Predictions in Eternal Inflation

Chris Smeenk

University of Western OntarioDepartment of Philosophy

Rotman Institute

Historical / philosophical question 1What different lines of argument support Eternal Inflation (aka theMultiverse)? What is their character? How strong are they?

Historical / philosophical question 2What are the prospects for using fine-tuning problems as a guide (soleguide?) for developing fundamental physics and cosmology?

Anthropic PredictionsPrediction Pobs(αi) for parameter α (or set of parameters):

Probability distribution Pi(αi): variation of αi across themultiverse (ensemble of “pocket universes”)

“Typical” observer, chosen randomly from anthropic subset A

ChallengesTechnical: measure problem, dealing with ∞Philosophical: what is the evidential value of anthropicpredictions?

Anthropic PredictionsPrediction Pobs(αi) for parameter α (or set of parameters):

Probability distribution Pi(αi): variation of αi across themultiverse (ensemble of “pocket universes”)

“Typical” observer, chosen randomly from anthropic subset A

ChallengesTechnical: measure problem, dealing with ∞Philosophical: what is the evidential value of anthropicpredictions?

Outline

Claims about Anthropic Predictions- Compatibility check rather than strong evidence, contrast with

other cases of predictive success

- Weaker than other arguments in favor of Eternal Inflation

1 Routes to Eternal Inflation2 Anthropic Predictions3 Other Arguments for EI

Outline

Claims about Anthropic Predictions- Compatibility check rather than strong evidence, contrast with

other cases of predictive success

- Weaker than other arguments in favor of Eternal Inflation

1 Routes to Eternal Inflation2 Anthropic Predictions3 Other Arguments for EI

Introduction Eternal Inflation Anthropic Predictions Alternatives Summary

Routes to Eternal Inflation

Landscape Route

Compactification →multiple minima, “scan” Λ

Instability of dS to vacuumfluctuations, transition tolower minima

Inflationary Cosmology Route

Historically first (Vilenkin,Linde, ...)

Expansion ends locally

AssumptionSimilar accounts of global causal structure of universe.

Introduction Eternal Inflation Anthropic Predictions Alternatives Summary

Routes to Eternal Inflation

Landscape Route

Compactification →multiple minima, “scan” Λ

Instability of dS to vacuumfluctuations, transition tolower minima

Inflationary Cosmology Route

Historically first (Vilenkin,Linde, ...)

Expansion ends locally

AssumptionSimilar accounts of global causal structure of universe.

Introduction Eternal Inflation Anthropic Predictions Alternatives Summary

Routes to Eternal Inflation

Landscape Route

Compactification →multiple minima, “scan” Λ

Instability of dS to vacuumfluctuations, transition tolower minima

Inflationary Cosmology Route

Historically first (Vilenkin,Linde, ...)

Expansion ends locally

AssumptionSimilar accounts of global causal structure of universe.

Introduction Eternal Inflation Anthropic Predictions Alternatives Summary

Successes for Inflation

WMAP angular power spectrum (Spergel et al. 2006)

Uniformity

Flatness

Spectrum of densityperturbations (nearly scaleinvariant, Gaussian,adiabatic)

Consequences of dynamicalevolution of “inflaton,” scalarfield φ

Introduction Eternal Inflation Anthropic Predictions Alternatives Summary

Starting Inflation

Image from Guth (2007)

Stochastic Inflation- Fluctuations “up the hill” → continued expansion- Inflation never ends globally

Other Approaches- Tunneling and bubble nucleation; topological inflation

Introduction Eternal Inflation Anthropic Predictions Alternatives Summary

Starting Inflation

Image from Guth (2007)

Stochastic Inflation- Fluctuations “up the hill” → continued expansion- Inflation never ends globally

Other Approaches- Tunneling and bubble nucleation; topological inflation

Introduction Eternal Inflation Anthropic Predictions Alternatives Summary

Eternal Inflation

Pocket universes withdifferent low energyphysics

Variation depends onmechanism generatingpocket universes

Image: Andrei Linde

Introduction Eternal Inflation Anthropic Predictions Alternatives Summary

... what can we predict?

In an eternally inflating universe, anything that can happenwill happen; in fact, it will happen an infinite number oftimes. Thus, the question of what is possible becomes trivial— anything is possible, unless it violates some absoluteconservation law. To extract predictions from the theory, wemust therefore learn to distinguish the probable from theimprobable. (Guth 2007)

Introduction Eternal Inflation Anthropic Predictions Alternatives Summary

Exemplar: Weinberg on Λ

“What a typical observer (or other reference class) will measure forαi” (Principle of Mediocrity):

Pobs(αi) = N(αi)Pi(αi) (1)

Ingredients (cf. Aguirre 2007)- α: vary Λ, other parameters fixed

- N(α) =: normalized number of large gravitationally bound systems (proxy forobservers); only non-zero in small window, due to Λ’s effect on structureformation

- Pi(α) =: prior probability; expect this to be uniform, because anthropically

allowed region small compared to particle physics energy scales

Introduction Eternal Inflation Anthropic Predictions Alternatives Summary

Anthropic Prediction vs. QFT Calculation

Anthropic Prediction

Vacuum energy density close to:

ρv = 13.3ρm

(cf. Martel et al. 1998, Vilenkin 2007,

updated parameters)

Observed value: ρv = 2.3ρm.Probability = .156!

QFT calculation of vacuumenergy

Λ: quartically divergent,radiative corrections

120 orders of magnitude!

Introduction Eternal Inflation Anthropic Predictions Alternatives Summary

Anthropic Prediction vs. QFT Calculation

Anthropic Prediction

Vacuum energy density close to:

ρv = 13.3ρm

(cf. Martel et al. 1998, Vilenkin 2007,

updated parameters)

Observed value: ρv = 2.3ρm.Probability = .156!

QFT calculation of vacuumenergy

Λ: quartically divergent,radiative corrections

120 orders of magnitude!

Introduction Eternal Inflation Anthropic Predictions Alternatives Summary

Measure on the Multiverse

Evaluating N(α), Pi(α)

- Implicit choice of measure µ

- What is assigned “equal measure”: spacetime volume, “pocket”universe, length of world-line, ... ?

Measure Problem- Multiverse ensemble Σ and measure µ

- Uniqueness: Causal structure sufficient to constrain µ?- Probabilities:

· non-normalizable µ(Σ) = ∞, recover probabilities viaregularization (limiting procedure)?

· conditional probabilities (conglomerability)?

Introduction Eternal Inflation Anthropic Predictions Alternatives Summary

Measure on the Multiverse

Evaluating N(α), Pi(α)

- Implicit choice of measure µ

- What is assigned “equal measure”: spacetime volume, “pocket”universe, length of world-line, ... ?

Measure Problem- Multiverse ensemble Σ and measure µ

- Uniqueness: Causal structure sufficient to constrain µ?- Probabilities:

· non-normalizable µ(Σ) = ∞, recover probabilities viaregularization (limiting procedure)?

· conditional probabilities (conglomerability)?

Introduction Eternal Inflation Anthropic Predictions Alternatives Summary

Example

Figure: Vilenkin 2006

Introduction Eternal Inflation Anthropic Predictions Alternatives Summary

Debates regarding Measures

Desiderata for Measure

Independent of InitialConditions

“Calculable” (NO(αi))

Foliation-independent

...

Paradoxes

Youngness paradox

Q catastrophe

Boltzmann brains / freakobservers

...

State of the Debate (?)- “Testing” different proposed measures by considering paradoxes

- Disagreement regarding desiderata(e.g., Aguirre et al. 2007; Winitzki 2009; Freivogel 2011; Vilenkin)

Assume that a suitable µ has been found ...- Agreement on list of desiderata for µ

- Uncontroversially satisfies all desiderata

... what would we then be able to discover about EI?

Assume that a suitable µ has been found ...- Agreement on list of desiderata for µ

- Uncontroversially satisfies all desiderata

... what would we then be able to discover about EI?

From Measure to ProbabilityWhat justifies “equal measure with respect to µ” → equal probability?

Objective Probabilities- “Phase space measure” µ (Gibbons, Hawking and Stewart 1987;

Ashtekar and Sloan 2011; Schiffrin and Wald 2012)- Statistical mechanics arguments connecting µ to physical

probability 9 cosmologyEpistemic Probabilities

- SSA: cosmologists should reason as if they are “typical” (w/r/t µ)among reference class A

- Dependent on reference class

From Measure to ProbabilityWhat justifies “equal measure with respect to µ” → equal probability?

Objective Probabilities- “Phase space measure” µ (Gibbons, Hawking and Stewart 1987;

Ashtekar and Sloan 2011; Schiffrin and Wald 2012)- Statistical mechanics arguments connecting µ to physical

probability 9 cosmology

Epistemic Probabilities- SSA: cosmologists should reason as if they are “typical” (w/r/t µ)

among reference class A- Dependent on reference class

From Measure to ProbabilityWhat justifies “equal measure with respect to µ” → equal probability?

Objective Probabilities- “Phase space measure” µ (Gibbons, Hawking and Stewart 1987;

Ashtekar and Sloan 2011; Schiffrin and Wald 2012)- Statistical mechanics arguments connecting µ to physical

probability 9 cosmologyEpistemic Probabilities

- SSA: cosmologists should reason as if they are “typical” (w/r/t µ)among reference class A

- Dependent on reference class

Introduction Eternal Inflation Anthropic Predictions Alternatives Summary

Value of Anthropic Predictions

Multiverse ensemble Σ

- How does this differ from “random” ensemble – “anything goes”(variation of all parameters αi)?

Measure µ

- Well-motivated? (Jerry-mandering to insure correct predictions)- Unique? (Testing measure + theory, or theory)

Anthropic subset A- Σ|A ≈ Σ ′|A?- Extent of anthropic subset: isolated “islands” in parameter space

Introduction Eternal Inflation Anthropic Predictions Alternatives Summary

Value of Anthropic Predictions

Multiverse ensemble Σ

- How does this differ from “random” ensemble – “anything goes”(variation of all parameters αi)?

Measure µ

- Well-motivated? (Jerry-mandering to insure correct predictions)- Unique? (Testing measure + theory, or theory)

Anthropic subset A- Σ|A ≈ Σ ′|A?- Extent of anthropic subset: isolated “islands” in parameter space

Introduction Eternal Inflation Anthropic Predictions Alternatives Summary

Value of Anthropic Predictions

Multiverse ensemble Σ

- How does this differ from “random” ensemble – “anything goes”(variation of all parameters αi)?

Measure µ

- Well-motivated? (Jerry-mandering to insure correct predictions)- Unique? (Testing measure + theory, or theory)

Anthropic subset A- Σ|A ≈ Σ ′|A?- Extent of anthropic subset: isolated “islands” in parameter space

Introduction Eternal Inflation Anthropic Predictions Alternatives Summary

Generic PredictionsAnthropic predictions “robust” to changes in Σ, µ,A

... vice rather than virtue. Do not support specific multiversetheory in detail, as opposed to compatibility check of generalproposal.

On the Importance of Being ExactContrast with exemplary historical cases:

Successful predictions quantitatively sharp

Relationship to phenomena tightly constrains theory

Introduction Eternal Inflation Anthropic Predictions Alternatives Summary

Generic PredictionsAnthropic predictions “robust” to changes in Σ, µ,A... vice rather than virtue. Do not support specific multiversetheory in detail, as opposed to compatibility check of generalproposal.

On the Importance of Being ExactContrast with exemplary historical cases:

Successful predictions quantitatively sharp

Relationship to phenomena tightly constrains theory

Introduction Eternal Inflation Anthropic Predictions Alternatives Summary

Generic PredictionsAnthropic predictions “robust” to changes in Σ, µ,A... vice rather than virtue. Do not support specific multiversetheory in detail, as opposed to compatibility check of generalproposal.

On the Importance of Being ExactContrast with exemplary historical cases:

Successful predictions quantitatively sharp

Relationship to phenomena tightly constrains theory

Introduction Eternal Inflation Anthropic Predictions Alternatives Summary

Alternative Arguments for EI

1 Metaphysical2 Theoretical Consequence3 Eliminative

Introduction Eternal Inflation Anthropic Predictions Alternatives Summary

Metaphysical Argument

Mathematical Universe Hypothesis (e.g., Tegmark 2007)

MUH: “Our external physical reality is a mathematical structure”

MUH → multiverse hierarchy, including EI (among all otherconsistent mathematical structures!)

As a defense of EI?Depends on contentious views regarding application ofmathematics, metaphysics

EI and empirical results in cosmology need not play any role

Introduction Eternal Inflation Anthropic Predictions Alternatives Summary

Metaphysical Argument

Mathematical Universe Hypothesis (e.g., Tegmark 2007)

MUH: “Our external physical reality is a mathematical structure”

MUH → multiverse hierarchy, including EI (among all otherconsistent mathematical structures!)

As a defense of EI?Depends on contentious views regarding application ofmathematics, metaphysics

EI and empirical results in cosmology need not play any role

Introduction Eternal Inflation Anthropic Predictions Alternatives Summary

Indirect Argument

Implied by Successful Theory?“Inflation is generically eternal”

- What is the domain of validity of theoretical calculations of onsetof inflation?

- Validity of semi-classical picture of EI?

String theory and the landscape

Introduction Eternal Inflation Anthropic Predictions Alternatives Summary

Indirect Argument

Implied by Successful Theory?“Inflation is generically eternal”

- What is the domain of validity of theoretical calculations of onsetof inflation?

- Validity of semi-classical picture of EI?

String theory and the landscape

Introduction Eternal Inflation Anthropic Predictions Alternatives Summary

Indirect Argument

Implied by Successful Theory?“Inflation is generically eternal”

- What is the domain of validity of theoretical calculations of onsetof inflation?

- Validity of semi-classical picture of EI?

String theory and the landscape

Introduction Eternal Inflation Anthropic Predictions Alternatives Summary

Eliminative ArgumentHow often have I said to you that when you have eliminated theimpossible, whatever remains, however improbable, must be thetruth? (Sherlock Holmes)

Introduction Eternal Inflation Anthropic Predictions Alternatives Summary

Eliminative ArgumentHow often have I said to you that when you have eliminated alldynamical solutions to the cosmological constant problem asimpossible, whatever remains — the multiverse — howeverimprobable, must be the truth?

Introduction Eternal Inflation Anthropic Predictions Alternatives Summary

Eliminative Arguments

Question 1: complete list of suspects?- Explore space of possible theories- Example: PPN formulation of solar system tests of GR

Question 2: criteria for elimination?- Empirical anomalies or logical inconsistencies- Heuristics: naturalness

Introduction Eternal Inflation Anthropic Predictions Alternatives Summary

Eliminative Arguments

Question 1: complete list of suspects?- Explore space of possible theories- Example: PPN formulation of solar system tests of GR

Question 2: criteria for elimination?- Empirical anomalies or logical inconsistencies- Heuristics: naturalness

Introduction Eternal Inflation Anthropic Predictions Alternatives Summary

What different lines of argument support Eternal Inflation?

Anthropic predictions as compatibility check, not detailedpositive evidence.

Other lines of argument: consequence of inflation / string theory;eliminative argument. Explicitly theoretical.

Introduction Eternal Inflation Anthropic Predictions Alternatives Summary

Fine-tuning problems as a guide for developing physics andcosmology?

Some features of fundamental physics as “environmental:”legitimate explanatory stopping point

Not sufficient to support development and refinement of theories