[en] The Cosmic Microwave Background (CMB) is a key cosmological probe, that sets tight constraints on the ΛCDM model of the Universe. Released 380000 years after the big bang, it exhibits tiny anisotropies in temperature and polarisation which trace the cosmic inhomogeneities at different epochs of the Universe. On the one hand, primary anisotropies give access to inflation, during which the primordial perturbations are generated. On the other hand, secondary anisotropies trace inhomogeneities in the recent Universe, which have evolved into large scale structures through gravity, starting from the primordial ones. Hence CMB anisotropies are a powerful probe of both the origin of inhomogeneities in the very early Universe, and their evolved state in the late-time Universe. This thesis deals with two aspects of inhomogeneities by first considering their production in an extension of the inflationary scenario, and second by predicting the impact of magnetic fields in large scale structures on the secondary CMB polarised anisotropies. Despite its successes, inflation does not solve the initial big bang singularity issue, where gravity might need to be quantised. In Loop Quantum Cosmology (LQC), this singularity is replaced by a quantum bounce. Single field LQC with quadratic potential has already been studied and predicts an inflation phase following the bounce. Then, primordial inhomogeneities are not only produced during inflation, but also during the bounce and the contraction preceding it. Here, I considered a multifield extension of LQC with two fields: a massive one as being the inflaton, and a massless one used as an internal clock. I first studied the background evolution of the Universe both analytically and numerically. I showed that far in the contraction, the massive field dominates the energy budget. I have also checked that inflation remains likely to happen, despite the presence of the massless field. Secondly, I investigated how perturbations are produced. Unlike the one-field case, they are now described by an isocurvature component in addition to the standard adiabatic one, the former being characteristic of multifield models, for which Planck has put upper limits. In the remote past of the contraction, these two kinds of perturbations are highly coupled. I showed how to set their initial conditions by using appropriate variables mixing both kinds of perturbations, making the coupling subdominant. These perturbations remain to be propagated through the bounce down to the end of inflation to get their primordial (cross)spectra, to be subsequently compared to observational constraints. Since its released, the CMB traveled through large scale structures before reaching us. This leads to secondary anisotropies by its interaction with these structures, like e.g. gravitational deflection or the SZ effect in clusters. Magnetic fields have been observed in galaxies and larger structures. Since these structures are also filled with free electrons, this should lead to the Faraday Rotation (FR) effect which rotates the primordial linear polarisation, turning E into B modes, and to the Faraday Conversion (FC) effect which converts linear into circular polarisation. I revisited these sources of secondary anisotropies by computing the angular power spectra of the FR angle and the FC rate by large-scale structures. I used the halo model paying special attention to the impact of magnetic field projections. I found angular power spectra peaking at multipoles l ∼ 10⁴. Assuming a mass-independent magnetic field, the angular power spectra scale with the amplitude of matter perturbations as ∼ σ₈³. This scaling is however degenerated with the one of the magnetic field with halos' mass. I finally detail how to compute the full angular power spectra of polarised anisotropies, starting from the FR and FC power spectra. I also show how to reconstruct the FR and FC fields from the CMB adapting the estimators developed for lensing reconstruction. (author)