Limiti Cosmologici su teorie f(R) che riproducono la dinamica di Loop Quantum Cosmology

This thesis presents a theory of Modified Gravity, inspired from Loop Quantum Cosmology (LQC), where the Big Bang is replaced with the Big Bounce, generated from quantum gravity effects. The theoretical framework of f(R) in Palatini formalism allows to find an effective covariant action which reproduce the dynamics of LQC, with also the Cosmological Perturbation Theory it is possible to study how the modifications of gravity affects the cosmological observations. The focus is on scalar perturbations, actually in Palatini formalism the f(R) introduces a new degree of freedom, called scalaron, that affects the devolution of the Universe. In the last part of this work, a comparison with experimental data is provided. The code used in order to constrain the theory is CosmoMC, which is a parameter sampling code and it is bundled up with likelihood codes from the most recent dataset.