We test a class of holographic models for the very early universe against cosmological observations and find that they are competitive to the standard ΛCDM 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 ΛCDM, they still provide an excellent fit to data (within their regime of validity). By comparing the Bayesian evidence for the models, we find that ΛCDM does a better job globally, while the holographic models provide a (marginally) better fit to data without very low multipoles (i.e. l 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.Observations of the cosmic microwave background (CMB) offer a unique window into the very early Universe and Planck scale physics. The standard model of cosmology, the so-called ΛCDM model, provides an excellent fit to observational data with just six parameter. Four of these parameters describe the composition and evolution of the Universe, while the other two are linked with the physics of the very early Universe. These two parameters, the tilt n s and and the amplitude ∆ 2 0 (q * ), parameterize the power spectrum of primordial curvature perturbations,where q * , the pivot, is an an arbitrary reference scale. This form of the power spectrum is a good approximation for slow-roll inflationary models and has the ability to fit the CMB data well. Indeed, a near-power-law scalar power spectrum may be considered as a success of the theory of cosmic inflation. The theory of inflation is an effective theory. It is based on gravity coupled to (appropriate) matter perturbatively quantized around an accelarating FLRW background. At sufficiently early times the curvature of the FLRW spacetime becomes large and the perturbative treatment is expected to break down -in this regime we would need a full-fledged theory of quantum gravity. One of the deepest insights about quantum gravity that emerged in recent times is that it is expected to be holographic [1][2][3], meaning that there should be an equivalent description of the bulk physics using a quantum field theory with no gravity in one dimension less. One may thus seek to use holography to model the very early Universe.Holographic dualities were originally developed for spacetimes with negative cosmological constant (the AdS/CFT duality) [3] and soon afterwards the extension to de Sitter and cosmology was considered [4][5][6][7][8]. In this context, the statement of the duality is that the partition func...

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.Comment: 25 pages, 10 figures, updated to match version to appear in PR

It is shown that the 33 complex rays in three dimensions used by Penrose to prove the Bell-Kochen-Specker theorem have the same orthogonality relations as the 33 real rays of Peres, and therefore provide an isomorphic proof of the theorem. It is further shown that the Peres and Penrose rays are just two members of a continuous three-parameter family of unitarily inequivalent rays that prove the theorem.Keywords Kochen-Specker theorem · Bell's theorem · Foundations of quantum mechanics Some time back Peres [1] gave a proof of the Bell-Kochen-Specker (BKS) theorem [2, 3] using 33 real rays (or directions) in three dimensions. Penrose [4] later gave a different proof of the theorem using 33 complex rays in three dimensions. Penrose pointed out that his set of rays is essentially complex (i.e., there is no basis in which the components of all the rays can be made real) and that there is no Hilbert space rotation that will take his rays into those of Peres. It might therefore be thought that the proofs of the BKS theorem based on the two sets of rays are essentially different. However we show in this paper that the Kochen-Specker diagrams of the Peres and Penrose rays are identical, and that they therefore furnish isomorphic proofs of the BKS theorem. We exploit the common cubic symmetry of both sets of rays to give a unified proof of the BKS theorem for them that is shorter than the one given by Peres. Finally, we demonstrate that the Peres and Penrose rays are just two members of a continuous three-parameter family of unitarily inequivalent rays that prove the theorem.The 33 rays of Peres can be visualized in terms of the geometry of a cube. Each ray goes out from the center of a cube to a point on its surface as follows: three