[Paper Review] Heretics of the False Vacuum: Gravitational Effects On and Of Vacuum Decay 2

Tom Banks|ArXiv.org|Nov 18, 2002

Cosmology and Gravitation Theories24 references62 citations

TL;DR

This paper reevaluates vacuum decay in quantum gravity, arguing that decay into stable flat or anti-de Sitter (AdS) vacua is inconsistent due to gravitational effects like Big Crunch singularities. Instead, vacuum decay generically leads to open Friedmann-Robertson-Walker (FRW) cosmologies, and dS-to-dS transitions may occur via thermal-like instantons, challenging the standard instanton picture in effective field theory.

ABSTRACT

This paper reexamines the question of vacuum decay in theories of quantum gravity. In particular it suggests that decay into stable flat or AdS vacua, never occurs. Instead, vacuum decay occurs, if at all, into a cosmological spacetime. If the latter has negative cosmological constant, it undergoes a Big Crunch, which suggests that the whole picture is inconsistent. The question of decay of de Sitter space must be very carefully defined.

Motivation & Objective

• To re-express the concept of false vacuum decay within a full theory of quantum gravity, challenging assumptions from effective field theory.
• To address the inconsistency of decay into stable flat or AdS vacua due to gravitational collapse (e.g., Big Crunch singularities).
• To examine whether dS-to-dS vacuum decay can be consistently defined, especially in light of quantum mechanics and observer dependence.
• To assess whether decay into open FRW universes with vanishing or negative cosmological constant can be physically viable in quantum gravity.
• To critique the widespread use of the thin-wall approximation and instanton methods in vacuum decay studies, arguing they obscure deeper gravitational constraints.

Proposed method

• Reinterprets Coleman-De Luccia (CDL) instanton solutions in the context of full quantum gravity, focusing on global spacetime structure.
• Analyzes the gravitational backreaction of bubble nucleation, showing that the true vacuum is not maximally symmetric but an open FRW spacetime.
• Applies the principle of Asymptotic Darkness and results from asymptotically AdS quantum gravity to question the validity of the effective potential formalism.
• Considers observer-dependent interpretations of instantons, especially in dS space, to address quantum mechanical consistency.
• Evaluates the number of observable states in the resulting spacetimes to assess whether decay is physically meaningful (e.g., requiring more states in the true vacuum).
• Uses cosmological solutions with negative cosmological constant to argue that Big Crunch singularities signal inconsistency in decay into AdS vacua.

Experimental results

Research questions

• RQ1 Can vacuum decay into a stable flat or AdS vacuum occur in a consistent theory of quantum gravity?
• RQ2 What is the correct global spacetime geometry of the true vacuum resulting from false vacuum decay in the presence of gravity?
• RQ3 Is dS-to-dS vacuum decay consistent with quantum mechanics, especially given the finite state count in dS space?
• RQ4 How do observer-dependent interpretations and measurement theory affect the meaning of CDL instantons in dS spacetime?
• RQ5 To what extent is the effective potential formalism, used in instanton calculations, valid in full quantum gravity?

Key findings

• Decay into stable flat or AdS vacua does not occur in consistent quantum gravity due to gravitational collapse into a Big Crunch singularity.
• The true vacuum resulting from decay is generically an open FRW cosmology, not a maximally symmetric spacetime, contradicting the thin-wall approximation.
• dS-to-dS transitions may occur via thermal-like instantons, but their interpretation is highly observer-dependent and raises foundational quantum gravity questions.
• The number of observable states in the resulting open FRW universe must exceed that in the false vacuum for decay to be physically meaningful, which holds for a range of parameters.
• The effective potential formalism underlying instanton calculations has limited applicability in quantum gravity, especially in asymptotically AdS or dS spacetimes.
• The thin-wall approximation misrepresents the global geometry and leads to misleading conclusions about vacuum decay in quantum gravity.