# Swampland conjecture in $f(R)$ gravity by the Noether Symmetry Approach

## TL;DR

This paper explores swampland criteria within $f(R)$ gravity models with duality symmetry, showing certain models align with string landscape principles and are consistent with cosmological observations.

## Contribution

It demonstrates that duality symmetry in $f(R)$ gravity can serve as a Noether symmetry, linking swampland conjecture criteria to specific viable models.

## Key findings

- Duality symmetry emerges as a Noether symmetry in $f(R)$ gravity.
- Selected $f(R)$ models satisfy swampland conjecture criteria.
- Models are compatible with both early and late-time cosmology.

## Abstract

Swampland conjecture has been recently proposed to connect early time cosmological models with the string landscape, and then to understand if related scalar fields and potentials can come from some fundamental theory in the high energy regime. In this paper, we discuss swampland criteria for $f(R)$ gravity considering models where duality symmetry is present. In this perspective, specific $f(R)$ models can naturally belong to the string landscape. In particular, it is possible to show that duality is a Noether symmetry emerging from dynamics. The selected $f(R)$ models, satisfying the swampland conjecture, are consistent, in principle, with both early and late-time cosmological behaviors.