Probing Inflation with CMB Polarization

Transcription

1 Probing Inflation with CMB Polarization Daniel Baumann High Energy Theory Group Harvard University Chicago, July 2009

2 How likely is it that B-modes exist at the r=0.01 level? the organizers Daniel Baumann High Energy Theory Group Harvard University Chicago, July 2009

3 I don t know! Daniel Baumann High Energy Theory Group Harvard University Chicago, July 2009

4 What can we learn from a B-mode detection at the r=0.01 level? Daniel Baumann High Energy Theory Group Harvard University Chicago, July 2009

5 Based on CMBPol Mission Concept Study: Probing Inflation with CMB Polarization Daniel Baumann, Mark G. Jackson, Peter Adshead, Alexandre Amblard, Amjad Ashoorioon, Nicola Bartolo, Rachel Bean, Maria Beltran, Francesco de Bernardis, Simeon Bird, Xingang Chen, Daniel J. H. Chung, Loris Colombo, Asantha Cooray, Paolo Creminelli, Scott Dodelson, Joanna Dunkley, Cora Dvorkin, Richard Easther, Fabio Finelli, Raphael Flauger, Mark P. Hertzberg, Katherine Jones-Smith, Shamit Kachru, Kenji Kadota, Justin Khoury, William H. Kinney, Eiichiro Komatsu, Lawrence M. Krauss, Julien Lesgourgues, Andrew Liddle, Michele Liguori, Eugene Lim, Andrei Linde, Sabino Matarrese, Harsh Mathur, Liam McAllister, Alessandro Melchiorri, Alberto Nicolis, Luca Pagano, Hiranya V. Peiris, Marco Peloso, Levon Pogosian, Elena Pierpaoli, Antonio Riotto, Uros Seljak, Leonardo Senatore, Sarah Shandera, Eva Silverstein, Tristan Smith, Pascal Vaudrevange, Licia Verde, Ben Wandelt, David Wands, Scott Watson, Mark Wyman, Amit Yadav, Wessel Valkenburg, and Matias Zaldarriaga White Paper of the Inflation Working Group arxiv:

6 Outline PART 1: THE PRESENT 1. Classical Dynamics of Inflation 2. Quantum Fluctuations from Inflation 3. Current Observational Evidence PART 2: THE FUTURE 1. B-modes 2. Non-Gaussianity

7 Part 1: THE PRESENT

8 Inflation The Quantum Origin of Structure in the Early Universe

9 Inflation Guth (1980) A period of accelerated expansion ä>0 ds 2 = dt 2 a(t) 2 dx 2 sourced by a nearly constant energy density ä a =(H2 + Ḣ) > 0 H = ρ 3 const. and negative pressure ä a = ρ 6 (1 + 3w) > 0 w< 1 3

10 Inflation Guth (1980) A period of accelerated expansion =0 solves the horizon and flatness problems i.e. explains why the universe is so large and old! H 1 horizon creates a nearly scale-invariant spectrum of primordial fluctuations 0 stretches microscopic scales to superhorizon sizes correlates spatial regions over apparently acausal distances time

11 The Shrinking Hubble Sphere The comoving horizon shrinks during inflation and grows after inflation comoving scales (ah) 1 a 1 2 (1+3w) (ah) 1 w< 1 3 w> 1 3 today time inflation reheating hot big bang

12 Goodbye and Hello-again large-scale correlations can be set up causally! comoving scales horizon exit horizon re-entry (ah) 1 sub-horizon super-horizon sub-horizon k 1 today time inflation reheating hot big bang

13 Conditions for Inflation negative pressure w < 1 3 d(ah) 1 dt shrinking comoving horizon accelerated expansion < 0 ä > 0 at the heart of the solution of the horizon and flatness problems and crucial for the generation of perturbations

14 What is the Physics of the Inflationary Expansion?

15 We don t know! This is why we are here!

16 Classical Dynamics Parameterize the decay of the inflationary energy by a scalar field Lagrangian inflation L = 1 2 ( φ)2 V (φ) ɛ M 2 pl 2 ( V V η Mpl 2 V A flat potential drives acceleration slow-roll conditions ɛ, η < 1 V ) 2 end of inflation clock Linde (1982) Albrecht and Steinhardt (1982)

17 Quantum Dynamics Quantum fluctuations lead to a local time delay in the end of inflation and density fluctuations after reheating δρ reheating

18 Zeta in the Sky inflaton fluctuations δφ reheating curvature perturbations on uniform density hypersurfaces ζ density perturbations δρ CMB anisotropies T

19 Zeta in the Sky curvature perturbations on uniform density hypersurfaces ds 2 = dt 2 a 2 (t) e 2ζ(t,x) dx 2 gauge-invariant freeze on super-horizon scales!

20 Zeta in the Sky curvature perturbation on uniform density hypersurfaces ds 2 = dt 2 a 2 (t) e 2ζ(t,x) dx 2 two-point correlation function ζ(x)ζ(x ) power spectrum evaluated at horizon crossing ζ k ζ k = (2π) 3 δ(k + k ) P ζ (k)

21 The Inverse Problem comoving scales (ah) 1 k 1 inflation reheating hot big bang today time DB: TASI Lectures on Inflation (2009)

22 The Inverse Problem comoving scales (ah) 1 ˆζ k sub-horizon zero-point fluctuations k 1 inflation reheating hot big bang today time DB: TASI Lectures on Inflation (2009)

23 The Inverse Problem comoving scales (ah) 1 ˆζ k sub-horizon zero-point fluctuations ζ k ζ k k 1 horizon exit inflation reheating hot big bang today time DB: TASI Lectures on Inflation (2009)

24 The Inverse Problem comoving scales (ah) 1 ζ 0 sub-horizon ζ k ζ k super-horzion k 1 ˆζ k zero-point fluctuations horizon exit today time inflation reheating hot big bang DB: TASI Lectures on Inflation (2009)

25 observed comoving scales The Inverse Problem predicted by inflation ζ 0 horizon re-entry (ah) 1 ˆζ k sub-horizon zero-point fluctuations ζ k ζ k super-horzion transfer function T projection C l k 1 horizon exit CMB recombination today time inflation reheating hot big bang DB: TASI Lectures on Inflation (2009)

26 observed comoving scales The Inverse Problem predicted by inflation ζ 0 horizon re-entry (ah) 1 ˆζ k sub-horizon zero-point fluctuations ζ k ζ k super-horzion transfer function T projection C l k 1 horizon exit CMB recombination today time inflation reheating hot big bang DB: TASI Lectures on Inflation (2009)

27 Prediction from Inflation Scalar Fluctuations 2 s k3 2π 2 P ζ(k) = ( H 2π ) 2 ( Ḣ φ ) 2 δφ δφ ζ de Sitter fluctuations evaluated at horizon crossing conversion k = ah

28 Prediction from Inflation Scalar Fluctuations 2 s k3 2π 2 P ζ(k) = ( H 2π ) 2 ( Ḣ φ ) 2 how the power is distributed over the scales is determined by the expansion history during inflation H(t) scale-dependence 2 s = A s k n s 1 e.g. slow-roll inflation n s 1=2η 6ɛ

29 Prediction from Inflation Scalar Fluctuations 2 s k3 2π 2 P ζ(k) = ( H 2π ) 2 ( Ḣ φ ) 2 Different shapes for the inflationary potential reheating 0 2πf lead to slightly different predictions!

30 Observations

31 Flatness Observational Evidence Inflation predicts WMAP sees 1 Ω k = 0 (±10 5 ) < Ω k < WMAP 5yrs.+BAO: 95% C.L.

32 Observational Evidence Scalar Fluctuations Inflation predicts percent-level deviations from n s =1 WMAP sees n s = σ n s =1 away from

33 Observational Evidence Scalar Fluctuations Inflation predicts Gaussian and Adiabatic Fluctuations WMAP sees Gaussian and Adiabatic Fluctuations

34 Observational Evidence Scalar Fluctuations Inflation predicts Correlations of Superhorizon Fluctuations WMAP sees Correlations of Superhorizon Fluctuations at Recombination temperature-polarization (l + 1)C l T E /2π [µk 2 ] cross-correlation θ > 1 Multipole moment

35 Fingerprints of the Early Universe We have only just begun to probe the fluctuations created by inflation: Scalar Fluctuations density fluctuations Tensor Fluctuations detected hints of scale-dependence superhorizon nature confirmed first constraints on Gaussianity and Adiabaticity not yet detected gravitational waves The next decade of experiments will be tremendously exciting!

36 Part 2: THE FUTURE

37 How can we probe the Physical Origin of Inflation?

38 How do we constrain the Inflationary Action? like in all of physics we ultimately want to know the action L = f [ ( φ) 2, ( ψ) 2, φ,... ] V (φ, ψ) field content potential, kinetic terms interactions symmetries couplings to gravity etc.

39 How do we constrain the Inflationary Action? like in all of physics we ultimately want to know the action minimal models: single-field slow-roll L = 1 2 ( φ)2 V (φ) Gaussian fluctuations A s shape all information in Scalars n s α s V V, V V, V V power spectra scale! Tensors A t V

40 How do we constrain the Inflationary Action? minimal models: single-field slow-roll like in all of physics we ultimately want to know the action non-minimal models: - non-minimal coupling to gravity - multiple fields - higher-derivative interactions fluctuations can be non-gaussian and non-adiabatic information beyond the power spectra bispectrum, trispectum, etc.

41 How do we constrain the Inflationary Action? like in all of physics we ultimately want to know the action What do different parameter regimes for observables teach us about high-energy physics? e.g. r>0.01 large tensors f local NL > 1 large non-gaussianity (this talk) (the coffee break)

42 Primordial Gravitational Waves

43 Tensors Besides scalar fluctuations inflation produces tensor fluctuations: ds 2 = dt 2 a 2 (t)(1 + h ij )dx i dx j 2 t (k) = 8 ( H ) 2 gravitational waves massless gravitons M 2 pl 2π de Sitter fluctuations of any light field robust prediction of inflation!

44 Tensors The tensor-to-scalar ratio r 2 t 2 s is model-dependent because scalars are! 2 s (k) = ( H 2π ) 2 ( Ḣ φ ) 2 strong model-dependence!

45 Tensors The tensor-to-scalar ratio r 2 t 2 s is model-dependent because scalars are! In contrast, The prediction for tensors is simple and the same in all models! 2 t H 2

46 Detecting Tensors via B-modes

47 E- and B-modes Polarization is a rank-2 tensor field. One can decompose it into a divergence-like E-mode and a vorticity-like B-mode. E-mode B-mode

48 Seljak and Zaldarriaga, Kamionkowski et al. The B-mode Theorem B-modes are only created by gravitational waves (tensor modes not scalar modes!) ζ scalars h ij tensors E > 0 B > 0 E < 0 B < 0

49 Seljak and Zaldarriaga, Kamionkowski et al. The B-mode Theorem ζ h ij Challinor

50 Seljak and Zaldarriaga, Kamionkowski et al. The B-mode Theorem B-modes are only created by gravitational waves (tensor modes not scalar modes!) Detection of primordial B-modes is often considered a smoking gun of inflation. So far only upper-limits, but many experiments now in Komatsu et al. (2008) WMAP 5 yrs. r<0.22 tensor-to-scalar ratio operation or in planning.

51 DB and Zaldarriaga Superhorizon B-modes C B(θ) [mk 2 ] unambiguous signature of inflation! θ [ ] -1-2 superhorizon at recombination like the TE test for superhorizon scalars Spergel and Zaldarriaga

52 B-modes as a Probe of High-Energy Physics

53 Energy Scale of Inflation Tensors measure the energy scale of inflation ( r ) 1/4 E inf V 1/4 = GeV 0.01 Single most important data point about inflation! r > 0.01 If we observe tensors it proves that inflation occurred at the GUT-scale!

54 Energy Scale of Inflation Tensors measure the energy scale of inflation ( r ) 1/4 E inf V 1/4 = GeV 0.01 Single most important data point about inflation! r > 0.01 It is hard to overstate the importance of such a result for the high-energy physics community which currently only has two indirect clues about physics at that scale: 1. Apparent Unification of Gauge Couplings 2. Lower Bound on the Proton Lifetime

55 The Lyth Bound tensors scalars 2 t (k) = 8 M 2 pl ( H 2π ) 2 2 s (k) = ( H 2π ) 2 ( Ḣ φ ) 2 tensor-to-scalar ratio r 2 t 2 s where =8 ( dφ dn e 1 M pl ) 2 dn e Hdt = d ln a

56 The Lyth Bound tensor-to-scalar ratio r 2 t 2 s =8 ( dφ dn e 1 M pl ) 2 field evolution over 60 e-folds φ M pl ( r 0.01 ) 1/2

57 The Lyth Bound φ M pl ( r 0.01 ) 1/2 If we observe tensors it proves r > 0.01 that the inflaton field moved over a super-planckian distance! φ M pl

58 The Lyth Bound i.e. we require a smooth potential over a range φ M pl few M pl But, in an effective field theory with cutoff Λ <M pl Λ we generically don t expect a smooth potential over a super-planckian range

59 Effective Field Theory E M pl UV-completion e.g. string theory M s M KK M X M susy M Y Λ low-energy EFT H m φ

60 Effective Field Theory E If we know the complete theory: integrate out heavy fields M>Λ UV-completion e.g. string theory M pl M s M KK M X M susy V (φ, ψ) V eff (φ) Λ M Y low-energy EFT H m φ

61 Effective Field Theory E If we know the complete theory: integrate out heavy fields M>Λ low-energy effective potential receives (computable) corrections UV-completion e.g. string theory Λ M pl M s M KK M X M susy M Y V = O δ M δ 4 low-energy EFT H m φ

62 Effective Field Theory E If we know the complete theory: integrate out heavy fields M>Λ low-energy effective potential receives (computable) corrections UV-completion e.g. string theory Λ M pl M s M KK M X M susy M Y Typically, we don t know the complete theory: low-energy EFT H m φ parameterize our ignorance about the UV, i.e. add all corrections consistent with symmetries. V = δ O δ Λ δ 4 Wilson

63 Large-Field Inflation UV sensitivity of inflation is especially strong in any model with observable gravitational waves

64 Large-Field Inflation 1. No Shift Symmetry in the UV Effective Field Theory with Cutoff Λ <M pl ) 2p V eff (φ) = 1 2 m2 φ λφ4 + λ p φ 4 ( φ Λ p=1 we generically don t expect a smooth potential over a super-planckian range Λ

65 Large-Field Inflation 2. Shift Symmetry in the UV If the action is invariant under φ φ + const. then the dangerous corrections are forbidden by symmetry ) 2p V eff (φ) = 1 2 m2 φ λφ4 + λ p φ 4 ( φ Λ p=1

66 Large-Field Inflation 2. Shift Symmetry in the UV φ φ + const. With such a shift symmetry chaotic inflation is technically natural e.g. V eff (φ) = 1 2 m2 φ 2 few M pl

67 Large-Field Inflation 2. Shift Symmetry in the UV Seeing B-modes would show that the inflaton field respected a shift symmetry up to the Planck scale! We know fields with that property: axions 1 1 The first controlled large-field models using axions have recently been constructed in string theory.

68 Large-Field vs. Small-Field

69 Small-Field φ M pl Primordial B-modes undetectable The Patch Problem For inflation to start the inflaton field has to be homogeneous over a distance that is a few times the horizon size at that time! H 1 physical horizon Since H 1 r 1/2 homogeneous patch L>H 1 this seems to be a bigger problem for small-field (low-r) models.

70 Small-Field φ M pl Primordial B-modes undetectable The Patch Problem The Overshoot Problem For inflation to start the field has to reach the flat part of the potential with small speed. φ V 1/2 overshoot This problem is worse for smallfield (low-r) models.

71 Small-Field φ M pl Primordial B-modes undetectable The Patch Problem The Overshoot Problem Fine-Tuned Potentials Boyle, Steinhardt and Turok (2005) ɛ =1 ɛ 1 For single-field models the transition φ end φ cmb r = 16 ɛ 1 ɛ =1 within 60 e-folds requires fine-tuned potentials!

72 Small-Field φ M pl Primordial B-modes undetectable The Patch Problem The Overshoot Problem Fine-Tuned Potentials These qualitative fine-tuning problems of smallfield inflation are hard to quantify! Typically, the arguments run into the illunderstood measure problem!

73 Small-Field φ M pl Primordial B-modes undetectable The Patch Problem The Overshoot Problem Fine-Tuned Potentials Large-Field φ M pl Primordial B-modes detectable! Potentials are Simple Functions e.g. V (φ) = 1 2 m2 φ 2 but are corrections under control?

74 Small-Field φ M pl Primordial B-modes undetectable The Patch Problem The Overshoot Problem Large-Field φ M pl Primordial B-modes detectable! Potentials are Simple Functions Attractor Solutions Fine-Tuned Potentials

75 Small-Field φ M pl Primordial B-modes undetectable The Patch Problem The Overshoot Problem Fine-Tuned Potentials Large-Field φ M pl Primordial B-modes detectable! Potentials are Simple Functions Attractor Solutions Improved Initial Conditions

76 Small-Field φ M pl Primordial B-modes undetectable The Patch Problem The Overshoot Problem Fine-Tuned Potentials Large-Field φ M pl Primordial B-modes detectable! Potentials are Simple Functions Attractor Solutions Improved Initial Conditions A convincing argument that the tensor amplitude has to be large does NOT exist! HOWEVER, there is also no convincing argument that it has to be small!

77 Small-Field φ M pl Primordial B-modes undetectable The Patch Problem The Overshoot Problem Fine-Tuned Potentials Large-Field φ M pl Primordial B-modes detectable! Potentials are Simple Functions Attractor Solutions Improved Initial Conditions My prediction: Before we (theorists) come up with such an argument, YOU will have DETECTED B-modes!

78 Conclusions

79 How likely is it that B-modes exist at the r=0.01 level? 50% The Wagner Principle

80 How likely is it that B-modes exist at the r=0.01 level? 50% If something can either happen or not happen The Wagner Principle black holes at the LHC destroying the Earth? the chances are Walter Wagner

81 More seriously:

82 Inflation has been remarkably successful at explaining all current observations i.e. flatness and homogeneity of the universe and a primordial spectrum of nearly scale-invariant, Gaussian and adiabatic scalar fluctuations. However, in some sense this may be viewed as a postdiction (debatable) (We knew the universe was homogeneous and had small density fluctuations)

83 Inflation has been remarkably successful at explaining all current observations i.e. flatness and homogeneity of the universe and a primordial spectrum of nearly scale-invariant, Gaussian and adiabatic scalar fluctuations. Tensor modes are a robust prediction of inflation. Seeing their B-mode signature would be a remarkable achievement. It would teach us a great deal about the physics of inflation and rule out all alternative theories.

84 A B-mode detection would teach us a great deal about the physics of inflation: 1. Inflation occured! 2. It happened near the GUT-scale! 3. The inflaton field moved over a super-planckian distance! 3. Its potential was controlled by a shift symmetry. i.e. the inflaton was something like an axion

85 Thank you for your attention!

86 There is more to be learnt from Scalars! Non-Gaussianity and Non-Adiabaticity probe further details of the inflationary action: field content, interactions, symmetries,... I didn t have time to describe this, but see: CMBPol Mission Concept Study: Probing Inflation with CMB Polarization White Paper of the Inflation Working Group arxiv: