In physics, infinity appears linked to the continuum problem of the mathematical representations used by the various theories and, therefore, to the possibility of infinite divisibility (the infinitely small) and the infinite extension (the infinitely large) of the geometry of space-time and of the measurable physical concepts and magnitudes. The standard model of particle physics considers that elementary particles are «infinitely» small and calculations arise with infinite results for certain physical quantities. To eliminate those infinities, we use methods of renormalization, which are also used in classical cosmology and in the standard model of the Big Bang cosmology in order to tame the infinities (black holes and initial singularity). Research in quantum gravity considers that space is not infinitely divisible and multiverse models assume infinite times and spaces for the Universe. Since our theories are always limited and perfectible, it seems that we cannot prove, in physics, that the Universe is physically infinite.