Holographic predictions for cosmological 3-point functions

Abstract

We present the holographic predictions for cosmological 3-point correlators, involving both scalar and tensor modes, for a universe which started in a non-geometric holographic phase. Holographic formulae relate the cosmological 3-point functions to stress tensor correlation functions of a holographically dual three-dimensional non-gravitational QFT. We compute these correlators at 1-loop order for a theory containing massless scalars, fermions and gauge fields, and present an extensive analysis of the constraints due to Ward identities showing that they uniquely determine the correlators up to a few constants. We define shapes for all cosmological bispectra and compare the holographic shapes to the slow-roll ones, finding that some are distinguishable while others, perhaps surprisingly, are not.

Figures (4)

• Figure 1: 1-loop contribution to the stress tensor 3-point function.
• Figure 2: Isoperimetric plots displaying the holographic and slow-roll shape functions, as well as the difference between them ( e.g., $\Delta \mathcal{S}(\hat{\gamma}^{(+)}\hat{\gamma}^{(+)}\hat{\gamma}^{(+)})=\mathcal{S}(\hat{\gamma}^{(+)}\hat{\gamma}^{(+)}\hat{\gamma}^{(+)})-\mathcal{S}_{SR}(\hat{\gamma}^{(+)}\hat{\gamma}^{(+)}\hat{\gamma}^{(+)})$). The invariance of the shape functions under a rescaling $q_i\rightarrow \lambda q_i$ of all momenta has been exploited to set $q_1+q_2+q_3=1$, constraining the allowed momentum values to those displayed. Each plot is symmetric under interchange of the appropriate momenta as expected. Note that $\mathcal{S}(\hat{\gamma}^{(+)}\hat{\gamma}^{(+)}\hat{\gamma}^{(-)})$ (shown in plot (a)) coincides for the holographic and slow-roll models. In plots (\ref{['fig:Holppp']}) and (\ref{['fig:Deltappp']}) we have set $\mathcal{N}_\psi=\mathcal{N}_{(A)}$ to maximise $\Delta \mathcal{S}(\hat{\gamma}^{(+)}\hat{\gamma}^{(+)}\hat{\gamma}^{(+)})$ for illustrative purposes.
• Figure 3: Isoperimetric plots for holographic and slow-roll shape functions continued. In plots (\ref{['fig:Holzpm']}) and (\ref{['fig:SRzpm']}) note that both shape functions are actually finite along the line $q_3=1/2-q_2$ ( i.e., $q_1=1/2$); we have simply restricted the plot range to exhibit the overall shape more clearly.
• Figure 4: Labelling of momenta