From Planck Data to Planck Era: Observational Tests of Holographic Cosmology

We test a class of holographic models for the very early Universe against cosmological observations and find that they are competitive to the standard cold dark matter model with a cosmological constant ($\mathrm{\Lambda }\mathrm{CDM}$) of cosmology. These models are based on three-dimensional perturbative superrenormalizable quantum field theory (QFT), and, while they predict a different power spectrum from the standard power law used in $\mathrm{\Lambda }\mathrm{CDM}$, they still provide an excellent fit to the data (within their regime of validity). By comparing the Bayesian evidence for the models, we find that $\mathrm{\Lambda }\mathrm{CDM}$ does a better job globally, while the holographic models provide a (marginally) better fit to the data without very low multipoles (i.e., $l\lesssim 30$), where the QFT becomes nonperturbative. Observations can be used to exclude some QFT models, while we also find models satisfying all phenomenological constraints: The data rule out the dual theory being a Yang-Mills theory coupled to fermions only but allow for a Yang-Mills theory coupled to nonminimal scalars with quartic interactions. Lattice simulations of 3D QFTs can provide nonperturbative predictions for large-angle statistics of the cosmic microwave background and potentially explain its apparent anomalies.

Figure 1

Angular power spectrum of CMB temperature anisotropies, comparing Planck 2015 data with best fit $\mathrm{\Lambda }\mathrm{CDM}$ (dotted blue curve) and holographic cosmology (solid red curve) models, for $l\ge 30$. The lower panel shows the relative residuals, where the green shaded region indicates the 68% region of Planck 2015 data.

Figure 2

Plot of $1\sigma$ and $2\sigma$ regions in parameter space for holographic cosmology $g$ and $\ln (\beta )$ values for WMAP (blue line, right), Planck (red line, middle), Planck with $l<30$ values removed (green line, left), and Planck with $l>700$ values ignored (purple dashed line). We see that higher resolution data progressively push $g$ to lower negative values.

Figure 3

Bayesian evidence using $l\ge 30$ data only, where the perturbative expansion (2) can be trusted. An error is indicated by the shaded region around the lines.