Observational constraints on modified gravity models

In the first part of this Thesis, we study the gravitational clustering of spherically symmetric overdensities and the statistics of the resulting dark matter haloes in the symmetron model, in which a new long range force is mediated by a Z2 symmetric scalar field. Depending on the initial radius of the overdensity, we identify two distinct regimes: for small initial radii the symmetron mediated force affects the spherical collapse at all redshifts; for initial radii larger than some critical size, this force vanishes before collapse because of the symmetron screening mechanism. As a consequence, haloes with initial radii smaller than some critical value collapse earlier than in the LCDM and statistically tends to form more massive dark matter haloes. In the second part of this Thesis, we analyze the constraints that we get on the modified gravity parameter Y in a ࢠmodel-independentࢠway: this parameter can be estimated by comparing with the current redshift-space distortions measurements and with the forecasted measurements of Euclid-like redshift survey. Finally, we produce a forecast of a cosmological exclusion plot on the Yukawa strength and range parameters, which complements similar plots on laboratory scales but explores scales and epochs reachable only with large-scale galaxy surveys. We find that future data can constrain the Yukawa strength to within 3% of the Newtonian one if the range is around a few Megaparsec.