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 $\langle TJJ \rangle$ 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 $\langle TJJ \rangle$ correlator to the cross-correlations between metric perturbations and the bulk magnetic monopole field, specifically mapping to the non-Gaussianities $\langle ξ\tilde{A} \tilde{A} \rangle$ and $\langle γ\tilde{A} \tilde{A} \rangle$. 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, $f_{NL}^{ξ\tilde{A} \tilde{A}} = 0$, while the tensor-monopole cross-correlation yields a non-zero $f_{NL}^{γ\tilde A\tilde A}$. 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.