# Horndeski in the Swampland

## TL;DR

This paper explores how string Swampland criteria constrain Horndeski theories of gravity, especially in cosmology, indicating that derivative interactions significantly impact the viability of these models under observational and theoretical limits.

## Contribution

It analyzes the compatibility of Horndeski Lagrangians with Swampland criteria, highlighting the effects of derivative interactions on cosmological dynamics and constraints.

## Key findings

- Derivative self-interactions modify scalar dynamics.
- Tight constraints on Swampland parameter c from cosmological data.
- Implications for Horndeski and related scalar-tensor theories.

## Abstract

We investigate the implications of string Swampland criteria for alternative theories of gravity. Even though this has not rigorously been proven, there is some evidence that exact de-Sitter solutions with a positive cosmological constant cannot be successfully embedded into string theory, and that the low energy effective field theories containing a scalar field $\pi$ with a potential $V$ in the habitable landscape should satisfy the Swampland criteria $|V'|/V\ge c\sim\mathcal{O}(1)$. As a paradigmatic class of modified gravity theories for inflation and dark energy, we consider the extensively studied family of Horndeski Lagrangians in view of cosmological observations. Apart from a possible potential term, they contain derivative self-interactions as the Galileon and non-minimal couplings to the gravity sector. Hence, our conclusions on the Galileon sector can be also applied to many other alternative theories with scalar helicity modes containing derivative interactions such as massive gravity and generalized Proca. In the presence of such derivative terms, the dynamics of the scalar mode is substantially modified, and imposing the cosmological evolution constrained by observations places tight constraints on $c$ within the Swampland conjecture.