The quantum de Sitter root of quasi de Sitter observables: a pedagogical review

TL;DR

This review explains how the quantum Fisher information in de Sitter space predicts the spectral index and its running in inflationary cosmology, providing model-independent insights into primordial quantum features.

Contribution

It summarizes previous work on the implementation of primordial scaling laws via the de Sitter quantum Fisher information, highlighting its predictive power for cosmological observables.

Findings

Predicts spectral index n_s = 0.9672 independently of tensor-to-scalar ratio.

Forecasts a small running of the spectral index compatible with current data.

Establishes the dSQFI as a model-independent tool for understanding primordial quantum features.

Abstract

In inflationary cosmology the quasi de Sitter graceful exit allows us to measure the quantum features of the primordial dS phase, in particular, the lack of scale invariance parametrized by the spectral index $n_s$. In this review we summarize previous work on how the underlying primordial scaling law is implemented in the dS quantum Fisher information of the dS planar ground state (dSQFI). At large scales the dSQFI unequivocally sets, without any qdS input, the value of $n_s$ to be $0.9672$. This value is independent of the tensor to scalar ratio whose value requires model dependent input. In addition the dSQFI predicts, at large scales, a small running compatible with the current experimental results. Other phenomenological consequences of the dSQFI for small scales, will be discussed in a future review.