In this talk, we present a method to define the Energy-Momentum Tensor (EMT) of a theory in a discretized space. In particular, the Holographic Cosmology project uses lattice simulations to obtain decisive results which may validate the holographic principle applied to cosmology. In this framework, all the cosmological observables are obtained by computing correlators of a QFT in 3D euclidean space.

One of the most important and fundamental quantity we need for this project is the EMT of the dual theory. This tensor is the conserved current associated to the translational symmetry, which is broken on the lattice. By consequence, the EMT correlators will produce additional divergences which can be renormalized using a set of translational Ward-Takahashi identities.