Toward a first full test of holographic cosmological models

Toward a first full test of holographic cosmological models

This project is focused on the study of field theories relevant for building holographic cosmological models. These models use three dimensional QFT to model holographically the laws of physics in the very early universe and make predictions for cosmological observables such as the cosmic microwave background (CMB). Our analysis aims to provide the predictions of these new models (describing a non-geometric very early universe) to be tested against data from observational cosmology, and also to constrain the existence of such dual theories.

Holographic cosmological models were shown [1,2] to describe well the CMB spectrum as measured by the Planck satellite. However, the observables from the dual theory were only computed in perturbation theory, which likely suffers from unphysical infrared divergences, limiting the predictivity of the model. As already demonstrated through our DiRAC project [3], these divergences are just artefacts of perturbation theory, a result conjectured in 1981 [4,5]. This was established for a specific class of field theories relevant for holographic models, scalar SU(N) theories in the adjoint representation and in a Euclidean three-dimensional space.

We are now currently studying short distance singularities in the correlation of the energy-stress tensor between two points in the space of the dual theory. This correlation function is related to the CMB spectrum through the holographic dictionary. We are investigating strategies to filter out these singularities by smoothly removing contact points in space. If successful, it will allow us to map our simulation to the Planck satellite data, and directly test holographic cosmological models based on a purely scalar dual theory. We presented preliminary results at the Lattice 2022 conference in Bonn [6].

Figure 1 – Filtered energy-stress tensor correlation function in frequency space for an SU(2) scalar dual theory. The correlation functions are filtered by smoothly removing the contact region in position space. The red curve corresponds to a more aggressive filtering than the blue one, resulting in a significant loss of signal.


[1]: N. Afshordi, C. Corianò, L. D. Rose, E. Gould, and K. Skenderis, From Planck Data to Planck Era: Observational Tests of Holographic Cosmology, Phys.Rev.Lett. 118 (2017) 4, 041301.

[2]: N. Afshordi, E. Gould, and K. Skenderis, Constraining Holographic Cosmology Using Planck Data, Phys.Rev.D 95 (2017) 12, 123505.

[3]: G. Cossu, L. D. Debbio, A. Juttner, B. Kitching-Morley, J. K. L. Lee, A. Portelli, H. B. Rocha, and K. Skenderis, Nonperturbative Infrared Finiteness in Super-Renormalisable Scalar Quantum Field Theory, Phys.Rev.Lett. 126 (2021) 22, 221601.

[4]: R. Jackiw and S. Templeton, How Super-Renormalizable Interactions Cure Their Infrared Divergences, Phys.Rev.D 23 (1981), 2291.

[5]: T. Appelquist and R. D. Pisarski, High-Temperature Yang-Mills Theories and Three-Dimensional Quantum Chromodynamics, Phys.Rev.D 23 (1981), 2305.

[6]: H.B. Rocha, L. D. Debbio, A. Juttner, B. Kitching-Morley, J. K. L. Lee, A. Portelli, and K. Skenderis, Position-Space Renormalisation of the Energy-Momentum Tensor, PoS LATTICE2022 (2023) 205, arXiv:2212.09469