Accelerating Universes and String Theory

TL;DR

The article surveys the challenges of incorporating time and a positive cosmological constant into string theory, emphasizing de Sitter space and its holographic prospects. It analyzes de Sitter holography proposals, including dS/CFT and mass/RG-flow interpretations, and develops a framework for defining de Sitter mass via holographic counterterms and a maximum mass conjecture. It then details the KKLT scenario for metastable de Sitter vacua, the role of fluxes and non-perturbative effects in moduli stabilization, and the ongoing quest for explicit realizations and realistic models. Finally, it discusses the string landscape and anthropic considerations, potential inflationary scenarios, and the remaining theoretical hurdles in achieving a fully realistic, small-positive cosmological constant within string theory.

Abstract

This article reviews recent developments in the study of universes with a positive cosmological constant in string theory.

Figures (2)

• Figure 1: (A) Global de Sitter space is a hyperboloid (see eq. \ref{['dsglobal']}). Time runs up and equal time sections are spheres. (B) Penrose diagram of de Sittter space. Horizons are dashed lines, Regions I (shaded) and II are the inflating and static patches respectively. The left boundary and the right boundary (marked N and S) are the north and south poles of the equal time sections of the global spacetime. The Euclidean surfaces at the top and bottom boundaries are future and past infinity. (C) de Sitter (dS) and Euclidean anti de Sitter (EAdS) are hyperboloids of revolution around the vertical axis. The two sheets with $|T|>|X|$ in the figure are both EAdS, while the lines with $|X| > |T|$ are part of a single hyperboloid of revolution around the $T$ axis that makes up global de Sitter as in (A). Note that EAdS and dS share the same asymptotic boundary structure as $|T|,|X| \to \infty$ and hence will share the same asymptotic isometry group.
• Figure 2: (A) General form for the potential for one Kahler modulus $\sigma$ after including non-perturbative corrections. The extremum gives a supersymmetric AdS vacuum (B) General form for the potential after breaking SUSY by addition of anti-D3 branes. The positive local extremum is a metastable de Sitter vacuum which decays by tunneling to the supersymmetric vacuum at large $\sigma$.