Cosmology with an Extra-dimension

The purpose of this contribution is to give an introduction to a new vision of extra-dimensions: the so-called “braneworld” picture. In this scenario, ordinary matter is trapped in a threedimensional space, called ‘brane’, embedded in a higher dimensional space. This idea must be contrasted with the traditional view of extra dimensions, the KaluzaKlein picture, where matter fields live everywhere in compact extra dimensions. Any such higher dimensional field can be described, via a Fourier expansion, as an infinite collection of fourdimensional fields, the so-called Kaluza-Klein modes, with masses depending on the size of the extra-dimensions. Non-observation of Kaluza-Klein modes in colliders thus gives an upper bound on the size of the extra-dimension, typically