Holographic Cosmology $n$-point function map from the Wavefunction of the Universe

TL;DR

This paper extends the holographic cosmology framework by explicitly deriving n-point functions from the wavefunction of the universe, confirming previous 2-point results and computing the 3-point non-Gaussianities, demonstrating a versatile method for cosmological observables.

Contribution

It provides a straightforward extension of Maldacena's map to higher-point functions in holographic cosmology, enabling calculation of complex observables from the wavefunction.

Findings

Confirmed 2-point function relations match CMBR data

Derived 3-point functions for scalar and tensor fluctuations

Calculated monopole non-Gaussianity from current correlators

Abstract

In this note we show explicitly that, applying an extension of Maldacena's map for the wavefunction of the Universe $Z[\phi]=\Psi[\phi]$ from de Sitter inflation to holographic cosmology, we find the relations previously derived for 2-point functions, $\langle h_{ij}(p) h_{kl}(-p)\rangle \sim 1/[{\rm Im}\langle T_{ij}(-ip)T_{kl}(+ip)\rangle]$ and a similar one for currents, which were used to show that holographic cosmology matches CMBR data and solves Big Bang problems as well as inflation. Higher point functions are done similarly, and as an application, we check the result for the 3-point functions of scalar and tensor fluctuations and find the result for the monopole non-Gaussianity arising from the 3-point functions of currents. The method is simple and potentially could be applied to calculate any observable in holographic cosmology.