Predictions in Eternal Inflation · 2015. 10. 1. · Introduction Eternal Inflation Anthropic...
Transcript of Predictions in Eternal Inflation · 2015. 10. 1. · Introduction Eternal Inflation Anthropic...
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