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Can the universe afford inflation?

Andreas Albrecht, Lorenzo Sorbo

TL;DR

The paper questions whether inflation is the most probable origin of our universe within a meta-universe framework. It first analyzes the Dyson–Kleban–Susskind (DKS) causal-patch approach, which makes inflation exponentially unlikely compared with non-inflationary Big Bang fluctuations. It then presents a semiclassical tunneling calculation, using established methods, that shows inflation to be exponentially favored over alternative histories, highlighting a tension between the two frameworks. The work emphasizes that reconciling these divergent results—potentially by refining ergodicity, measure, or quantum-gravity effects—could have profound implications for our understanding of the early universe and the role of inflation. Overall, the paper advances a concrete, testable contrast between competing initial-condition formalisms and calls for deeper theoretical development to resolve the discrepancy.

Abstract

Cosmic inflation is envisioned as the ``most likely'' start for the observed universe. To give substance to this claim, a framework is needed in which inflation can compete with other scenarios and the relative likelihood of all scenarios can be quantified. The most concrete scheme to date for performing such a comparison shows inflation to be strongly disfavored. We analyze the source of this failure for inflation and present an alternative calculation, based on more traditional semiclassical methods, that results in inflation being exponentially favored. We argue that reconciling the two contrasting approaches presents interesting fundamental challenges, and is likely to have a major impact on ideas about the early universe.

Can the universe afford inflation?

TL;DR

The paper questions whether inflation is the most probable origin of our universe within a meta-universe framework. It first analyzes the Dyson–Kleban–Susskind (DKS) causal-patch approach, which makes inflation exponentially unlikely compared with non-inflationary Big Bang fluctuations. It then presents a semiclassical tunneling calculation, using established methods, that shows inflation to be exponentially favored over alternative histories, highlighting a tension between the two frameworks. The work emphasizes that reconciling these divergent results—potentially by refining ergodicity, measure, or quantum-gravity effects—could have profound implications for our understanding of the early universe and the role of inflation. Overall, the paper advances a concrete, testable contrast between competing initial-condition formalisms and calls for deeper theoretical development to resolve the discrepancy.

Abstract

Cosmic inflation is envisioned as the ``most likely'' start for the observed universe. To give substance to this claim, a framework is needed in which inflation can compete with other scenarios and the relative likelihood of all scenarios can be quantified. The most concrete scheme to date for performing such a comparison shows inflation to be strongly disfavored. We analyze the source of this failure for inflation and present an alternative calculation, based on more traditional semiclassical methods, that results in inflation being exponentially favored. We argue that reconciling the two contrasting approaches presents interesting fundamental challenges, and is likely to have a major impact on ideas about the early universe.

Paper Structure

This paper contains 15 sections, 38 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Review of the DKS results
  3. The general scheme
  4. Problems for Inflation
  5. The reason for the problem
  6. An extension of DKS
  7. The generality of the problem for inflation
  8. The problem for the Standard Big Bang
  9. The problem according to DKS
  10. Extended DKS solves the SBB problem
  11. Boltzmann's Brain
  12. The semiclassical calculation
  13. Discussion and Conclusions
  14. Calculating Tunneling Rates
  15. Relationship to issues raised by Penrose and others

Figures (1)

  • Figure 1: The values of $F_I + F_O$ (top three curves) and $\hat{F}$ (the highly overlapping bottom curves) as a function of the rescaled mass parameter $\psi_S$ over the range $10^{-10} < \psi_S < \psi_{cr}$.The three values of the pair ($m_I/m_P$,$\lambda$) shown here are given by ($0.5$,$33.5$), ($0.1$,$838$), and ($0.05$,$3350$) in order of increasing $\psi_{cr}$. The main point of this figure is that $F_I + F_O \gg \hat{F}$ for all relevant values of $\psi_S$ for any realistic value of $\lambda$. More detailed features of this plot are discussed in the text.