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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 3d 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.

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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 3D massless SU(N) scalar matrix field theory with a 𝜙 4 interaction. On the lattice, the energymomentum tensor (EMT) in this theory can mix with the operator 𝜙 2 . We utilize the Wilson Flow to renormalize the EMT on the lattice, and present numerical results for the mixing coefficient for 𝑁 = 2. Obtaining the renormalized EMT will allow us to make predictions for the CMB power spectra in the regime where the dual QFT is non-perturbative.

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 3D massless SU(N) scalar matrix field theory with a φ 4 interaction. On the lattice, the energymomentum tensor (EMT) in this theory can mix with the operator φ 2 . We utilize the Wilson Flow to renormalize the EMT on the lattice, and present numerical results for the mixing coefficient for N = 2. Obtaining the renormalized EMT will allow us to make predictions for the CMB power spectra in the regime where the dual QFT is non-perturbative.

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In a class of holographic models for cosmology, the dual theory is given by a massless superrenormalisable QFT in 3 dimensions. In order to obtain cosmological observables, correlators of this QFT may be obtained via lattice field theory. Previous work has focused on scalar 4 matrix theories in the adjoint representation of SU(N). In this work we present preliminary results in the critical behaviour and phase structure of the theory with an SU(N) scalar field coupled to gauge fields by utilising the Heatbath-Overrelaxation (HBOR) algorithm in lattice field theory.