Personal web page : http://jstarck.cosmostat.org
Laboratory link : http://www.cosmostat.org
The Euclid satellite, to be launched in 2023, will observe the sky in the optical and infrared, and will be able to map large scale structures and weak lensing distortions out to high redshifts. Weak gravitational lensing is thought to be one of the most promising tools of cosmology to constrain models. Weak lensing probes the evolution of dark-matter structures and can help distinguish between dark energy and models of modified gravity. Cosmological parameters are traditionally estimated using a Gaussian likelihood based on theoretical predictions of second order statistic such as the power spectrum or the two point correlation functions. This requires to build a covariance matrices, and therefore need a lot of very heavy n-body simulations. This approach presents also several additional drawbacks: First, second order statistics captures all available information in the data only in the case of Gaussian Random Fields, while matter distribution is highly non-Gaussian showing many features such filaments, walls or clusters. Second, the covariance matrix is cosmology dependent and the noise it generally not Gaussian, both aspects being generally poorly taken into account. Finally, all systematic effects such as masks, intrinsic alignement, baryonic feedback are very difficult to take into account. For all these reasons, a new approach has recently emerged, called likelihood-free cosmological parameter inference which are based on a forward modelling. It has the great advantage to not need covariance matrices anymore, avoiding the storage of huge simulated data set (we typically need 10000 n-body realisations for each set of cosmological parameters). Furthermore, it opens us the door to use high order statistical information and it is relatively straightforward to include all systematics effect. It has however two serious drawbacks, the firsts one is the need of huge GPU ressources to process surveys such as Euclid and the second is that the solution relies on the accuracy of simulations, which could lead to infinite discussion in case the results are different from what is expected. Thanks to a recent breakthrough (Codis, 2021), we have now theoretical tools to predict, for a given set of cosmological parameters, the multi-scale density probability function (pdf) of convergence maps such as the one that will be observed with Euclid.
The goal of this PhD work is to develop an hybrid approach, consisting in a likelihood-free cosmological parameter inference which would be based on the high order statics theoretical prediction rather than n-body simulations. It would therefore have the advantage of both previously described approaches, as it will not need to store huge data set to compute a covariance matrix and it will not require huge CPU/GPU ressources as the forward modelling method. This intense frugality will make this approach highly competitive to constraint the cosmological model using high order statistics in future surveys.
To achieve this goal, the first step will be to build a map emulator, similar to what has been done for 2 point statistics (i.e. the flask method), but which respects accurately the high order predictions. Using this emulator, it will then be possible to use it as a bypass in a recently developed Likelihood Free Inference code. This will allow the use of high order statics such as the l1-norm of the wavelet transform of the convergence to constrain the cosmological parameters, which is an extremely powerful summary statistic (Ajani et al, 2021). The developed method will be used first on the CFIS survey and then on Euclid.
References
Barthelemy A., Codis S. and Bernardeau F., "Probability distribution function of the aperture mass field with large deviation theory", 2021, MNRAS, 503, 5204;
V. Ajani, J.-L. Starck and V. Pettorino, "Starlet l1-norm for weak lensing cosmology", Astronomy and Astrophysics, 645, L11, 2021.