Cross-Correlations of Metric and Monopole Perturbations from Holographic Cosmology

Abstract

In this paper, we present the 1-loop calculation of the three-point function $⟨TJJ⟩$ of the stress-energy tensor and two insertions of $SO(3)$ global currents, using a 3d toy model for holographic cosmology. By applying the holographic dictionary that relates these QFT $n$-point functions to cosmological correlators, together with the $Sl(2,\mathbb{Z})$ duality that maps the electric Noether current to a magnetic vortex current dual to cosmological magnetic monopoles, we relate the $⟨TJJ⟩$ correlator to the cross-correlations between metric perturbations and the bulk magnetic monopole field, specifically mapping to the non-Gaussianities $⟨\xi \tilde{A}\tilde{A}⟩$ and $⟨\gamma \tilde{A}\tilde{A}⟩$. We calculate the semi-local contact terms necessary to achieve the exact factorization of the cosmological correlators in the squeezed limit, $p_1\to 0$. Finally, we evaluate the effective non-linear parameters, showing that the scalar-monopole cross-correlation vanishes at leading order, $f_{NL}^{\xi \tilde{A}\tilde{A}}=0$, while the tensor-monopole cross-correlation yields a non-zero $f_{NL}^{\gamma \tilde{A}\tilde{A}}$. These results respect the expected amplitude hierarchy of the non-Gaussian correlators, while pointing at new directions in which holographic cosmology can be tested experimentally.

45 pages, 1 figure; appendix and clarifying remarks added, reference added