Super-inflation and perturbations in LQC, and scaling solutions in curved FRW universes

We investigate phenomenologies arising from two distinct sets of modifications introduced in Loop Quantum Cosmology (LQC), namely, the inverse volume and the holonomy corrections. We find scaling solutions in each setting and show they give rise to a period of super-inflation soon after the universe starts expanding. This type of inflation is explicitly shown to resolve the horizon problem with far fewer number of e-foldings compared to the standard inflationary model. Scalar field perturbations are obtained and we demonstrate their near scale invariance in agreement with the latest observations of the Cosmic Microwave Background (CMB). Consideration of tensor perturbations of the metric results in a large blue tilt for these fluctuations, which implies their amplitude will be suppressed by many orders of magnitude on the CMB compared to the predictions of the standard inflation. This LQC result is shared by the ekpyrotic model and the model of a universe sourced by a phantom field. Exploring a correspondence map at the cosmological background level between braneworld cosmologies and the inverse volume corrected LQC, we discover this map not to hold at the level of linear perturbations. This is found to be due to the different behaviour of the rate of the Hubble parameter in the two classes of models. A complete dynamical analysis of Friedmann-Robertson-Walker spacetimes we carry out results in the most general forms of late time attractor scaling solutions. Our examination includes expanding and contracting universes when a scalar field evolves along a positive or a negative potential. Known results in the literature are demonstrated to correspond to certain limits of our solutions