Constraining holographic cosmology using Planck data

TL;DR

The paper tests holographic cosmology, which derives early-universe observables from a dual three-dimensional QFT, against Planck data. It contrasts a non-geometric, perturbative HC regime with standard ΛCDM inflation, using CosmoMC and MultiNest to fit an empirical HC spectrum and compare to ΛCDM and ΛCDM with running. Across full Planck data HC is disfavored, but when low multipoles (where perturbation theory breaks) are excluded, HC fits as well as ΛCDM and Bayesian evidence becomes inconclusive, highlighting the need for non-perturbative methods (e.g., lattice QFT) to fully test HC at large angles. The work points to future lattice studies and holographic reheating scenarios as avenues to extend HC’s confrontations with observations and potentially explain large-angle CMB anomalies.

Abstract

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 $Λ$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.

Figures (10)

• Figure 1: A sketch of the Penrose diagram describing holographic cosmology (HC). The early Universe is non-geometric and is described by a dual QFT, which is located at the end of the non-geometric phase.
• Figure 2: A triangle plot of the likelihoods of parameters for holographic cosmology. The blue plots showing the case without low $l$s is less symmetric than the red plots with the full data set due to the reduced amount of data. The contours show the $68\%$ and $95\%$ confidence levels.
• Figure 3: TT power spectra of Planck 2015, $\Lambda$CDM and HC. Error bars are shown for low $l$. In the insert ($l\le40$), the blue line ($\Lambda$CDM) is noticeably above the red one (HC). The green shaded region in the difference plot shows the Planck relative error.
• Figure 4: Plots of EE (left) and TE (right) polarization for Planck 2015 (black), $\Lambda$CDM (blue) and HC (red). The green shaded region in the difference plot shows the Planck error.
• Figure 5: Plot of the primordial power spectrum for HC and $\Lambda CDM$. The parameters used to produce the curves are the best fit values in Table \ref{['tab:bfhl']}. The error (seen in the lighter shaded regions above and below the curves) is determined by assuming the same relative error as the Planck cls. It is included in order to give a sense of the error, not as the actual error. The red line indicating holographic cosmology starts significantly lower and increases rapidly at low $q$ values.