De Sitter Space and the Swampland (1806.08362v3)

Abstract: 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 $|\nabla V|\geq\ c \cdot V$ 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.

• The paper introduces a swampland conjecture using the inequality |∇V| ≥ c·V (with c ~ 1) to argue that meta-stable de Sitter vacua cannot arise in string theory.
• It revisits no-go theorems and examines various string theory compactifications to demonstrate that established models naturally obey the proposed potential bound.
• The findings imply significant cosmological consequences, aligning quintessence models with energy conditions and prompting further exploration of quantum gravity constraints.

De Sitter Space and the Swampland

The paper "De Sitter Space and the Swampland" by Georges Obied, Hirosi Ooguri, Lev Spodyneiko, and Cumrun Vafa presents a detailed analysis of the challenges associated with constructing meta-stable de Sitter (dS) vacua within the framework of string theory. This discourse posits that the difficulty in creating such vacua suggests their potential inclusion in the "swampland," a concept referring to low-energy effective field theories that, while consistent from a quantum field theory standpoint, cannot be embedded consistently into a quantum theory of gravity like string theory. The authors propose a swampland criterion that imposes a lower bound on the gradient of scalar field potentials, effectively prohibiting dS vacua.

Main Contributions

1. Swampland Conjecture: The critical conjecture proposed by the authors is the inequality $\lvert \nabla V \rvert \geq c \cdot V$, where $V$ is the potential and $c$ is a positive constant of order 1 in Planck units. This conjecture implies that in any low-energy theory of a consistent quantum theory of gravity, the potential of scalar fields can never be too flat.
2. No-go Theorems: The paper revisits several no-go theorems that already challenge the existence of dS vacua in string theory, extending these to more generalized accelerating universes. This is achieved by translating restrictions on scalar potentials into these constraints.
3. Examples from String Theory: The authors explore various string theory constructions, including compactifications in M theory and Type II string theories, to offer evidence of the conjecture's validity. These examples include heterotic string constructions and scenarios employing flux compactifications. The authors argue that these constructions inherently obey the proposed bound on $\lvert \nabla V \rvert / V$.
4. Theoretical Implications: This bound provides support to quintessence models, which describe cosmic acceleration with a slowly rolling scalar field, as these models naturally comply with the proposed swampland condition.
5. Energy Conditions: The paper scrutinizes the implications of both the Strong Energy Condition (SEC) and the Null Energy Condition (NEC) in relation to the swampland criteria. The bound derived from SEC is shown to be too restrictive for string theory contexts, while the NEC provides a more feasible condition although still yielding higher values than current experimental constraints suggest.

Implications and Future Directions

This paper is significant in broadening our understanding of the limitations imposed on cosmological models by string theory, particularly regarding the feasibility of de Sitter vacua, which underpin many cosmological theories, including inflation and dark energy models. The absence of these vacua in string theory could compel a reevaluation of current cosmological paradigms, potentially leading to novel insights in high-energy physics and cosmology.

The discussion of energy conditions further suggests that building a consistent cosmological model with string theory may require a nuanced approach, considering potential violations of these classical conditions. The conjecture provides a framework for assessing the consistency of proposed cosmological models with the broader framework of quantum gravity.

Moving forward, these results open up several avenues for further research, such as exploring more complex string models that might evade or comply with the conjecture, and refining the numerical value of $c$ based on additional theoretical and experimental insights. The interplay between string theory and cosmological observations remains a fertile ground for advancing our understanding of the universe's fundamental structure.