TY - JOUR

T1 - Fisher matrix decomposition for dark energy prediction

AU - Kitching, T. D.

AU - Amara, A.

AU - Kitching, Thomas

PY - 2009/10/1

Y1 - 2009/10/1

N2 - 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 top-hat basis set requires an even higher order. We
show that the common approach used for finding the marginalized
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.

AB - 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 top-hat basis set requires an even higher order. We
show that the common approach used for finding the marginalized
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.

UR - http://www.scopus.com/inward/record.url?scp=70349194887&partnerID=8YFLogxK

U2 - 10.1111/j.1365-2966.2009.15263.x

DO - 10.1111/j.1365-2966.2009.15263.x

M3 - Article

VL - 398

SP - 2134

EP - 2142

JO - Monthly Notices of the Royal Astronomical Society

JF - Monthly Notices of the Royal Astronomical Society

SN - 0035-8711

ER -