Gauge transformations and gauge-invariant cosmological perturbations

The study of cosmological perturbations brought to light misleading interpretations and solutions without physical meaning. In fact the invariance of General Relativity leads to the fact that different gauges, which yield to different solutions, are mathematically equivalent. The gauge problem is seen in detail in the non-comoving synchronous gauge and in the conformal Newtonian gauge, in which the absurdity of the results is more evident. The gauge problem is solved by the definition of gauge-invariant variables, through which it is possible to study cosmological perturbations in an unambiguous way. Following Bardeen’s approach perturbations equations are derived and solved. Bardeen’s potentials are studied in deep in the conformal Newtonian gauge, to understand their physical meaning in the study of perturbed Einstein’s equations.