  We test a class of holographic models for the very early universe against
cosmological observations and find that they are competitive to the standard
$\Lambda$CDM model of cosmology. These models are based on three dimensional
perturbative super-renormalizable Quantum Field Theory (QFT), and while they
predict a different power spectrum from the standard power-law used in
$\Lambda$CDM, they still provide an excellent fit to data (within their regime
of validity). By comparing the Bayesian evidence for the models, we find that
$\Lambda$CDM does a better job globally, while the holographic models provide a
(marginally) better fit to data without very low multipoles (i.e. $l\lesssim
30$), where the dual QFT becomes non-perturbative. Observations can be used to
exclude some QFT models, while we also find models satisfying all
phenomenological constraints: the data rules out the dual theory being
Yang-Mills theory coupled to fermions only, but allows for Yang-Mills theory
coupled to non-minimal scalars with quartic interactions. Lattice simulations
of 3d QFT's can provide non-perturbative predictions for large-angle statistics
of the cosmic microwave background, and potentially explain its apparent
anomalies.
