# Superspace and global stability in General Relativity

## TL;DR

This paper introduces a geometric framework for analyzing the global stability of cosmological models in General Relativity by utilizing the structure of superspace and generalized Jacobi equations.

## Contribution

It develops a formalism for stability analysis in superspace, incorporating covariant derivatives and applying it specifically to scalar field cosmological models.

## Key findings

- Framework enables global stability analysis of cosmological models.
- Derived equations facilitate dynamical analysis in superspace.
- Applied formalism to scalar field cosmologies.

## Abstract

A framework is developed enabling the global analysis of the stability of cosmological models using the local geometric characteristics of the infinite-dimensional superspace, i.e. using the generalised Jacobi equation reformulated for pseudo-Riemannian manifolds. We give a direct formalism for dynamical analysis in the superspace, the requisite equation pertinent for stability analysis of the universe by means of generalized covariant and Fermi derivative is derived. Then, the relevant definitions and formulae are retrieved for cosmological models with a scalar field.