  In the holographic approach to cosmology, cosmological observables are
described in terms of correlators of a three-dimensional boundary quantum field
theory. As a concrete model, we study the 3$d$ massless $SU(N)$ scalar matrix
field theory. In this work, we focus on the renormalisation of the
energy-momentum tensor 2-point function, which can be related to the CMB power
spectra. Here we present a non-perturbative procedure to remove divergences
resulting from the loss of translational invariance on the lattice, by imposing
Ward identities. This will allow us to make predictions for the CMB power
spectra in the regime where the dual QFT is non-perturbative.
