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Register a new userCosmological Parameter Biases from Doppler-Shifted Weak Lensing in Stage IV Experiments
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The advent of Stage IV weak lensing surveys will open up a new era in precision cosmology. These experiments will offer more than an order-of-magnitude leap in precision over existing surveys, and we must ensure that the accuracy of our theory matches this. Accordingly, it is necessary to explicitly evaluate the impact of the theoretical assumptions made in current analyses on upcoming surveys. One effect typically neglected in present analyses is the Doppler-shift of the measured source comoving distances. Using Fisher matrices, we calculate the biases on the cosmological parameter values inferred from a Euclid-like survey, if the correction for this Doppler-shift is omitted. We find that this Doppler-shift can be safely neglected for Stage IV surveys. The code used in this investigation is made publicly available.
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We study the significance of non-Gaussianity in the likelihood of weak lensing shear two-point correlation functions, detecting significantly non-zero skewness and kurtosis in one-dimensional marginal distributions of shear two-point correlation functions in simulated weak lensing data. We examine the implications in the context of future surveys, in particular LSST, with derivations of how the non-Gaussianity scales with survey area. We show that there is no significant bias in one-dimensional posteriors of $Omega_{rm m}$ and $sigma_{rm 8}$ due to the non-Gaussian likelihood distributions of shear correlations functions using the mock data ($100$ deg$^{2}$). We also present a systematic approach to constructing approximate multivariate likelihoods with one-dimensional parametric functions by assuming independence or more flexible non-parametric multivariate methods after decorrelating the data points using principal component analysis (PCA). While the use of PCA does not modify the non-Gaussianity of the multivariate likelihood, we find empirically that the one-dimensional marginal sampling distributions of the PCA components exhibit less skewness and kurtosis than the original shear correlation functions.Modeling the likelihood with marginal parametric functions based on the assumption of independence between PCA components thus gives a lower limit for the biases. We further demonstrate that the difference in cosmological parameter constraints between the multivariate Gaussian likelihood model and more complex non-Gaussian likelihood models would be even smaller for an LSST-like survey. In addition, the PCA approach automatically serves as a data compression method, enabling the retention of the majority of the cosmological information while reducing the dimensionality of the data vector by a factor of $sim$5.
We present cosmological parameter constraints from a tomographic weak gravitational lensing analysis of ~450deg$^2$ of imaging data from the Kilo Degree Survey (KiDS). For a flat $Lambda$CDM cosmology with a prior on $H_0$ that encompasses the most recent direct measurements, we find $S_8equivsigma_8sqrt{Omega_{rm m}/0.3}=0.745pm0.039$. This result is in good agreement with other low redshift probes of large scale structure, including recent cosmic shear results, along with pre-Planck cosmic microwave background constraints. A $2.3$-$sigma$ tension in $S_8$ and `substantial discordance in the full parameter space is found with respect to the Planck 2015 results. We use shear measurements for nearly 15 million galaxies, determined with a new improved `self-calibrating version of $lens$fit validated using an extensive suite of image simulations. Four-band $ugri$ photometric redshifts are calibrated directly with deep spectroscopic surveys. The redshift calibration is confirmed using two independent techniques based on angular cross-correlations and the properties of the photometric redshift probability distributions. Our covariance matrix is determined using an analytical approach, verified numerically with large mock galaxy catalogues. We account for uncertainties in the modelling of intrinsic galaxy alignments and the impact of baryon feedback on the shape of the non-linear matter power spectrum, in addition to the small residual uncertainties in the shear and redshift calibration. The cosmology analysis was performed blind. Our high-level data products, including shear correlation functions, covariance matrices, redshift distributions, and Monte Carlo Markov Chains are available at http://kids.strw.leidenuniv.nl.
In this manuscript of the habilitation `a diriger des recherches (HDR), the author presents some of his work over the last ten years. The main topic of this thesis is cosmic shear, the distortion of images of distant galaxies due to weak gravitational lensing by the large-scale structure in the Universe. Cosmic shear has become a powerful probe into the nature of dark matter and the origin of the current accelerated expansion of the Universe. Over the last years, cosmic shear has evolved into a reliable and robust cosmological probe, providing measurements of the expansion history of the Universe and the growth of its structure. I review the principles of weak gravitational lensing and show how cosmic shear is interpreted in a cosmological context. Then I give an overview of weak-lensing measurements, and present observational results from the Canada-France Hawaii Lensing Survey (CFHTLenS), as well as the implications for cosmology. I conclude with an outlook on the various future surveys and missions, for which cosmic shear is one of the main science drivers, and discuss promising new weak cosmological lensing techniques for future observations.
Residual errors in shear measurements, after corrections for instrument systematics and atmospheric effects, can impact cosmological parameters derived from weak lensing observations. Here we combine convergence maps from our suite of ray-tracing simulations with random realizations of spurious shear. This allows us to quantify the errors and biases of the triplet $(Omega_m,w,sigma_8)$ derived from the power spectrum (PS), as well as from three different sets of non-Gaussian statistics of the lensing convergence field: Minkowski functionals (MF), low--order moments (LM), and peak counts (PK). Our main results are: (i) We find an order of magnitude smaller biases from the PS than in previous work. (ii) The PS and LM yield biases much smaller than the morphological statistics (MF, PK). (iii) For strictly Gaussian spurious shear with integrated amplitude as low as its current estimate of $sigma^2_{sys}approx 10^{-7}$, biases from the PS and LM would be unimportant even for a survey with the statistical power of LSST. However, we find that for surveys larger than $approx 100$ deg$^2$, non-Gaussianity in the noise (not included in our analysis) will likely be important and must be quantified to assess the biases. (iv) The morphological statistics (MF,PK) introduce important biases even for Gaussian noise, which must be corrected in large surveys. The biases are in different directions in $(Omega_m,w,sigma_8)$ parameter space, allowing self-calibration by combining multiple statistics. Our results warrant follow-up studies with more extensive lensing simulations and more accurate spurious shear estimates.
Sunyaev-Zeldovich (SZ) surveys are promising probes of cosmology - in particular for Dark Energy (DE) -, given their ability to find distant clusters and provide estimates for their mass. However, current SZ catalogs contain tens to hundreds of objects and maximum likelihood estimators may present biases for such sample sizes. In this work we use the Monte Carlo approach to determine the presence of bias on cosmological parameter estimators from cluster abundance as a function of the area and depth of the survey, and the number of cosmological parameters fitted. Assuming perfect knowledge of mass and redshift some estimators have non-negligible biases. For example, the bias of $sigma_8$ corresponds to about $40%$ of its statistical error bar when fitted together with $Omega_c$ and $w_0$. Including a SZ mass-observable relation decreases the relevance of the bias, for the typical sizes of current surveys. The biases become negligible when combining the SZ data with other cosmological probes. However, we show that the biases from SZ estimators do not go away with increasing sample sizes and they may become the dominant source of error for an all sky survey at the South Pole Telescope (SPT) sensitivity. The results of this work validate the use of the current maximum likelihood methods for present SZ surveys, but highlight the need for further studies for upcoming experiments. [abridged]
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