[Paper Review] De Sitter Space and the Swampland

Georges Obied, Hirosi Ooguri+2 more|arXiv (Cornell University)|Jun 21, 2018

Black Holes and Theoretical PhysicsPhysics and Astronomy21 references420 citations

TL;DR

The paper proposes a swampland bound | abla V| 6 V with a positive constant c, arguing that de Sitter vacua are forbidden in any consistent quantum gravity theory and testing this bound across string/M-theory constructions.

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 $| abla V|\geq\ c \cdot V$ 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.

Motivation & Objective

• Motivate a swampland criterion that forbids metastable de Sitter vacua in quantum gravity.
• Review and extend no-go theorems for de Sitter space in string theory and M-theory.
• Explore how the proposed bound constrains scalar potentials in various compactifications and dimensions.
• Discuss implications for quintessence and accelerating universes.
• Relate the bound to energy conditions and to known string theory constructions.

Proposed method

• Introduce a universal bound | abla V| 6 V for scalar potentials in any consistent quantum gravity theory.
• Derive lower bounds on | abla V|/V from M-theory compactifications, heterotic strings, and Type II supergravity with fluxes and orientifolds.
• Express potentials in terms of volume moduli and compute gradients to obtain c  O(1) bounds.
• Relate results to strong and null energy conditions and discuss their limitations in string theory.
• Generalize no-go theorems to accelerating universes beyond pure de Sitter vacua.

Experimental results

Research questions

• RQ1 Does a universal lower bound on | abla V|/V exist for all consistent quantum gravity theories?
• RQ2 Can string/M-theory compactifications saturate or approach the proposed bound c  O(1)?
• RQ3 Do the no-go theorems and energy conditions imply the absence of metastable de Sitter vacua across broad classes of compactifications?
• RQ4 What are the implications of the bound for quintessence-like scenarios and accelerating cosmologies?
• RQ5 How does relaxing energy conditions affect the feasibility of de Sitter or accelerating solutions?

Key findings

• A swampland bound | abla V| 6 V is proposed, with c of order 1 in Planck units, forbidding metastable de Sitter vacua.
• M-theory compactifications to d dimensions yield | abla V|/V 6 6/sqrt{(d-2)(11-d)}; for d=4 this gives ~1.6, realized by AdS4 x S7.
• In a non-supersymmetric heterotic string (O(16) x O(16)), the effective 10D potential yields | abla V|/V 9 5/sqrt{2}  approx 3.5, indicating c e bounded by ~3.5 in that case.
• Generalized no-go theorems for Type II supergravity with fluxes and localized sources imply positive lower bounds on | abla V|/V in many setups (e.g., Table 1 bounds all exceed sqrt{2}).
• Consequences of SEC/NEC show SEC implies a bound differing from NEC, but both are too strong to guarantee realistic accelerating universes; NEC-based bounds are closer to observed cosmology but still restrictive.