Testing the boundaries of standard cosmological models

The standard cosmological model is based on the assumption that the universe is homogeneous and isotropic on sufficiently large scales, and can be modeled with a FRW metric. Another important feature of standard cosmological models is the prediction of a scale invariant power spectrum for curvature perturbations.; We explore the possibility of a not scale invariant spectrum studying slow roll inflationary models with strongly running spectral index, and determine a new approximate consistency condition relating the first order slow roll parameter epsilon and the spectral index of scalar perturbation n s. We test the approximate condition numerically providing the probability distribution of the difference between the scale of the extremum of epsilon and the zero of ns - 1. Numerical results show a dependence on the strength of the running in agreement with the analytical prediction.; We then explore some possible alternatives to standard FRW models with dark energy studying the compatibility of the observed luminosity distance of type Ia supernovae and inhomogeneous solutions of Einstein's field equations of LTB type without dark energy. We derive a inversion method which we then use to find a LTB model which successfully reproduces the observed luminosity distance.; We finally study the local observability of the averaged acceleration defined via spatial averaging of LTB models, showing that averaged quantities are not observable when the averaging scale is beyond the events horizon of the central observer.