Unveiling the Universe with gravitational lensing and cosmic voids

This is an amazing time for Cosmology. In the last 60 years astronomical observations and achievements of particle physics laid the foundation for the Big Bang model, letting Cosmology evolve from the myth to science. The Big Bang idea was originally proposed at the end of the ’20s with the discovery of the Universe expansion by Edwin Hubble. In the ’60s this hypothesis got consolidated with the observations of the Cosmic Microwave Background Radiation (CMB) and the measurement of light-element abundance. In the last 25 years a quantitative model was developed, the so called Standard Model of Cosmology or ΛCDM model. The ΛCDM model relies on two pillars of the XX century physics: Einstein’s theory of General Relativity, which describes gravity by means of curved spacetime, and the Standard Model of Particle Physics, the relativistic quantum field theory which describes the electromagnetic, weak, and strong interactions. The ΛCDM model, in its fundamental aspects, can be easily explained. About 13.8 billion years ago, when the density and temperature were incredibly high, the Universe started inflating. The first moments are not yet understood since we do not know the physical laws governing this high-energy regime, but after some picoseconds the Universe cooled down to a temperature about 10 15 K. From this point on, General Relativity, the Standard Model of Particle Physics, and Thermodynamics let us predict what happened: unstable particles disappeared and the Universe became a hot plasma made by protons, neutrons, electrons, photons, neutrinos, and hypothetical dark matter particles. Within the first three minutes, nuclear reactions led to the formation of light nuclei, then the Universe continued expanding and cooling for 300 thousands years, when it became cold enough so that electrons and protons became bound to form electrically neutral hydrogen atoms. After this process, matter became transparent to light, which started to free-stream across the Universe, becoming what now is known as the Cosmic Microwave Background. From this moment, gravity got the upper hand and dark matter played a crucial role in the formation of the large scale structure of the Universe. After some billion years, while the Universe expansion looked to be slowing down, a new character enters the scene, the Dark Energy, giving a new impetus to the Universe expansion. This is the history of the Universe as we know it, from its very beginning, through its evolution and until the present configuration of the cosmic web with galaxies, stars, and planets: in one of them we are wondering about how all this happened. The ΛCDM model gives a consistent explanation of all these observations: it well explains the hydrogen and helium abundances and predicts with great accuracy the CMB temperature fluctuations. The agreement between data and predictions is astonishing and confirms that we are capturing at least small sparks of the truth. Although its success, we are aware that the ΛCDM model is an incomplete theory, with several points left unsettled. In particular, visible matter gives a contribution of about 5% to the Universe energetic budget and we explain the remaining part with the two unknown entities already mentioned, Dark Matter and Dark Energy. The former behaves like an invisible slow (cold) matter which is not predicted by the Standard Model of Particles, hence the name Cold Dark Matter. The latter, usually indicated by the letter Λ, is even more mysterious as represents a fluid with negative pressure permeating the Universe: we have no solid ideas about its origin. In order to shed light on the dark side of the Universe, several experiments are being led in the world and more are coming. These experiments try to produce Dark Matter particles in accelerators or to detect them in underground detectors. We have not a convincing explanation of the Universe first moments. Although the inflation era, a very early period of extremely rapid expansion, is by now quite commonly accepted by the scientific community, we still need to characterize its mechanism in detail. Furthermore, as the astronomic datasets available grew up in quality and details, the cosmological community started to make high precision measurements using different kind of probes. Although the qualitative picture of the ΛCDM has been confirmed, there are still several tensions among different measurements of cosmological parameters. In particular, there is a tension on the exact value of the parameter which quantifies the current expansion rate of the Universe, the Hubble constant. In order to understand these problems, the cosmological community is working along many directions. New theoretical tools are being developed, in order to sharpen our comprehension of the Cosmos and make accurate predictions. New experiments are being carried out and designed. In the next decades, a wealth of new observations will be available via new CMB temperature and polarization probes, gravitational wave observatories, underground dark matter and neutrino detectors, and large scale galaxy surveys. These are among the most prominent tools that will be available to study our Universe with unprecedented accuracy, and possibly unveil the nature of its dark components and/or new physics. In order to extract as much information as possible, we need to develop also the correct data analysis tools, identifying the most interesting observables and understanding how to correctly model summary statistics. One of the forthcoming galaxy survey is Euclid, a mission of the European Space Agency (ESA). It will be one the widest redshift survey ever performed, covering an area of 15000 square degrees, corresponding to one third of the sky, up to a redshift z ∼ 2.5. Euclid will comprise two main instruments, one to measure light in the visible band and another one dedicated to both photometric and spectroscopic measurements in the near-infrared band. The main cosmological probes are weak gravitational lensing and galaxy clustering. The former, also called Cosmic Shear, is the gravitational deviation of photon paths due to the gravitational interaction with matter along the line of sight and is measured from galaxy shapes. The latter is produced by the galaxy trend not to be randomly distributed in space, but rather to cluster because of gravity, building up a complicated cosmic large scale structure. The joint analysis of these two cosmological probes will put unprecedented constraints on cosmological parameters and sharpen our knowledge of the Cosmos. However, weak lensing and galaxy clustering do not capture all the information encoded in a galaxy survey and there are a number of further additional probes that can be used to extract additional information. Cosmic voids are among the most promising novel probes of the large scale structure of the Universe; in particular, they are sensitive to the effects of Dark Energy and neutrinos. In this thesis, for the first time in literature, I performed a forecast on the Euclid measurement errors of cosmological parameters using the cross-correlation between weak lensing and cosmic voids, based on state-of-the-art theory and N-body simulations. This work confirms that using cosmic voids we can push further the sensitivity of the Euclid mission.