[Paper Review] The Anthropic Landscape of String Theory

Leonard Susskind|ArXiv.org|Feb 27, 2003

Black Holes and Theoretical Physics7 references580 citations

TL;DR

This paper proposes that string theory admits a vast landscape of metastable vacua—each with different vacuum energies and low-energy physics—due to the existence of an enormous number of compactifications with broken supersymmetry. The anthropic principle is invoked to explain the observed small cosmological constant, with de Sitter vacua defined as resonant states in a generalized S-matrix, suggesting that the universe's evolution is governed by tunneling between these vacua toward supersymmetric endpoints on the supermoduli space.

ABSTRACT

In this lecture I make some educated guesses, about the landscape of string theory vacua. Based on the recent work of a number of authors, it seems plausible that the lanscape is unimaginably large and diverse. Whether we like it or not, this is the kind of behavior that gives credence to the Anthropic Principle. I discuss the theoretical and conceptual issues that arise in developing a cosmology based on the diversity of environments implicit in string theory.

Motivation & Objective

• To address the observed small but non-zero cosmological constant, which cannot be explained by a unique vacuum in string theory.
• To argue that the landscape of string theory vacua is not just large but astronomically vast—on the order of googols or googolplexes—making the anthropic principle a necessary framework.
• To develop a theoretical framework for defining de Sitter vacua in quantum gravity, using scattering amplitudes and resonances despite their metastable nature.
• To reconcile the apparent irreversibility of cosmological evolution with the microscopic reversibility of quantum mechanics by modeling de Sitter phases as resonances in a generalized S-matrix.
• To explore the idea that the universe evolves through tunneling between vacua, ultimately approaching supersymmetric solutions on the supermoduli space in its far future and past.

Proposed method

• Model the landscape as a space of scalar fields (moduli) with a potential V(Φ), where minima correspond to vacua with distinct cosmological constants.
• Distinguish the supermoduli space (supersymmetric, V=0, flat) from the broader landscape (non-supersymmetric, V≠0, with hills and valleys).
• Treat metastable de Sitter vacua as resonances in a generalized S-matrix, using the concept of asymptotic states in causal patches.
• Use time-reversal symmetry and micro-reversibility to define initial and final states as time-reversed versions of each other, with the final state approaching the supermoduli space.
• Apply the idea of tunneling between vacua to describe cosmological evolution, with domain walls separating regions in different vacua.
• Consider the possibility that the initial and final states may not be four-dimensional, with compactification moduli rolling to infinity, leading to higher-dimensional universes.

Experimental results

Research questions

• RQ1 Why does the observed cosmological constant have such a small but non-zero value, and can this be explained within string theory?
• RQ2 What is the mathematical definition of a de Sitter vacuum in quantum gravity, given its metastable nature and lack of exact symmetry?
• RQ3 How can the apparent arrow of time in cosmology be reconciled with the microscopic reversibility of quantum mechanics?
• RQ4 Can the landscape of string theory vacua be described as a set of resonances in a generalized S-matrix, even though these vacua are not true ground states?
• RQ5 What is the role of the supermoduli space in the cosmological evolution of the universe, and how do causal patches evolve toward it?

Key findings

• The landscape of string theory vacua is expected to be astronomically large, with a number of metastable vacua on the order of googols or googolplexes, making the anthropic principle a necessary explanation for the observed cosmological constant.
• The cosmological constant is not uniquely determined by the theory but is instead a statistical outcome of the vast number of possible vacua, with the observed value being a rare but possible configuration.
• Metastable de Sitter vacua can be mathematically defined as resonances in a generalized S-matrix, providing a quantum mechanical description despite their instability.
• The final state of cosmological evolution is expected to be an open FRW universe approaching a point on the supermoduli space, corresponding to a supersymmetric, flat solution.
• The initial state of the universe, under time reversal, is expected to be the time-reversed version of such a final state, suggesting a symmetric role for initial and final asymptotic conditions in the S-matrix framework.
• The compactification moduli may roll to infinity in the far future or past, leading to higher-dimensional universes, implying that the initial and final states of the causal patch may not be four-dimensional.