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.
Highlights
The standard cosmological paradigm relies on the existence of hypothetical scalar fields causing two phases of accelerated expansion during the evolution history of the universe
We have applied the de Sitter swampland conjecture to Horndeski scalar-tensor theories, which represent a prominent class of alternative theories of gravity based on an additional scalar field
The quintessence model corresponds to just a restricted subclass of this general scalar-tensor theories. The presence of these derivative self-interactions crucially influences the dynamics of the scalar field
Summary
The standard cosmological paradigm relies on the existence of hypothetical scalar fields causing two phases of accelerated expansion during the evolution history of the universe. In order to account for inflation and time evolving dark energy, one has to introduce additional fields beyond the standard model and extend the underlying theory In this context, modifications of gravity have been considered, with the most studied ones containing an additional scalar field. The cosmological implications of this new swampland conjecture are multifaceted, in particular, quintessence-type models for inflation and dark energy are highly constrained [6] (see [7] for some other related discussions) These string-theory criteria can be used to constrain alternative theories of gravity. Still remaining within the class of theories containing one additional scalar field, we consider the Horndeski scalar-tensor theories with derivative self-interactions They can be applied to both inflationary scenarios and concrete dark-energy models. Going beyond the Galileon interactions, the class of Horndeski theories where the Galileon invariance is weakly broken, is insensitive to loop corrections on quasi–de Sitter backgrounds [13]
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