As a proxy for a Quantum Gravity theory, String Theory introduces new degrees of freedom and symmetries that should play a major role in the physics of the early universe. We motivate the introduction of these ingredients as we review some of the issues of the inflationary paradigm. Among these new ingredients, T-duality may help us to solve the Big Bang singularity and yield a new cosmological scenario. Thus, we review how this has been thought in the context of Double Field Theory, which aims to build a covariant field theory under T-duality's group, and consider its cosmological applications.