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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 $3D$ massless $SU(N)$ scalar matrixfield theory with a $\phi^4$ interaction. On the lattice, the energy-momentumtensor (EMT) in this theory can mix with the operator $\phi^2$. We utilize theWilson Flow to renormalize the EMT on the lattice, and present numericalresults for the mixing coefficient for $N = 2$. Obtaining the renormalized EMTwill allow us to make predictions for the CMB power spectra in the regime wherethe dual QFT is non-perturbative.

Renormalization of the $3D$ $SU(N)$ scalar energy-momentum tensor using the Wilson flow