[Paper Review] On the Limits of Effective Quantum Field Theory: Eternal Inflation, Landscapes, and Other Mythical Beasts

Tom Banks|arXiv (Cornell University)|Oct 28, 2019

Black Holes and Theoretical Physics86 references14 citations

TL;DR

This paper argues that Eternal Inflaton and the String Landscape—central concepts in modern effective quantum field theory (EQFT)—are not viable in a true theory of quantum gravity, but instead belong to the 'Swampland.' Using evidence from Matrix Theory, AdS/CFT, and black hole physics, Banks shows that EQFT's notion of metastable vacua and bubble nucleation fails in quantum gravity due to black hole formation and non-unitary S-matrices, implying that the landscape and eternal inflation are mathematical artifacts, not physical realities.

ABSTRACT

We recapitulate multiple arguments that Eternal Inflation, and the String Landscape are actually part of the Swampland: ideas in Effective Quantum Field Theory that do not have a counterpart in genuine models of Quantum Gravity.

Motivation & Objective

• To challenge the validity of Eternal Inflation and the String Landscape as physical frameworks in quantum gravity.
• To demonstrate that effective field theory's treatment of metastable vacua and bubble nucleation breaks down in quantum gravity due to black hole formation.
• To show that different points in moduli space do not represent distinct quantum states of a single Hamiltonian, contradicting EQFT assumptions.
• To argue that the S-matrix in Minkowski space is not unitary in Fock space due to IR divergences and failure of Borel summability in string perturbation theory.
• To reconcile the emergence of Minkowski space dynamics from AdS/CFT with the non-existence of a Fock space with infinite entropy in quantum gravity.

Proposed method

• Analyzes the Hilbert space structure of EQFT with finite spatial volume, showing that different vacuum states become orthogonal in the infinite volume limit.
• Applies Coleman-De Luccia instanton methods to gravitational tunneling, showing that bubble nucleation in dS space does not support eternal inflation.
• Uses AdS/CFT correspondence to study flat space scattering amplitudes via boundary CFT correlators, focusing on the arena construction and code subspace encoding.
• Applies the error-correcting code picture of bulk states in AdS/CFT to show that the Minkowski vacuum must be a maximally entropic state on the code subspace.
• Examines the role of soft gravitons and IR divergences in Fock space, showing that S-matrix elements vanish between Fock states due to entanglement with soft modes.
• Leverages Matrix Theory and HST to define a unitary state space in quantum gravity, contrasting it with the ill-defined Fock space of EQFT.

Experimental results

Research questions

• RQ1 Can the concept of eternal inflation be consistently realized in a quantum gravity framework?
• RQ2 Do different vacua in the String Landscape represent distinct quantum states of a single underlying Hamiltonian?
• RQ3 Is the S-matrix in Minkowski space unitary in the Fock space formalism, given IR divergences and non-Borel-summable amplitudes?
• RQ4 How does the AdS/CFT correspondence realize Minkowski space dynamics, and what does this imply for the Hilbert space structure of quantum gravity?
• RQ5 What is the role of black hole formation in invalidating the EQFT picture of vacuum decay via bubble nucleation?

Key findings

• Eternal inflation cannot be supported by quantum field theory in de Sitter space or by Coleman-De Luccia tunneling, as the assumption of equal probability per 4-volume for tunneling events lacks foundation.
• Field excursions larger than the Planck scale inevitably form black holes, making it impossible to create large regions with different vacuum expectation values via scattering.
• Different points in the moduli space of supersymmetric string models do not correspond to different quantum states of a single Hamiltonian, as high-energy scattering amplitudes differ significantly.
• The S-matrix in Minkowski space is not unitary in Fock space due to IR divergences and the failure of Borel summability in string perturbation theory, implying that Fock states are not the correct basis.
• In the AdS/CFT correspondence, the Minkowski vacuum is realized as a maximally entropic state on a finite-dimensional code subspace, consistent with the idea that quantum gravity has a finite-dimensional Hilbert space.
• The infinite entropy of the Minkowski vacuum is interpreted as a collection of soft gravitons, which entangle Fock states and prevent the existence of matrix elements between them.