  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.

High Energy Physics - Theory;Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology