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The recently introduced swampland criterion for de Sitter (arXiv:1806.08362) can be viewed as a (hierarchically large) bound on the smallness of the slow roll parameter $epsilon_V$. This leads us to consider the other slow roll parameter $eta_V$ more closely, and we are lead to conjecture that the bound is not necessarily on $epsilon_V$, but on slow roll itself. A natural refinement of the de Sitter swampland conjecture is therefore that slow roll is violated at ${cal O}(1)$ in Planck units in any UV complete theory. A corollary is that $epsilon_V$ need not necessarily be ${cal O}(1)$, if $eta_V lesssim -{cal O}(1)$ holds. We consider various tachyonic tree level constructions of de Sitter in IIA/IIB string theory (as well as closely related models of inflation), which superficially violate arXiv:1806.08362, and show that they are consistent with this refined version of the bound. The phrasing in terms of slow roll makes it plausible why bo
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Among Swampland conditions, the distance conjecture characterizes the geometry of scalar fields and the de Sitter conjecture constrains allowed potentials on it. We point out a connection between the distance conjecture and a refined version of the de Sitter conjecture in any parametrically controlled regime of string theory by using Boussos covariant entropy bound. The refined version turns out to evade all counter-examples at scalar potential maxima that have been raised. We comment on the relation of our result to the Dine-Seiberg problem.
Quantum consistency suggests that any de Sitter patch that lasts a number of Hubble times that exceeds its Gibbons-Hawking entropy divided by the number of light particle species suffers an effect of quantum breaking. Inclusion of other interactions makes the quantum break-time shorter. The requirement that this must not happen puts severe constraints on scalar potentials, essentially suppressing the self-reproduction regimes. In particular, it eliminates both local and global minima with positive energy densities and imposes a general upper bound on the number of e-foldings in any given Hubble patch. Consequently, maxima and other tachyonic directions must be curved stronger than the corresponding Hubble parameter. We show that the key relations of the recently-proposed de Sitter swampland conjecture follow from the de Sitter quantum breaking bound. We give a general derivation and also illustrate this on a concrete example of $D$-brane inflation. We can say that string theory as a consistent theory of quantum gravity nullifies a positive vacuum energy in self-defense against quantum breaking.
Motivated by the coincidence of scrambling time in de Sitter and maximum lifetime given by the $textit{Trans-Planckian Censorship Conjecture}$ (TCC), we study the relation between the de Sitter complementarity and the Swampland conditions. We study thermalization in de Sitter space from different perspectives and show that TCC implies de Sitter space cannot live long enough to be considered a thermal background. We also revisit $alpha$-vacua in light of this work and show that TCC imposes multiple initial condition/fine-tuning problems on any conventional inflationary scenario.
The de Sitter constraint on the space of effective scalar field theories consistent with superstring theory provides a lower bound on the slope of the potential of a scalar field which dominates the evolution of the Universe, e.g., a hypothetical inflaton field. Whereas models of single scalar field inflation with a canonically normalized field do not obey this constraint, it has been claimed recently in the literature that models of warm inflation can be made compatible with it in the case of large dissipation. The de Sitter constraint is known to be derived from entropy considerations. Since warm inflation necessary involves entropy production, it becomes necessary to determine how this entropy production will affect the constraints imposed by the swampland conditions. Here, we generalize these entropy considerations to the case of warm inflation and show that the condition on the slope of the potential remains essentially unchanged and is, hence, robust even in the warm inflation dynamics. We are then able to conclude that models of warm inflation indeed can be made consistent with the swampland criteria.
It has been notoriously difficult to construct a meta-stable de Sitter (dS) vacuum in string theory in a controlled approximation. This suggests the possibility that meta-stable dS belongs to the swampland. In this paper, we propose a swampland criterion in the form of $| abla V|geq c cdot V$ for a scalar potential $V$ of any consistent theory of quantum gravity, for a positive constant $c$. In particular, this bound forbids dS vacua. The existence of this bound is motivated by the abundance of string theory constructions and no-go theorems which exhibit this behavior. We also extend some of the well-known no-go theorems for the existence of dS vacua in string theory to more general accelerating universes and reinterpret the results in terms of restrictions on allowed scalar potentials.
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