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Constructing observables in cosmology : towards new probes of the dark sector

Abstract : The nature of dark energy and dark matter is still a mystery. Future surveys will observe the property and distribution of billions of galaxies but what is the best way to constrain the physics of these unknown components from this data deluge? The goal of this thesis is to search for new probes of the dark sector of the universe within the linear and non-linear regime of structure formation. The physics of the dark sector leaves specific imprints in the distribution of Large-Scale Structures (LSS) at a given time (i.e. in real space). However their apparent distribution as seen by a given observer (i.e. in redshift space) slightly differs from the real one. This is because messengers (light) are perturbed in their path from the sources to the observer. What is the relation between real space and redshift space? How to extract cosmological information from these subtle Redshift-Space Distortions (RSD)? The main part of my work was to produce simulated observables taking into account all relativistic effects at first order in the weak field approximation. Weak Lensing (WL) modifies the apparent angular position of an object, as well as its properties (shape, luminosity). Redshift perturbations change the apparent radial distance of an object. To address these questions, we perform a large and highly resolved N-body simulation ideal to investigate halos from Milky-Way size to galaxy cluster size. We then perform backward ray-tracing directly integrating the geodesic equations using as its only assumption the weak field approximation. We develop a geodesic-finder to guaranty that light-rays connect all the sources to the observer. The lensing distortion matrix is then computed by launching a beam of light-rays while the redshift is directly computed from its definition in general relativity. Thanks to this unique ray-tracing library we construct halo catalogs including relativistic effects. Based on these catalogs we are able to recover standard results about RSD, WL and Integrated Sachs Wolfe (ISW) effect with high accuracy. We also investigate the subtle coupling between RSD and lensing: Doppler lensing. Finally we explore in detail relativistic RSD. Thanks to the large statistics of our simulations we are able for the first time to compute the dipole of the halo cross-correlation from 5 to 150 h − 1 Mpc including all relativistic terms. At large-scale we recover the results from linear calculation: the dipole is dominated by Doppler effect in the presence of a finite distant observer. However at smaller non-linear scales the dipole is dominated by the gravitational redshift perturbation. The dipole can therefore be a new probe of the potential and therefore of the dark sector. This work opens a wide range of applications: the cross-correlation between each observable (related to relativistic effects) for different sources at different location can possibly be new powerful probe of the dark sector.
Keywords : Dark sector
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Michel-Andrès Breton. Constructing observables in cosmology : towards new probes of the dark sector. Astrophysics [astro-ph]. Université Sorbonne Paris Cité, 2018. English. ⟨NNT : 2018USPCC023⟩. ⟨tel-02114661⟩

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