Prague Sept 2018 INFLATION AND THE MULTIVERSE Remote regions beyond our horizon are strikingly different from what we observe here Review of inflation Multiverse scenario How can we test ID: 1025804
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1. Alex Vilenkin Tufts Institute of Cosmology Prague, Sept. 2018INFLATION AND THE MULTIVERSE
2. Remote regions beyond our horizon are strikingly different fromwhat we observe here.Review of inflationMultiverse scenarioHow can we test this?The multiverse picture that has emerged from inflationary cosmology.
3. InflationDuring inflation:Negative pressure (tension): “Slow roll” Our vacuum scalar field (inflaton) – fast, accelerated expansion in the early universeVV
4. InflationDuring inflation:Negative pressure (tension):Accelerated expansion: (repulsive gravity)Horizon distance: . “Slow roll” – scale factor. Our vacuum scalar field (inflaton) – fast, accelerated expansion in the early universeVV
5. timeInflationary scenario Inflation “Big bang”Start with a high-energy field region of size R > H-1.It expands by a huge factor.Field energy thermalizes into hot plasma.Explains some puzzling features of the big bang. Guth (1981); Linde (1982)Large-scale homogeneity and flatness.Small density perturbations.Mukhanov & Chibisov (1981)
6. Conditions for inflation “Slow roll” Our vacuum Slow roll:
7. Conditions for inflation “Slow roll” Our vacuum Slow roll:Conditions for slow roll: – Planck mass Planck units:
8. “Slow roll”Amount of inflation: We need .Number of e-folds:Amount of inflation
9. Variety of modelsSome of the predictions are robust & confirmed by the data: Flat large-scale geometry (at ~1% accuracy). Nearly scale-invariant spectrum of adiabatic, Gaussian density perturbations. WMAP, Planck,Galaxy surveysModels with multiple scalar fields.false vacuumScalar Field Energy Density “Slow roll” “Slow roll”Focus on this
10. Beyond the horizon: eternal inflation
11. In models where false vacuum decays through quantum tunneling:False vacuum “Bubble universes”false vacuumScalar Field Energy Density “Slow roll” You are hereInflation is eternal
12. Spacetime of a bubble universetxNucleationBubble wallBig bangA momentof timeWe cannot travel to other bubbles.Viewed from inside, each bubble is an infinite universe.
13. Bubbles of all types will be produced in the course of eternal inflation.Bousso & Polchinski (2000)Susskind (2003)The multiverseParticle theories with extra dimensions (including string theory) predict a vast landscape of vacua with diverse properties.
14. How can we test multiverse models?
15. This would be a direct test of eternal inflation.Bubble collisions can leave an imprint on the CMB (round hot spots).Chang, Kleban & Levi (2008)Feeney, Johnson, Mortlock & Peiris (2010)Polarization signal.Czech et.al. (2011)How can we test multiverse models?The search is now on…
16. This would be a direct test of eternal inflation.Bubble collisions can leave an imprint on the CMB (round hot spots).Chang, Kleban & Levi (2008)Feeney, Johnson, Mortlock & Peiris (2010)Polarization signal.Czech et.al. (2011)How can we test multiverse models?Indirect tests: Predicting the values of the constants of Nature The search is now on…
17. Constants of Nature:Appear to be fine-tunedfor our existence.Electron mass 0.00511 (in GeV)Higgs mass 125Neutrino mass < 10-9Planck mass 1019 Cosmological constant 10-46
18. Anthropic principle:We can live only in bio-friendlybubbles. This explains the fine-tuning.We can try to turn this into testable (statistical) predictions.
19. Anthropic principle:We can live only in bio-friendlybubbles. This explains the fine-tuning.Strategy:Find the probability distribution P(X) for the values of some parameter X measured by a randomly picked observer. Make a prediction for a range of X at a specified confidence level.This assumes we are typical observers: We can try to turn this into testable (statistical) predictions. P(X)XPrinciple of mediocrity.
20. The cosmological constantEnergy densityof our vacuumFrom particle physics:Observation:Riess et. al. (1998)Perlmutter et. al. (1998)Why is so small? – The cosmological constant problem.Why is ? – The coincidence problem.
21. The cosmological constantEnergy densityof our vacuumFrom particle physics:Observation:Riess et. al. (1998)Perlmutter et. al. (1998)Why is so small? – The cosmological constant problem.Why is ? – The coincidence problem. Fraction of volume (from particle physics and theory of inflation).In the multiverse:Number of observersper unit volume(in the range of interest).Anthropic range:Weinberg (1987)(All other parameters are fixed.)
22. “Drake equation”:Fraction of massin large galaxies Number of starsper unit mass# of observersper starNot very sensitive to .
23. “Drake equation”:Fraction of massin large galaxies Number of starsper unit mass# of observersper starPress & Schechter (1974)amplitude of density perturbations on galactic scale.During the matter era: . The distribution is peaked at y ~ 1.At domination ( ), y ~ 1 means Q ~ 1 galaxies are formed.This is close to the present epoch.Not very sensitive to .
24. Too fewgalaxiesUnnecessaryfine-tuning95%Explains the coincidence: is expected to dominate near the end of galaxy formation epoch.The agreement is better if extinctions by supernovae are takeninto account. Our first evidence for the multiverse?Weinberg (1987), A.V. (1995), Efstathiou (1995), Martel, Shapiro & Weinberg (1998)No alternative explanations.(Before measurement)Totani et al. (2018)
25. Too fewgalaxiesUnnecessaryfine-tuning95%Explains the coincidence: is expected to dominate near the end of galaxy formation epoch.The agreement is better if extinctions by supernovae are takeninto account. Our first evidence for the multiverse?The distribution for Q, Ne , etc. depends on our model of the multiverse. Weinberg (1987), A.V. (1995), Efstathiou (1995), Martel, Shapiro & Weinberg (1998)No alternative explanations.(Before measurement)Totani et al. (2018)
26. A GAUSSIAN MULTIVERSE
27. A simple model of landscape: a random Gaussian fieldThe landscape is characterized by thecorrelation function – N-dimensional field space.We shall assume (in Planck units).Masoumi, A.V. & Yamada (2017, 2018)e.g.,X
28. A simple model of landscape: a random Gaussian fieldThe landscape is characterized by thecorrelation function – N-dimensional field space.We shall assume (in Planck units).Masoumi, A.V. & Yamada (2017, 2018)e.g., Typical values:X Slow roll conditions are strongly violated.Inflation can occur only in rare regions where V’ and V” are very small in some direction – most likely near saddle points (V’ = 0) or inflection points (V” = 0).
29. XExpand the potential near inflaton trajectory: Other fields are dynamically important if .Typical smallest mass:Inflation is typically single-field.Yamada & A.V. (2018)No isocurvature fluctuations.Negligible non-Gaussianity.Single-field or multi-field inflation?
30. Inflection point inflation Inflectionpoint: V” = 0. Inflation range:
31. Inflection point inflation Inflectionpoint: V” = 0. Inflation range: The number of e-folds: Probability distribution for Ne:
32. The distribution for Gaussian variables can be expressed in terms of correlators :, where .etc. , and similar for . Probability of inflation with Ne e-folds:
33. Distribution for the amplitude of density fluctuations: (over a wide range of values and falls off beyond that range) The distribution for the spectral index ns is also consistent with the data.
34. SUMMARY Successful prediction of . Low-energy physics may be different in different bubbles. We can make statistical predictions. Inflation is a never ending process, with new “bubble universes” constantly being formed.A simple model of sub-Planckian random Gaussian landscape is consistent with the present data.
35. BLACK HOLES FROM THE MULTIVERSE
36. As the inflaton field “rolls” towards our vacuum, it may tunnel to another vacuum.Our vacuum
37. Scalar Field 1Energy DensityOurVacuumScalar Field 2Bubbles of a lower-energy vacuum nucleate and expand during the slow roll: . Coleman & De Luccia (1980) Bubble nucleation
38. Time of nucleation t = tn:At t > tn : Scale-invariant size distribution:Nucleation rate Bubble nucleation
39. What happens to the bubbles when inflation ends? MatterThe bubble wall initially expands relativistically relative to matter.It is quickly slowed down by particle scattering.An expanding relativistic shell of matter is formed (a shock wave).The bubble eventually comes within the horizon and collapses to a black hole. But there is more to the story…All bubbles are initially bigger than the horizon.
40. Matter What happens inside the bubble? Bubbles of radius collapse to a singularity.interior horizon
41. Matter What happens inside the bubble? Bubbles of radius collapse to a singularity.interior horizonIf the bubble expands to a radius , its interior begins to inflate:But the universe outside the bubble is expanding much slower.
42. Inflatingbaby universeExteriorFRW regionThe “wormhole” is seen as a black hole by exterior observers. Black holes of mass have inflating baby universes inside.
43. Penrose diagram FutureinfinityLight propagatesat 45o.ShockSome matter may follow the bubble into the wormhole. This changes the black hole mass. Need numerical simulations to determine Mbh. .
44. The affected region expands as . The universe outside of it is unperturbed.The size of this region when it comes within the horizon is .The largest BH that can fit into this region has mass Upper bound on BH mass
45. The baby universes will inflate eternally.Bubbles of all possible vacua, including ours, will be formed.Global structure of spacetime
46. 46 Linde (1988)The big picture
47. Black hole massDepending on microphysics, may take a wide range of values. M ~ Mmax (saturates the bound)Deng & A.V. (2018)
48. Mass distribution of black holesFraction of dark matter density in black holes of mass ~ M : Use and .
49. Mass distribution of black holes. – mass within the horizon at teq. Bubble nucleation rateFraction of dark matter density in black holes of mass ~ M : Minimal BH mass: . The mass distribution depends on 3 parameters: A discovery of black holes with the predicted distribution of masses would provide evidence for inflation – and for the multiverse.
50. Observational bounds1-Gamma-ray background from BH evaporation with .2-CMB spectral distortions by accreting BH with 123
51. BH merger rate observed by LIGO requires for .. Sasaki et al (2016) Accounting for LIGO observationsNote: BH produced by bubbles are non-rotating..
52. Supermassive black holes.The largest BH we can expect to find in a galaxy has mass .Early formation of massive halos.May have interesting signatures in CMB spectral distortions. . Deng, A.V. & Yamada (2018)
53. Vacuum bubbles may nucleate during inflation, leading to the formation of black holes with a wide spectrum of masses.These black holes have inflating universes inside.A discovery of black holes with the predicted distribution of masses would provide evidence for inflation – and for the multiverse.These BH might act as seeds for supermassive BH and might have formed the binaries LIGO is currently observing. Summary
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56. Numerical simulationsHeling Deng & A.V. (2017) Exterior region:Radiation fluid:– comoving coordinates.Assume that radiation cannot penetrate the bubble (reflecting b.c.). The bubble wall is at .
57. Distribution for the amplitude of density fluctuations: (over a wide range of values and falls off beyond that range) Combine this with the distribution for : Peaked at y ~ 1 dominates at the epoch of galaxy formation.Favors largervalues of Q.Q is likely to be near its largest anthropically allowed value.(Great extinctions on Earth occurred once in ~ 108 years, which is comparable to the time it took intelligent life to evolve.) The distribution for the spectral index ns is also consistent with the data.
58. Numerical simulationsHeling Deng & A.V. (2017) Exterior region:Radiation fluid:– comoving coordinates.Assume that radiation cannot penetrate the bubble (reflecting b.c.). The bubble wall is at .Interior region: de Sitter spaceIsrael’s matching conditions at the bubble wall. .
59. Shock propagationInitial density in the shocked region is
60. Shock propagationInitial density in the shocked region isIt drops to , but comes back to when the BH is formed.
61. Shock propagationAt later times the BH is surrounded by a thin overdense shell, followed by a thicker underdense shell, propagating in a nearly uniform radiation.The overall mass deficit in the shells is .
62. The measure problemAll possible values of any parameter X will be measured an infinite number of times in the course of eternal inflation.To find the probability distribution for X, we need to compare infinities.Probabilities can be defined by introducing a time cutoff. But the answers depend on the choice of “time” – which is largely arbitrary in GR.Source of the problem: the number of observers grows exponentially. Most of them are concentrated near the cutoff.Current statusMuch progress has been made in studying different measure proposals. Some were ruled out as they suffer from paradoxes.Measure from the fundamental theory?Holographic ideas; quantum cosmology.Garriga & A.V. Bousso, Freivogel et.al.Nomura