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

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.