Fisher matrices is
sensitive to both the maximum order of the expansion and the basis set choice.
We investigate the Fisher matrix formalism in the case that a particular
function is expanded in some basis set. As an example we show results for an
all sky weak lensing tomographic experiment. We show that the set of
eigenfunctions is not unique and that the best constrained functions are only
reproduced accurately at very higher order N > 100, a tophat basis set requires
an even higher order. We show that the common approach used for finding the
marginalised eigenfunction errors is sensitive to the choice of non-w(z)
parameters and priors. The eigendecomposition of Fisher matrices is a
potentially useful tool that can be used to determine the predicted accuracy
with which an experiment could constrain w(z). It also allows for the
reconstruction of the redshift sensitivity of the experiment to changes in
w(z). However the technique is sensitive to both the order and the basis set
choice. Publicly available code is available as part of iCosmo at
http://www.icosmo.org .
