# Towards a Fisher-information description of complexity in de Sitter universe

## TL;DR

This paper explores the connection between quantum information theory and de Sitter universe cosmology, showing that complexity measures like Fisher information can describe holographic entanglement and action, extending to modified gravity theories.

## Contribution

It establishes a Fisher information measure framework for de Sitter spacetime complexity, linking tensor networks, entanglement entropy, and action in a unified information-theoretic approach.

## Key findings

- Tensor network complexity corresponds to Fisher information measure in dS universe.
- Holographic entanglement entropy admits an information-theoretic interpretation.
- Complexity/action duality holds for de Sitter spacetime and extends to $f(R)$ gravity.

## Abstract

Recent developments on holography and quantum information physics suggest that quantum information theory come to play a fundamental role in understanding quantum gravity. Cosmology, on the other hand, plays a significant role in testing quantum gravity effects. How to apply this idea to a realistic universe is still missing. Here we show some concepts in quantum information theory have their cosmological descriptions. Particularly, we show complexity of a tensor network can be regarded as a Fisher information measure(FIM) of a dS universe, followed by several observations: (i) the holographic entanglement entropy has a tensor-network description and admits a information-theoretical interpretation, (ii) on-shell action of dS spacetime has a same description of FIM, (iii) complexity/action(CA) duality holds for dS spacetime. Our result is also valid for $f(R)$ gravity, whose FIM exhibits the same features of a recent proposed $L^n$ norm complexity.