# Duality Invariant Cosmology to all Orders in $\alpha'$

## TL;DR

This paper classifies all-order duality invariant $oldsymbol{ ext{α'} }$ corrections in string-inspired cosmological models, deriving equations and solutions that include de Sitter vacua and are invariant under duality transformations.

## Contribution

It provides the first comprehensive classification of duality invariant $oldsymbol{ ext{α'} }$ corrections for time-dependent backgrounds to all orders, including non-perturbative solutions.

## Key findings

- Derived all-order duality invariant Friedmann equations.
- Constructed non-perturbative solutions with de Sitter vacua.
- Demonstrated integrability of equations perturbatively to any order.

## Abstract

While the classification of $\alpha'$ corrections of string inspired effective theories remains an unsolved problem, we show how to classify duality invariant $\alpha'$ corrections for purely time-dependent (cosmological) backgrounds. We determine the most general duality invariant theory to all orders in $\alpha'$ for the metric, $b$-field, and dilaton. The resulting Friedmann equations are studied when the spatial metric is a time-dependent scale factor times the Euclidean metric and the $b$-field vanishes. These equations can be integrated perturbatively to any order in $\alpha'$. We construct non-perturbative solutions and display duality invariant theories featuring string-frame de Sitter vacua.