## Optimal weak lensing tomography for CFHTLenS

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##### Date

2012-11-28##### Author

Grocutt, Emma Liana

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Weak gravitational lensing is a powerful astronomical tool for constraining
cosmological parameters that is entering its prime. Lensing occurs because
gravitational fields deflect light rays and measuring this deflection through a
statistic known as cosmic shear allows us to directly measure the properties of
dark matter and dark energy on large scales. In principle, gravitational lensing
is a clean probe of the cosmology of the Universe, as it depends on gravity alone
and not on incomplete astrophysical models or approximations. In practice,
however, there are several factors that limit the accuracy and precision of lensing
measurements. These include accurate measurement of galaxy shapes, correctly
accounting for distortions to galaxy images due to the point spread function of
the telescope, the presence of intrinsic alignments (IAs) of galaxy shapes due
to physical processes, and inaccuracies in commonly-used galaxy photometric
redshift information. These effects may all introduce systematic errors in lensing
measurements which must be carefully accounted for to ensure that cosmological
constraints from lensing are unbiased and as precise as possible.
The Canada-France-Hawaii-Telescope Lensing Survey (CFHTLenS) is the
largest weak lensing survey completed to date, covering 154 square degrees of the
sky in 5 optical bands, with photometric redshift information for every survey
galaxy. With lensing measurements from more galaxies than ever before, the
statistical uncertainties on parameter estimates will be the lowest ever achieved
from weak lensing. If left unaccounted for, sources of systematic error would
dominate over the statistical uncertainty, potentially biasing parameter estimates
catastrophically. A technique known as tomography in which galaxies are sorted
into bins based on their redshift can help constrain cosmological parameters
more precisely. This is because utilising the redshifts of survey galaxies retains
cosmological information that would otherwise be lost, such as the behaviour of dark energy and the growth of structure over time. Tomography, however,
increases the demand for systematics-free galaxy catalogues as the technique is
strongly sensitive to the IA signal and photometric redshift errors. Therefore,
future lensing analyses will require a more sophisticated treatment of these
effects to extract maximal information from the lensing signal. A thorough
understanding of the error on lensing measurements is necessary in order to
produce meaningful cosmological constraints. One of the key features of cosmic
shear is that it is highly correlated over di erent angular scales, meaning that
error estimates must take into account the covariance of the data over different
angular scales, and in the case of tomography, between different redshift bins.
The behaviour and size of the (inverse) covariance matrix is one of the limiting
factors in such a cosmological likelihood analysis, so constructing an accurate,
unbiased estimate of the covariance matrix inverse is essential to cosmic shear
analysis.
This thesis presents work to optimise tomographic weak lensing analysis
and achieve the tightest parameter constraints possible for a CFHTLenS-like
survey. N-body simulations and Gaussian shear fields incorporating an IA model
(known as the `non-linear alignment' model) with a free parameter are used to
estimate fully tomographic covariance matrices of cosmic shear for CFHTLenS.
We simultaneously incorporate for the first time the error contribution expected
from the non-linear alignment model for IAs and realistic photometric redshift
uncertainties as measured from the CFHTLenS. We find that non-Gaussian
simulations that incorporate nonlinearity on small scales are needed to ensure
the covariance is not underestimated, and that the covariance matrix is shot-noise
dominated for almost all tomographic correlations. The number of realisations
of the simulations used to estimate the covariance places a hard limit on the
maximum number of tomographic bins that one can use in an analysis. Given
the available number of lines of sight generated from CFHTLenS-like simulations,
we find that up to ~ 15 tomographic bins may be utilised in a likelihood analysis.
The estimated tomographic covariance matrices are used in a least-squares
likelihood analysis in order to find the combination of both angular and
tomographic bins that gives the tightest constraints on some key cosmological
parameters. We find that the optimum binning is somewhat degenerate, with
around 6 tomographic and 8 angular bins being optimal, and limited by the available number of realisations of the simulations used to estimate the covariance.
We also investigate the bias on best- t parameter estimates that occurs if IAs
or photometric redshift errors are neglected. With our choice of IA model, the
effect of neglecting IAs on the best- t cosmological parameters is not significant
for a CFHTLenS-like survey, although this may not be true if the IA signal differs
substantially from the model, or for future wide-field surveys with much smaller
statistical uncertainties. Similarly, neglecting photometric redshift errors does
not result in significant bias, although we apply similar caveats.
Finally, we apply the results of this optimisation to the CFHTLenS cosmic
shear data, performing a preliminary analysis of the shear correlation function
to produce both 2D and optimal tomographic cosmological constraints. From
6-bin tomography, we constrain the matter density parameter
Ωm = 0:419+0:123-0:090,
the amplitude of the matter power spectrum σ8 = 0:623+0:101
-0:084 and the amplitude
parameter of the non-linear alignment model, A = -1:161+1:163
-0:597. We perform this
analysis to test the validity and limitations of the optimal binning on real data and
find that 6-bin tomography improves parameter constraints considerably, albeit
not as much as when performed on simulated data. This analysis represents
an important step in the development of techniques to optimise the recovery
of lensing information and hence cosmological constraints, while simultaneously
accounting for potential sources of bias in shear analysis.