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

Towards a holographic description of cosmology: Renormalisation of the energy-momentum tensor of the dual QFT