  Holographic cosmology offers a novel framework for describing the very early
Universe in which cosmological predictions are expressed in terms of the
observables of a three dimensional quantum field theory (QFT). This framework
includes conventional slow-roll inflation, which is described in terms of a
strongly coupled QFT, but it also allows for qualitatively new models for the
very early Universe, where the dual QFT may be weakly coupled. The new models
describe a universe which is non-geometric at early times. While standard
slow-roll inflation leads to a (near-)power-law primordial power spectrum,
perturbative superrenormalizable QFT's yield a new holographic spectral shape.
Here, we compare the two predictions against cosmological observations. We use
CosmoMC to determine the best fit parameters, and MultiNest for Bayesian
Evidence, comparing the likelihoods. We find that the dual QFT should be
non-perturbative at the very low multipoles ($l \lesssim 30$), while for higher
multipoles ($l \gtrsim 30$) the new holographic model, based on perturbative
QFT, fits the data just as well as the standard power-law spectrum assumed in
$\Lambda$CDM cosmology. This finding opens the door to applications of
non-perturbative QFT techniques, such as lattice simulations, to observational
cosmology on gigaparsec scales and beyond.
