Looking Beyond the Cosmological Horizon

Transcription

1 Looking Beyond the Cosmological Horizon 175 µk 175 µk Observable Universe Adrienne Erickcek in collaboration with Sean Carroll and Marc Kamionkowski A Hemispherical Power Asymmetry from Inflation Phys. Rev. D78: , Superhorizon Perturbations and the CMB Phys. Rev. D78: , Everhart Lecture: March 10, 2009 sponsored by the GSC and the Department of Student Affairs

2 Part 1: The Birth of the Universe I. Journey back to the Big Bang A brief history of the Universe The cosmological horizon II. The Cosmic Microwave Background A baby photo of the Universe Mysteries of the CMB III. Inflation A crazy idea... But it works! More unanswered questions Part 2: An Asymmetric Universe 2

3 Journey to the Big Bang WMAP Science Team 3

4 Journey to the Big Bang WMAP Science Team 3

5 A Brief History of the Universe The Cosmic Microwave Background First Stars Galaxies WMAP Science Team Inflation: an instant of extremely rapid expansion 13.7 billion years How do we know all of this? The Cosmologist s Toolbox: Electromagnetic observations: looking out = looking back in time Quantities of light elements made 2-3 minutes after Big Bang 4

6 Looking Back in Time Milky Way Stars 4-65,000 LY 4-65,000 Years 5

7 Looking Back in Time Milky Way Stars 4-65,000 LY 4-65,000 Years Other Galaxies 2.5 Mill Bill. LY 2.5 Mill Bill. Years 5

8 Looking Back in Time Milky Way Stars 4-65,000 LY 4-65,000 Years Other Galaxies 2.5 Mill Bill. LY 2.5 Mill Bill. Years Luminous Red Galaxies out to 4.9 Bill. LY back 4.1 Bill. Years 5

9 Looking Back in Time Milky Way Stars 4-65,000 LY 4-65,000 Years Quasars out to 28 Bill. LY back 12.8 Bill. Years Other Galaxies 2.5 Mill Bill. LY 2.5 Mill Bill. Years Luminous Red Galaxies out to 4.9 Bill. LY back 4.1 Bill. Years 5

10 Light Cones and the Cosmic Horizon You are here billion years after the Big Bang Other Galaxies 11.7 billion years and later Luminous Red Galaxies 9.6 billion years and later Time Space Quasars 1 billion years and later The Big Bang The Observable Universe: 93 billion lightyears across 6

11 Light Cones and the Cosmic Horizon You are here billion years after the Big Bang Other Galaxies 11.7 billion years and later Luminous Red Galaxies 9.6 billion years and later Time Space Quasars 1 billion years and later The Big Bang Cosmic Microwave Background 375,000 years The Observable Universe: 93 billion lightyears across 6

12 The Surface of Last Scatter e- p + e- e- e- p + p e- + p + p e- + e- H H e- H H e- SURFACE OF LAST SCATTER e- p + e- e- p + p + p + H 46 billion lyr H p + H H H H H H H H p + p + e- 375,000 years after the Big Bang, protons and electrons combined to form hydrogen atoms. Before hydrogen e- p + e- formation, the Universe was filled with opaque plasma. After hydrogen formation, photons could travel freely; the Universe became transparent. The photons that reach us from the last scattering surface make a cosmic microwave background. 7

13 The Cosmic Microwave Background NASA/WMAP Science Team 8

14 The Cosmic Microwave Background NASA/WMAP Science Team 8

15 A Partial History of the CMB 1978 Nobel Prize 2006 Nobel Prize A uniform glow outside the Galactic Plane: T = 2.7 Kelvin First detection of fluctuations: one part in 100,000 Wilkinson Microwave Anisotropy Probe Five years of data so far... WMAP Science Team 9

16 The Cosmic Microwave Background WMAP Science Team: Hinshaw, et al WMAP 5-year T (µk) The CMB is perfect black-body radiation: T = K There are very tiny (one part in 100,000) fluctuations. The characteristic size of these perturbations is 1. 10

17 Mystery 1: The Horizon Problem The CMB should not be so perfectly uniform! Time 13.7 billion years Space 375,000 years Last Scattering Surface The Big Bang At the last scattering surface, the horizon was across. Every 1 disk in the CMB is effectively a separate universe. These different patches should not have the same temperature! 1 11

18 Mystery 2: The Flatness Problem The characteristic angular size of the CMB fluctuations tells us about the geometry of the Universe. WMAP Science Team The physical size of the fluctuations is the horizon size at the last scattering surface. Open Flat Closed The geometry of the Universe determines the angular size of the fluctuations. 12

19 Mystery 2: The Flatness Problem The characteristic angular size of the CMB fluctuations tells us about the geometry of the Universe. WMAP Science Team Ω < 1 θ c < 1 Ω = 1 θ Ω > 1 θ c > 1 c 1 The physical size of the fluctuations is the horizon size at the last scattering surface. Open Flat Closed Energy in the Universe Energy required for flatness Ω The geometry of the Universe determines the angular size of the fluctuations. 12

20 Mystery 2: The Flatness Problem The characteristic angular size of the CMB fluctuations tells us about the geometry of the Universe. WMAP Science Team Ω < 1 θ c < 1 Ω = 1 θ Ω > 1 θ c > 1 c 1 Open Flat Closed Energy in the Universe Energy required for flatness Ω The physical size of the fluctuations is the horizon size at the last scattering surface. The geometry of the Universe determines the angular size of the fluctuations. = ± 0.007today 12

21 Mystery 2: The Flatness Problem The characteristic angular size of the CMB fluctuations tells us about the geometry of the Universe. WMAP Science Team Ω < 1 θ c < 1 Ω = 1 θ Ω > 1 θ c > 1 c 1 Open Flat Closed Energy in the Universe Energy required for flatness Ω Ω 1 < The physical size of the fluctuations is the horizon size at the last scattering surface. The geometry of the Universe determines the angular size of the fluctuations. = ± 0.007today 2 minutes after the Big Bang! 12

22 Mystery 3: Initial Fluctuations CMB Power Spectrum WMAP Science Team 13

23 Mystery 3: Initial Fluctuations CMB Power Spectrum characteristic fluctuations horizon at last scatter WMAP Science Team 13

24 Mystery 3: Initial Fluctuations CMB Power Spectrum characteristic fluctuations horizon at last scatter subhorizon plasma physics WMAP Science Team 13

25 Mystery 3: Initial Fluctuations CMB Power Spectrum characteristic fluctuations late-time effect horizon at last scatter subhorizon plasma physics WMAP Science Team 13

26 Mystery 3: Initial Fluctuations CMB Power Spectrum primordial fluctuations late-time effect characteristic fluctuations horizon at last scatter subhorizon plasma physics WMAP Science Team 13

27 Mystery 3: Initial Fluctuations CMB Power Spectrum primordial fluctuations WMAP Science Team 13

28 Mystery 3: Initial Fluctuations Where did CMB Power Spectrum these nearly scaleinvariant perturbations come from? primordial fluctuations WMAP Science Team 13

29 Mysteries of the CMB Three big questions about the beginning of the Universe: Why is the CMB so homogeneous? Why is the Universe so flat? What is the origin of the initial fluctuations? 14

30 Mysteries of the CMB Three big questions about the beginning of the Universe: Why is the CMB so homogeneous? Why is the Universe so flat? What is the origin of the initial fluctuations? INFLATION! 14

31 Mysteries of the CMB Three big questions about the beginning of the Universe: Why is the CMB so homogeneous? Why is the Universe so flat? What is the origin of the initial fluctuations? INFLATION! Breakdown of Energy in the Universe: Atoms Dark Matter 23% 5% Dark Energy 72% 14

32 Mysteries of the CMB Three big questions about the beginning of the Universe: Why is the CMB so homogeneous? Why is the Universe so flat? What is the origin of the initial fluctuations? Breakdown of Energy in the Universe: 5% atomic matter: protons, electrons, atoms stuff we know supported by He produced 3 min. after Big Bang Dark Matter 23% INFLATION! 5% Atoms Dark Energy 72% 14

33 Mysteries of the CMB Three big questions about the beginning of the Universe: Why is the CMB so homogeneous? Why is the Universe so flat? What is the origin of the initial fluctuations? Breakdown of Energy in the Universe: 5% atomic matter: protons, electrons, atoms stuff we know supported by He produced 3 min. after Big Bang 23% dark matter stable, neutral (at 3000 K) particle supported by galaxy motion Dark Matter Dark Energy 23% INFLATION! 5% Atoms 72% 14

34 Mysteries of the CMB Three big questions about the beginning of the Universe: Why is the CMB so homogeneous? Why is the Universe so flat? What is the origin of the initial fluctuations? Breakdown of Energy in the Universe: 5% atomic matter: protons, electrons, atoms stuff we know supported by He produced 3 min. after Big Bang 23% dark matter stable, neutral (at 3000 K) particle supported by galaxy motion 72% dark energy negative pressure causes cosmic acceleration supported by supernova observations Dark Matter Dark Energy 23% INFLATION! 5% Atoms 72% 14

35 Inflation: Accelerated Expansion The content of the Universe determines the expansion rate. radiation: R(t) t matter: R(t) t 2/3 The expansion decelerates Radius of Our Observable Universe (meters) billion LY Earth Radius Atomic Nucleus Time (seconds) 15

36 Inflation: Accelerated Expansion The content of the Universe determines the expansion rate. radiation: R(t) t matter: R(t) t 2/3 The expansion decelerates Radius of Our Observable Universe (meters) billion LY Now Earth Radius Atomic Nucleus Time (seconds) 15

37 Inflation: Accelerated Expansion The content of the Universe determines the expansion rate. radiation: R(t) t matter: R(t) t 2/3 The expansion decelerates Radius of Our Observable Universe (meters) billion LY Now CMB Earth Radius Atomic Nucleus Time (seconds) 15

38 Inflation: Accelerated Expansion The content of the Universe determines the expansion rate. radiation: R(t) t matter: R(t) t 2/3 The expansion decelerates Radius of Our Observable Universe (meters) billion LY Now He formed CMB Earth Radius Atomic Nucleus Time (seconds) 15

39 Inflation: Accelerated Expansion The content of the Universe determines the expansion rate. radiation: R(t) t matter: R(t) t 2/3 The expansion decelerates Radius of Our Observable Universe (meters) billion LY LHC Now He formed CMB Earth Radius Atomic Nucleus Time (seconds) 15

40 Inflation: Accelerated Expansion The content of the Universe determines the expansion rate. radiation: R(t) t matter: R(t) t 2/3 The expansion decelerates. INFLATION Alan Guth, 1981 The Universe s volume doubled at least 270 times instantly Radius of Our Observable Universe (meters) billion LY LHC Inflation Now He formed CMB Earth Radius Atomic Nucleus Time (seconds) 15

41 Inflation: Accelerated Expansion The content of the Universe determines the expansion rate. radiation: R(t) t matter: R(t) t 2/3 The expansion decelerates. INFLATION Alan Guth, 1981 The Universe s volume doubled at least 270 times instantly. during inflationr(t) eht scalar field: energy density is not diluted by expansion. inflation ends when scalar field decays into radiation Radius of Our Observable Universe (meters) billion LY LHC Inflation He formed Time (seconds) Now CMB Earth Radius Atomic Nucleus 15

42 Inflation Solves the Horizon Problem Inflation takes a tiny uniform patch of the early Universe and stretches it so that it covers the Observable Universe billion years 375,000 years second Last Scattering Surface The Big Bang Inflation 16

43 Inflation Solves the Flatness Problem Alan Guth s Notebook: December 7,

44 Inflation Solves the Flatness Problem Spectacular Realization: This kind of supercooling can explain why the universe today is so incredibly flat -- and therefore resolve the fine-tuning paradox... Alan Guth s Notebook: December 7,

45 Inflation Solves the Flatness Problem Spectacular Realization: This kind of supercooling can explain why the universe today is so incredibly flat -- and therefore resolve the fine-tuning paradox... Recall that Ω = 1 is unstable; a Universe that is initially curved will become even more curved as it evolves. Alan Guth s Notebook: December 7,

46 Inflation Solves the Flatness Problem Spectacular Realization: This kind of supercooling can explain why the universe today is so incredibly flat -- and therefore resolve the fine-tuning paradox... Recall that Ω = 1 is unstable; a Universe that is initially curved will become even more curved as it evolves. ( ) d curvature 2 dr d 2 R Ω 1 = 2 dt dt dt 2 expansion rate of Universe Alan Guth s Notebook: December 7,

47 Inflation Solves the Flatness Problem Spectacular Realization: This kind of supercooling can explain why the universe today is so incredibly flat -- and therefore resolve the fine-tuning paradox... Recall that Ω = 1 is unstable; a Universe that is initially curved will become even more curved as it evolves. ( ) d curvature 2 dr d 2 R Ω 1 = 2 dt dt dt 2 expansion rate of Universe d dt decelerating Ω 1 > 0 Alan Guth s Notebook: December 7,

48 Inflation Solves the Flatness Problem Spectacular Realization: This kind of supercooling can explain why the universe today is so incredibly flat -- and therefore resolve the fine-tuning paradox... Recall that Ω = 1 is unstable; a Universe that is initially curved will become even more curved as it evolves. ( ) d curvature 2 dr d 2 R Ω 1 = 2 dt dt dt 2 expansion rate of Universe d dt decelerating Ω 1 > 0 accelerating d dt Ω 1 < 0 Alan Guth s Notebook: December 7,

49 Inflation Solves the Flatness Problem Spectacular Realization: This kind of supercooling can explain why the universe today is so incredibly flat -- and therefore resolve the fine-tuning paradox... Recall that Ω = 1 is unstable; a Universe that is initially curved will become even more curved as it evolves. ( ) d curvature 2 dr d 2 R Ω 1 = 2 dt dt dt 2 expansion rate of Universe d dt decelerating Ω 1 > 0 accelerating d dt Ω 1 < 0 Inflation makes curved universes flat! Alan Guth s Notebook: December 7,

50 The Origin of Initial Fluctuations The energy density during inflation is not uniform; quantum fluctuations lead to hot and cold regions. 18

51 The Origin of Initial Fluctuations The energy density during inflation is not uniform; quantum fluctuations lead to hot and cold regions. In a decelerating Universe, quantum fluctuations pop in and out of existence. During inflation, quantum fluctuations are stretched outside the horizon and are frozen. 18

52 The Origin of Initial Fluctuations The energy density during inflation is not uniform; quantum fluctuations lead to hot and cold regions. In a decelerating Universe, quantum fluctuations pop in and out of existence. During inflation, quantum fluctuations are stretched outside the horizon and are frozen. = = horizon 18

53 The Origin of Initial Fluctuations The energy density during inflation is not uniform; quantum fluctuations lead to hot and cold regions. In a decelerating Universe, quantum fluctuations pop in and out of existence. During inflation, quantum fluctuations are stretched outside the horizon and are frozen. = = horizon Inflation produces nearly scale-invariant fluctuations! 18

54 Unanswered Questions What drove inflation? A scalar field called the inflaton... WMAP Science Team 19

55 Unanswered Questions What drove inflation? A scalar field called the inflaton... How big is our inflationary patch? At least as big as the Observable Universe... WMAP Science Team 19

56 Unanswered Questions WMAP Science Team What drove inflation? A scalar field called the inflaton... How big is our inflationary patch? At least as big as the Observable Universe... What was the Universe like before inflation?? 19

57 Unanswered Questions WMAP Science Team What drove inflation? A scalar field called the inflaton... How big is our inflationary patch? At least as big as the Observable Universe... What was the Universe like before inflation?? The answers are lurking beyond the cosmological horizon. 19

58 Part 2: An Asymmetric Universe I. Power Asymmetry from Superhorizon Structure What power asymmety? How can we make one? II. Superhorizon Structure and the CMB How would we see superhorizon structure? Bad news... III. A Power Asymmetry from the Curvaton What is a curvaton anyway? Does this model work? How do we test this model further? 20

59 An Asymmetric Universe! The mean fluctuation amplitude in the CMB on large angular scales (θ > 4 ) is asymmetric! Eriksen, Hansen, Banday, Gorski, Lilje 2004 Eriksen, Banday, Gorski, Hansen, Lilje µk CMB image from Eriksen, et al. astro-ph/ µk 21

60 An Asymmetric Universe! The mean fluctuation amplitude in the CMB on large angular scales (θ > 4 ) is asymmetric! Eriksen, Hansen, Banday, Gorski, Lilje 2004 Eriksen, Banday, Gorski, Hansen, Lilje 2007 Smoother 175 µk CMB image from Eriksen, et al. astro-ph/ µk Bumpier 21

61 An Asymmetric Universe! The mean fluctuation amplitude in the CMB on large angular scales (θ > 4 ) is asymmetric! Smoother Eriksen, Hansen, Banday, Gorski, Lilje 2004 Eriksen, Banday, Gorski, Hansen, Lilje 2007 Power asymmetry is maximized when the dividing plane is tilted with respect to the Galactic plane. The asymmetry is equally present at multiple frequencies. Fewer than 1% of simulated isotropic maps contain this much asymmetry. 175 µk CMB image from Eriksen, et al. astro-ph/ µk Bumpier 21

62 Hemispherical Power Asymmetry Dipole A ˆp A(ˆn ˆp) +A T(ˆn) = s(ˆn) [1 + A(ˆn ˆp)] CMB Modulation Temperature Gaussian field Amplitude with isotropic power North pole of asymmetry Isotropic s(ˆn) A = µk 175 µk Simulated maps courtesy of H. K. Eriksen 22

63 Hemispherical Power Asymmetry Dipole A (1 + A) A(ˆn ˆp) +A T(ˆn) = s(ˆn) [1 + A(ˆn ˆp)] CMB Modulation Temperature Gaussian field Amplitude with isotropic power North pole of asymmetry Isotropic s(ˆn) A = µk 175 µk Simulated maps courtesy of H. K. Eriksen 22

64 Hemispherical Power Asymmetry Dipole A (1 + A) A(ˆn ˆp) (1 A) +A T(ˆn) = s(ˆn) [1 + A(ˆn ˆp)] CMB Modulation Temperature Gaussian field Amplitude with isotropic power North pole of asymmetry Isotropic s(ˆn) A = µk 175 µk Simulated maps courtesy of H. K. Eriksen 22

65 Hemispherical Power Asymmetry Dipole A (1 + A) A(ˆn ˆp) (1 A) +A T(ˆn) = s(ˆn) [1 + A(ˆn ˆp)] CMB Modulation Temperature Gaussian field Amplitude with isotropic power North pole of asymmetry Isotropic s(ˆn) A = 0 Asymmetric A = µk 175 µk Simulated maps courtesy of H. K. Eriksen 175 µk 175 µk 22

66 Hemispherical Power Asymmetry Dipole A (1 + A) A(ˆn ˆp) (1 A) +A T(ˆn) = s(ˆn) [1 + A(ˆn ˆp)] CMB Modulation Temperature Gaussian field Amplitude with isotropic power North pole of asymmetry Isotropic s(ˆn) A = 0 Asymmetric A = µk 175 µk Simulated maps courtesy of H. K. Eriksen 175 µk 175 µk 22

67 Quantum Fluctuations Revisited Quantum fluctuations during inflation are the seeds of the CMB temperature fluctuations. General Relativity tells us Ṙ R H = expansion rate of the Universe 8πG 3 ρ energy density of the Universe Hawking 1982; Starobinsky 1982; Guth 1982; Bardeen, Steinhardt, Turner

68 Quantum Fluctuations Revisited Quantum fluctuations during inflation are the seeds of the CMB temperature fluctuations. General Relativity tells us V (φ) Ṙ R H = expansion rate of the Universe 8πG 3 ρ energy density of the Universe During inflation: ρ V (φ) nearly constant Hawking 1982; Starobinsky 1982; Guth 1982; Bardeen, Steinhardt, Turner 1983 Inflation φ (inflaton) Inflation ends 23

69 Quantum Fluctuations Revisited Quantum fluctuations during inflation are the seeds of the CMB temperature fluctuations. General Relativity tells us V (φ) Ṙ R H = expansion rate of the Universe 8πG 3 ρ energy density of the Universe During inflation: ρ V (φ) nearly constant Hawking 1982; Starobinsky 1982; Guth 1982; Bardeen, Steinhardt, Turner 1983 Inflation (inflaton) Quantum fluctuations: (δφ) rms = H infl 2π Fluctuations in φ are equivalent to fluctuations in time: δt = δφ φ φ Inflation ends expansion rate during inflation 23

70 Quantum Fluctuations Revisited Quantum fluctuations during inflation are the seeds of the CMB temperature fluctuations. General Relativity tells us V (φ) Ṙ R H = expansion rate of the Universe 8πG 3 ρ energy density of the Universe During inflation: ρ V (φ) nearly constant Inflation φ Inflation ends (inflaton) Quantum fluctuations: (δφ) rms = H infl 2π Fluctuations in φ are equivalent to fluctuations in time: δt = δφ φ T CMB = 1 δr T CMB 5 R = 1 5 Hδt how much space has expanded Hawking 1982; Starobinsky 1982; Guth 1982; Bardeen, Steinhardt, Turner 1983 expansion rate during inflation 23

71 Quantum Fluctuations Revisited Quantum fluctuations during inflation are the seeds of the CMB temperature fluctuations. General Relativity tells us V (φ) Ṙ R H = expansion rate of the Universe 8πG 3 ρ energy density of the Universe During inflation: ρ V (φ) nearly constant (inflaton) Quantum fluctuations: (δφ) rms = H infl 2π Fluctuations in φ are equivalent to fluctuations in time: δt = δφ φ ) ( ) T TC CMB = 1 δr T CMB 5 R = 1 5 Hδt ( TC T C rms T C how much space has expanded rms Hawking 1982; Starobinsky 1982; Guth 1982; Bardeen, Steinhardt, Turner 1983 Inflation φ Inflation ends expansion rate during inflation 23

72 Quantum Fluctuations Revisited Quantum fluctuations during inflation are the seeds of the CMB temperature fluctuations. General Relativity tells us V (φ) Ṙ R H = expansion rate of the Universe 8πG 3 ρ energy density of the Universe During inflation: ρ V (φ) nearly constant (inflaton) Quantum fluctuations: (δφ) expansion rate during inflation rms = H infl 2π Fluctuations in φ are equivalent to fluctuations in time: δt = δφ φ ) ( ) TC = 1 ( ) H 2 infl 5 2π φ = 1 ( ) T CMB 8G = 1 δr 5 6 φ V (φ) T CMB 5 R = 1 5 Hδt ( TC T C rms T C how much space has expanded rms Hawking 1982; Starobinsky 1982; Guth 1982; Bardeen, Steinhardt, Turner 1983 Inflation φ Inflation ends connection to quantum fluctuations 23

73 Asymmetry from a Supermode φ Observable Universe T The amplitude of quantum fluctuations depends on the background value of the inflaton field φ. ( TCMB T CMB ) rms V (φ) φ 24

74 Asymmetry from a Supermode φ φ Observable Universe T The amplitude of quantum fluctuations depends on the background value of the inflaton field φ. ( TCMB T CMB ) rms V (φ) φ Observable Universe T Half of the Supermode s Wavelength Create asymmetry by adding a large-amplitude superhorizon fluctuation: a supermode. Erickcek, Kamionkowski, Carroll

75 Asymmetry from a Supermode The observed modulation amplitude: A = 0.12 ± 0.04 P Corresponding power asymmetry: = 0.2 P 360 φ Observable Universe WMAP Science Team Generating this much asymmetry requires a BIG supermode. 25

76 Asymmetry from a Supermode The observed modulation amplitude: A = 0.12 ± 0.04 P Corresponding power asymmetry: = 0.2 P 360 φ Observable Universe WMAP Science Team Generating this much asymmetry requires a BIG supermode. Recall that the measured primordial fluctuations are scale-invariant. 25

77 Asymmetry from a Supermode The observed modulation amplitude: A = 0.12 ± 0.04 P Corresponding power asymmetry: = 0.2 P 360 φ Observable Universe Generating this much asymmetry requires a BIG supermode. Recall that the measured primordial fluctuations are scale-invariant. WMAP Science Team Different fluctuation wavelengths were created at different times during inflation, so the value of the inflaton varies with wavelength. 25

78 Asymmetry from a Supermode The observed modulation amplitude: A = 0.12 ± 0.04 P Corresponding power asymmetry: = 0.2 P 360 φ Observable Universe WMAP Science Team Generating this much asymmetry requires a BIG supermode. Recall that the measured primordial fluctuations are scale-invariant. Different fluctuation wavelengths were created at different times during inflation, so the value of the inflaton varies with wavelength. The fluctuation power is not very sensitive to the inflaton value. 25

79 Dipole Concerns With the supermode, the value of the inflaton field is very different on opposite sides of the Observable Universe. 26

80 Dipole Concerns With the supermode, the value of the inflaton field is very different on opposite sides of the Observable Universe. The supermode leads to an asymmetric CMB fluctuation amplitude. φ Observable Universe 26

81 Dipole Concerns With the supermode, the value of the inflaton field is very different on opposite sides of the Observable Universe. The supermode leads to an asymmetric CMB fluctuation amplitude. Will it also lead to an asymmetric mean CMB temperature? φ = Ψ = T CMB inflaton grav. potential Colder φ Observable Universe Hotter 26

82 Dipole Concerns With the supermode, the value of the inflaton field is very different on opposite sides of the Observable Universe. The supermode leads to an asymmetric CMB fluctuation amplitude. Will it also lead to an asymmetric mean CMB temperature? φ = Ψ = T CMB inflaton grav. potential The CMB does contain a dipolar anisotropy. usually attributed to our motion relative to the CMB T CMB = ±3.5mK Colder φ Observable Universe 3.5mK +3.5mK Hotter COBE Science Team 26

83 Dipole Concerns With the supermode, the value of the inflaton field is very Worry: different on opposite sides of the Observable Universe. The Will supermode a supermode leads large to enough an asymmetric to generate the CMB observed power fluctuation amplitude. asymmetry also generate Colder a Hotter Will temperature it also lead to dipole an that is too φ asymmetric large to match mean CMB observations? temperature? φ = Ψ = T CMB inflaton grav. potential The CMB does contain a dipolar anisotropy. usually attributed to our motion relative to the CMB T CMB = ±3.5mK Observable Universe 3.5mK +3.5mK COBE Science Team 26

84 The Dipole Sometimes Cancels... The SW Effect In a universe containing only matter, a superhorizon perturbation induces no CMB dipole. Grishchuk, Zel dovich Ψ Ψ Gravitational Gradient The Doppler Effect There is a Sachs-Wolfe dipole due to gravitational redshifts. There is a Doppler dipole due to our motion down the gravitational slope. + Ψ Ψ Gravitational Gradient These two effects exactly cancel if the Universe contains only matter. Will a superhorizon perturbation induce a CMB dipole in our Universe? 27

85 The Dipole Sometimes Cancels... The SW Effect In a universe containing only matter, a superhorizon perturbation induces no CMB dipole. Grishchuk, Zel dovich 1978 No!! + Ψ Ψ Gravitational Gradient The Doppler dipole always cancels The Doppler the Effect gravitational dipole, even with radiation and dark energy. Erickcek, Carroll, Kamionkowski Ψ Ψ Gravitational Gradient There is a Sachs-Wolfe dipole due to gravitational redshifts. There is a Doppler dipole due to our motion down the gravitational slope. These two effects exactly cancel if the Universe contains only matter. Will a superhorizon perturbation induce a CMB dipole in our Universe? 27

86 Going Beyond the CMB Dipole Decompose the CMB into multipole moments: T T (ˆn) = l,m a lm Y lm (ˆn) l = 2 Quadrupole l = 3 Octupole WMAP Science Team 28

87 Going Beyond the CMB Dipole Decompose the CMB into multipole moments: T T (ˆn) = a lm Y lm (ˆn) l,m Ψ( x, t) = Ψ SM (t) sin gravitational potential Supermode: Ψ l = 2 Quadrupole [( 2π L ) ] x + ϖ l = 3 Octupole phase of our location WMAP Science Team Ψ Observable Universe Erickcek, Kamionkowski, Carroll

88 Going Beyond the CMB Dipole Decompose the CMB into multipole moments: T T (ˆn) = a lm Y lm (ˆn) l,m Ψ( x, t) = Ψ SM (t) sin gravitational potential Supermode: Ψ l = 2 Quadrupole [( 2π L ) ] x + ϖ l = 3 Octupole phase of our location No induced quadrupole if ϖ = 0. WMAP Science Team Ψ Observable Universe Erickcek, Kamionkowski, Carroll

89 Going Beyond the CMB Dipole Decompose the CMB into multipole moments: T T (ˆn) = a lm Y lm (ˆn) l,m Ψ( x, t) = Ψ SM (t) sin gravitational potential Supermode: Ψ Ψ l = 2 Quadrupole [( 2π L ) ] x + ϖ l = 3 Octupole phase of our location WMAP Science Team Octupole Constraint: Ψ < [ 32 a SM 30 ] 1/3 = Observable Universe Erickcek, Kamionkowski, Carroll

90 Going Beyond the CMB Dipole Decompose the CMB into multipole moments: T T (ˆn) = a lm Y lm (ˆn) l,m Ψ( x, t) = Ψ SM (t) sin gravitational potential Supermode: Ψ Ψ l = 2 Quadrupole [( 2π L ) ] x + ϖ l = 3 Octupole phase of our location WMAP Science Team Octupole Constraint: Ψ < [ 32 a SM 30 ] 1/3 = Recall: P P inflaton φ Ψ Observable Universe Erickcek, Kamionkowski, Carroll

91 Going Beyond the CMB Dipole Decompose the CMB into multipole moments: T T (ˆn) = a lm Y lm (ˆn) l,m Ψ( x, t) = Ψ SM (t) sin gravitational potential Supermode: Ψ Ψ Observable Universe Erickcek, Kamionkowski, Carroll 2008 l = 2 Quadrupole [( 2π L ) ] x + ϖ l = 3 Octupole phase of our location WMAP Science Team Octupole Constraint: Ψ < [ 32 a SM 30 ] 1/3 = Recall: P inflaton φ Ψ P P P <

92 Going Beyond the CMB Dipole Decompose the CMB into multipole moments: T T (ˆn) = a lm Y lm (ˆn) l,m P Ψ( x, t) = Ψ SM (t) sin Supermode: Ψ Observed: gravitational potential Ψ Observable Universe l = 2 Quadrupole [( ) 2π L The observed asymmetry is too big to be created by an inflaton supermode! Erickcek, Kamionkowski, Carroll 2008 P 0.2 ] x + ϖ l = 3 Octupole phase of our location WMAP Science Team Octupole Constraint: Ψ < [ 32 a SM 30 ] 1/3 = Recall: P inflaton φ Ψ P P P <

93 Back to the chalkboard... The problem with the inflaton model is two-fold: The fluctuation power is weakly dependent on the inflaton s value, so the supermode must have a very large amplitude. The inflaton dominates the energy density of the universe, so a supermode in the inflaton field generates a huge potential perturbation. Ψ CMB octupole places upper bound on. P φ Ψ with no wiggle room. 29

94 Back to the chalkboard... The problem with the inflaton model is two-fold: The fluctuation power is weakly dependent on the inflaton s value, so the supermode must have a very large amplitude. The inflaton dominates the energy density of the universe, so a supermode in the inflaton field generates a huge potential perturbation. Ψ CMB octupole places upper bound on. P φ Ψ with no wiggle room. The solution: the primordial fluctuations could be generated by a secondary scalar field, the curvaton. In this model, there are two scalar fields: the inflaton and the curvaton. The fluctuation power depends strongly on the background curvaton value. The CMB constraints on Ψ do not directly constrain P. There is a new free parameter: the fraction of energy in the curvaton. 29

95 The Curvaton Model Mollerach 1990; Linde, Mukhanov 1997; Lyth, Wands 2002; Moroi, Takahashi 2001; and others... V (σ) The inflaton still dominates the energy density and drives inflation. The curvaton (σ) is a subdominant scalar field during inflation. ρ σ ρ φ subdominant V (σ) = 1 potential 2 m2 σσ 2 σ 30

96 The Curvaton Model Mollerach 1990; Linde, Mukhanov 1997; Lyth, Wands 2002; Moroi, Takahashi 2001; and others... V (σ) The inflaton still dominates the energy density and drives inflation. The curvaton (σ) is a subdominant scalar field during inflation. ρ σ ρ φ subdominant V (σ) = 1 potential 2 m2 σσ 2 σ m σ H, and the curvaton is frozen at its initial During inflation, value, but there are quantum fluctuations. 30

97 The Curvaton Model Mollerach 1990; Linde, Mukhanov 1997; Lyth, Wands 2002; Moroi, Takahashi 2001; and others... V (σ) The inflaton still dominates the energy density and drives inflation. The curvaton (σ) is a subdominant scalar field during inflation. ρ σ ρ φ subdominant V (σ) = 1 potential 2 m2 σσ 2 σ m σ H, and the curvaton is frozen at its initial During inflation, value, but there are quantum fluctuations. After inflation, when m σ H, the curvaton oscillates in its potential well. It is a pressureless fluid and behaves like cold gas. Still in the early Universe, the curvaton decays into radiation. 30

98 The Curvaton Model Mollerach 1990; Linde, Mukhanov 1997; Lyth, Wands 2002; Moroi, Takahashi 2001; and others... V (σ) The inflaton still dominates the energy density and drives inflation. The curvaton (σ) is a subdominant scalar field during inflation. ρ σ ρ φ subdominant V (σ) = 1 potential 2 m2 σσ 2 σ m σ H, and the curvaton is frozen at its initial During inflation, value, but there are quantum fluctuations. After inflation, when m σ H, the curvaton oscillates in its potential well. It is a pressureless fluid and behaves like cold gas. Still in the early Universe, the curvaton decays into radiation. After the end of inflation and prior to curvaton decay, the fractional energy in the curvaton grows. 30

99 Power Spectrum from the Curvaton Curvaton field fluctuations become gravitational potential fluctuations: Ψ (σ) = R 5 δρ σ ρ σ gravitational perturbation from curvaton ( TCMB T CMB = Ψ 3 where R 3 4 curvaton energy density ) ρ σ ρ r Γ=H and σ rad. evaluated just prior to curvaton decay R 1 keep the curvaton subdominant 31

100 Power Spectrum from the Curvaton Curvaton field fluctuations become gravitational potential fluctuations: Ψ (σ) = R 5 δρ σ ρ σ gravitational perturbation from curvaton ( TCMB T CMB = Ψ 3 where Fractional variation in the curvaton s energy density: R 3 4 curvaton energy density ) ρ σ ρ r Γ=H and σ rad. evaluated just prior to curvaton decay ( ) ( δρ σ δσ δσ = 2 + ρ σ σ σ R 1 keep the curvaton subdominant ) 2 derived from the curvaton potential 31

101 Power Spectrum from the Curvaton Curvaton field fluctuations become gravitational potential fluctuations: Ψ (σ) = R 5 ρ σ gravitational perturbation from curvaton Fractional variation in the curvaton s energy density: Quantum fluctuations: δρ σ ( TCMB T CMB = Ψ 3 where (δσ) rms = H infl 2π R 3 4 curvaton energy density ) ( ) ( δρ σ δσ δσ = 2 + ρ σ σ σ σ ρ σ ρ r Γ=H σ rad. evaluated just prior to curvaton decay expansion rate during inflation and R 1 keep the curvaton subdominant ) 2 derived from the curvaton potential 31

102 Power Spectrum from the Curvaton Curvaton field fluctuations become gravitational potential fluctuations: Ψ (σ) = R 5 ρ σ gravitational perturbation from curvaton Fractional variation in the curvaton s energy density: Quantum fluctuations: δρ σ ( TCMB T CMB = Ψ 3 where (δσ) rms = H infl 2π R 3 4 curvaton energy density ( ) ( δρ σ δσ δσ = 2 + ρ σ σ σ σ expansion rate during inflation CMB Power Spectrum from the curvaton: ) ρ σ ρ r Γ=H and σ rad. evaluated just prior to curvaton decay R 1 keep the curvaton subdominant ) 2 derived from the curvaton potential P (σ) R 2 ( Hinfl σ ) 2 31

103 Power Spectrum from the Curvaton Curvaton field fluctuations become gravitational potential fluctuations: Ψ (σ) = R 5 ρ σ gravitational perturbation from curvaton Fractional variation in the curvaton s energy density: Quantum fluctuations: δρ σ ( TCMB T CMB = Ψ 3 where (δσ) rms = H infl 2π R 3 4 curvaton energy density ( ) ( δρ σ δσ δσ = 2 + ρ σ σ σ σ expansion rate during inflation CMB Power Spectrum from the curvaton: ) ρ σ ρ r Γ=H and σ rad. evaluated just prior to curvaton decay R 1 keep the curvaton subdominant ) 2 derived from the curvaton potential P (σ) ( σ) 4 ( Hinfl σ ) 2 31

104 Power Asymmetry Spectrum from the Curvaton Curvaton field fluctuations become gravitational potential fluctuations: Ψ (σ) = R 5 Fractional variation in the curvaton s energy density: Quantum fluctuations: δρ σ ρ σ gravitational perturbation from curvaton ( TCMB T CMB = Ψ 3 where (δσ) rms = H infl 2π ( ) ( δρ σ δσ δσ = 2 + ρ σ σ σ σ expansion rate during inflation CMB Power Spectrum from the curvaton: P (σ) ( σ) 4 ( Hinfl σ ) 2 R 3 4 curvaton energy density ) δ σ ρ σ ρ r Γ=H and σ rad. evaluated just prior to curvaton decay ) 2 derived from the curvaton potential σ Observable Universe R 1 keep the curvaton subdominant T CMB 31

105 Power Asymmetry Spectrum from the Curvaton Curvaton field fluctuations become gravitational potential fluctuations: Ψ (σ) = R 5 Fractional variation in the curvaton s energy density: Quantum fluctuations: δρ σ ρ σ gravitational perturbation from curvaton ( TCMB T CMB = Ψ 3 (δσ) rms = H infl 2π ( ) ( δρ σ δσ δσ = 2 + ρ σ σ σ σ expansion rate during inflation CMB Power Spectrum from the curvaton: P (σ) P (σ) where = 2 σ σ R 3 4 curvaton energy density ) δ σ ρ σ ρ r Γ=H and σ rad. evaluated just prior to curvaton decay ) 2 derived from the curvaton potential σ Observable Universe R 1 keep the curvaton subdominant T CMB 31

106 Curvaton Supermodes in the CMB Curvaton supermode: δ σ( x, t) = σ SM (t) sin [( 2π L ) ] x + ϖ δ σ phase of our location σ δσ Observable Universe 32

107 Curvaton Supermodes in the CMB Curvaton supermode: δ σ( x, t) = σ SM (t) sin [( 2π L δ σ The curvaton supermode generates a superhorizon potential fluctuation, but it is suppressed. ) ] x + ϖ phase of our location σ Observable Universe δσ 32

108 Curvaton Supermodes in the CMB Curvaton supermode: δ σ( x, t) = σ SM (t) sin δ σ The curvaton supermode generates a superhorizon potential fluctuation, but it is suppressed. R 3ρ σ 4ρ just prior to decay [( 2π L Ψ = R 5 ) [ ] x + ϖ 2 ( δ σ σ phase of our location ) + σ Observable Universe ( δ σ σ ) 2 ] δρ σ ρ δσ 32

109 Curvaton Supermodes in the CMB Curvaton supermode: δ σ( x, t) = σ SM (t) sin δ σ The curvaton supermode generates a superhorizon potential fluctuation, but it is suppressed. R 3ρ σ 4ρ just prior to decay [( 2π L Ψ = R 5 [ 2 ( δ σ σ phase of our location ) + σ Observable Universe ( δ σ The potential perturbation is not sinusoidal! ) ] x + ϖ σ ) 2 ] The CMB quadrupole and octupole have complicated ϖ dependencies. There is no phase that eliminates the quadrupole for all values of σ SM. δρ σ ρ δσ 32

110 Curvaton Supermodes in the CMB phase of our Curvaton The CMB supermode: quadrupole [( ) location 2π implies ] an upper bound: δ σ( x, t) = σ SM ((t) sin ) 2 x + ϖ σ L σ δ σ The curvaton R supermode for ϖ = 0 σ < asm 20 generates a superhorizon P potential fluctuation, but it is suppressed. P R 3ρ σ 4ρ just prior to decay Ψ = R 5 [ 2 ( δ σ σ ) + δσ Most other phases Observable give Universe similar bounds. ( δ σ The potential perturbation is not sinusoidal! σ ) 2 ] The CMB quadrupole and octupole have complicated ϖ dependencies. There is no phase that eliminates the quadrupole for all values of σ SM. δρ σ ρ 32

111 Non-Gaussianity and the Curvaton The quantum fluctuations during inflation are Gaussian. P (δφ) H infl 2π 0 H infl 2π H infl 02π H infl 2π δφ 33

112 Non-Gaussianity and the Curvaton The quantum fluctuations during inflation are Gaussian. P (δφ) P ( TCMB T CMB ) temperature fluctuation T CMB T CMB = Ψ 3 gravitational potential H infl 2π 0 H infl 2π H infl 02π H infl ( T CMB )/T CMB π δφ 33

113 Non-Gaussianity and the Curvaton The quantum fluctuations during inflation are Gaussian. P (δφ) P ( TCMB T CMB from inflaton ) temperature fluctuation T CMB T CMB = Ψ 3 gravitational potential The CMB temperature fluctuations from the inflaton are Gaussian: Ψ δφ inflaton H infl 2π 0 H infl 2π H infl 02π H infl ( T CMB )/T CMB π δφ 33

114 Non-Gaussianity and the Curvaton The quantum fluctuations during inflation are Gaussian. P (δφ) P ( TCMB T CMB from inflaton H infl 2π ) 0 H infl 2π H infl 02π H infl ( T CMB )/T CMB π from curvaton δφ temperature fluctuation T CMB T CMB = Ψ 3 gravitational potential The CMB temperature fluctuations from the inflaton are Gaussian: The curvaton creates non-gaussian CMB temperature fluctuations: Ψ = R 5 gravitational potential fluctuation Ψ δφ inflaton [ 2 ( δσ σ ) Gaussian fluctuation + ( δσ σ Gaussian fluctuation squared ) 2 ] 33

115 Non-Gaussianity and the Curvaton The quantum fluctuations during inflation are Gaussian. P (δφ) P ( TCMB T CMB H infl 2π ) 0 H infl 2π H infl 02π H infl ( T CMB )/T CMB 10 5 Parametrize: 2π Ψ = Ψ g f NL Ψ 2 g δφ temperature fluctuation T CMB T CMB = Ψ 3 gravitational potential The CMB temperature fluctuations from the inflaton are Gaussian: The curvaton creates non-gaussian CMB temperature fluctuations: Ψ = R 5 gravitational potential fluctuation Ψ δφ inflaton [ 2 ( δσ σ ) Gaussian fluctuation + ( δσ σ Gaussian fluctuation squared ) 2 ] 33

116 Constraining the Curvaton Model The curvaton and inflaton both contribute to the CMB temperature fluctuations: ξ P (σ) P P σ = 2ξ P σ fractional power from curvaton power asymmetry 34

117 Constraining the Curvaton Model The curvaton and inflaton both contribute to the CMB temperature fluctuations: fractional power from curvaton ξ P (σ) P P σ = 2ξ P σ σ σ < 1 = ξ > 1 2 power asymmetry P Ψ P Ψ R = 0.75ρσ/ρ R = 0.75ρσ/ρ (σ) P P = 0.20 P P = 0.05 (σ) 34

118 Constraining the Curvaton Model The curvaton and inflaton both contribute to the CMB temperature fluctuations: fractional power from curvaton ξ P (σ) P P σ = 2ξ P σ σ σ < 1 = ξ > 1 2 CMB Quadrupole: R ( σ σ power asymmetry P Ψ P Ψ ) 2 < 5 2 (5.8Q) R = 0.75ρσ/ρ R = 0.75ρσ/ρ CMB quad. CMB quad (σ) (σ) P P = 0.20 P P =

119 Constraining the Curvaton Model Non-Gaussianity Constraints Ψ = R 5 gravitational potential fluctuation f NL 5ξ2 4R Amount of non-gaussianity Gaussian fluctuation squared Lyth, Ungarelli, Wands 2003; Ichikawa, Suyama, Takahashi, Yamaguchi 2008 Upper bound from WMAP: f NL < 100 [ ( ) ( ) ] 2 δσ δσ 2 + σ σ Gaussian fluctuation Komatsu et al Yadav, Wandelt 2008 R = 0.75ρσ/ρ R = 0.75ρσ/ρ CMB quad. CMB quad f NL 100 (σ) f NL 100 P P = 0.20 P P = 0.05 (σ) 34

120 Constraining the Curvaton Model The Allowed Region 5 4f < R NL,max ξ 2 < 58 a SM 20 ( P/P ) 2 Non-Gaussianity CMB Quadrupole Allowed window R = 0.75ρσ/ρ CMB quad f NL 100 P P = 0.20 (σ) The Dealbreaker P The window for P = 0.20 disappears if f NL,max 50 R = 0.75ρσ/ρ CMB quad. f NL 100 P P = 0.05 (σ) 34

121 Summary: How to Generate the Power Asymmetry There is a power asymmetry in the CMB. present at the 99% confidence level detected on large scales Hansen, Banday, Gorski, 2004 Eriksen, Hansen, Banday, Gorski, Lilje 2004 Eriksen, Banday, Gorski, Hansen, Lilje µk A superhorizon fluctuation during inflation generates a power asymmetry. Erickcek, Kamionkowski, Carroll Phys. Rev. D78: , Erickcek, Carroll, Kamionkowski Phys. Rev. D78: , Asymmetry from an inflaton of the observed asymmetry. P P = Observable Universe superhorizon fluctuation is ruled out. A curvaton fluctuation is a viable source σ δ σ Significant departures from Gaussianity are required to generate asymmetry. The supermode s amplitude is too large to be a quantum fluctuation. 175 µk T CMB 35

122 Future Observational Tests The Planck Satellite: set to launch in April Large Scale Structure Surveys: in progress Search for CMB polarization from inflationary gravitational waves: in progress SDSS Science Team Adrienne Erickcek Everhart Lecture: March 10,

123 Future Observational Tests The Planck Satellite: set to launch in April resolution CMB map higher frequencies for better foreground subtraction more f with error bars of ±10 measure power asymmetry both in temperature and confirm polarization fluctuations? NL Large Scale Structure Surveys: in progress Search for CMB polarization from inflationary gravitational waves: in progress SDSS Science Team Adrienne Erickcek Everhart Lecture: March 10,

124 Future Observational Tests The Planck Satellite: set to launch in April resolution CMB map higher frequencies for better foreground subtraction more f with error bars of ±10 measure power asymmetry both in temperature and confirm polarization fluctuations? NL Large Scale Structure Surveys: in progress f through statistics of galaxy measure distribution with error bars of ±10 for asymmetry in numbers of search galaxies and quasars NL Search for CMB polarization from inflationary gravitational waves: in progress SDSS Science Team Adrienne Erickcek Everhart Lecture: March 10,

125 What have we learned? Standard Inflation Curvaton Model with Relic Supermode 37

126 What have we learned? What drove inflation? Standard Inflation the inflaton Curvaton Model with Relic Supermode the inflaton, but a different field created the initial fluctuations 37

127 What have we learned? What drove inflation? How big is our inflationary patch? Standard Inflation the inflaton bigger than the Observable Universe Curvaton Model with Relic Supermode the inflaton, but a different field created the initial fluctuations just a little bigger than the Observable Universe 37

128 What have we learned? What drove inflation? How big is our inflationary patch? Standard Inflation the inflaton bigger than the Observable Universe Curvaton Model with Relic Supermode the inflaton, but a different field created the initial fluctuations just a little bigger than the Observable Universe What was there before inflation?? a subdominant scalar field with large fluctuations 37

129 What have we learned? What drove inflation? How big is our inflationary patch? Standard Inflation the inflaton bigger than the Observable Universe Curvaton Model with Relic Supermode the inflaton, but a different field created the initial fluctuations just a little bigger than the Observable Universe What was there before inflation?? a subdominant scalar field with large fluctuations The power asymmetry? a statistical fluke signature of superhorizon fluctuation in curvaton 37

130 What have we learned? What drove inflation? How big is our inflationary patch? Standard Inflation the inflaton bigger than the Observable Universe Curvaton Model with Relic Supermode the inflaton, but a different field created the initial fluctuations just a little bigger than the Observable Universe What was there before inflation?? a subdominant scalar field with large fluctuations The power asymmetry? Gaussian fluctuations? a statistical fluke signature of superhorizon fluctuation in curvaton Yes: No: f NL < 1 f NL > 50 37

131 A Bit of Cosmology Humor Mature paradigm with firm observational support seeks a fundamental theory in which to be embedded. Classified Ad in Fermilab s Newsletter February 14, 2008 Inflation s soulmate may be hiding beyond the cosmological horizon, but we can still find her! 38