Learning about Primordial Physics from Large Scale Structure

Transcription

1 Learning about Primordial Physics from Large Scale Structure Sarah Shandera Penn State University z = 0.00 Y [Mpc/h] X [Mpc/h]

2 From Monday, Ben Wandelt s three challenges: Light Matter Connection Non-linearity Paradigms for cosmic beginnings

3 From Monday, Ben Wandelt s three challenges: Light Matter Connection Non-linearity Paradigms for cosmic beginnings

4 From Monday, Ben Wandelt s three challenges: Light Matter Connection Non-linearity Paradigms for cosmic beginnings suggested by thinking about LSS observables

5 A question from Monday: Is there any observation (of the scalar sector) that would rule out inflation?

6 A question from Monday: Is there any observation (of the scalar sector) that would rule out inflation? What do constraints/measurements of NG tell us about particle physics at high scales? (Tuesday s talks)

7 A question from Monday: Is there any observation (of the scalar sector) that would rule out inflation? What do constraints/measurements of NG tell us about particle physics at high scales? (Tuesday s talks) How can we do better than Planck? How hard should we try? What do we need to do? (Wednesday and today)

8 A question from Monday: Is there any observation (of the scalar sector) that would rule out inflation? What do constraints/measurements of NG tell us about particle physics at high scales? (Tuesday s talks) How can we do better than Planck? How hard should we try? What do we need to do? (Wednesday and today) Answer a reason to push constraints on local NG

9 A question from Monday: Is there any observation (of the scalar sector) that would rule out inflation? What do constraints/measurements of NG tell us about particle physics at high scales? (Tuesday s talks) How can we do better than Planck? How hard should we try? What do we need to do? (Wednesday and today) Answer a reason to push constraints on local NG (a concrete/alternate approach to, or mini-version of, the landscape and measure problem?)

10 Power spectrum: Inflation Spectrum of scaleinvariant, adiabatic, super horizon modes as initial conditions

11 Power spectrum: Inflation Spectrum of scaleinvariant, adiabatic, super horizon modes as initial conditions Bispectrum, trispectrum, etc?

12 Power spectrum: Inflation Spectrum of scaleinvariant, adiabatic, super horizon modes as initial conditions Bispectrum, trispectrum, etc? Mathematically independent...

13 Power spectrum: Inflation Spectrum of scaleinvariant, adiabatic, super horizon modes as initial conditions Bispectrum, trispectrum, etc? Mathematically independent... (Smith)...up to relationships of the type τ NL (6/5f NL ) 2

14 Power spectrum: Inflation Spectrum of scaleinvariant, adiabatic, super horizon modes as initial conditions Bispectrum, trispectrum, etc? Mathematically independent... (Smith)...up to relationships of the type τ NL (6/5f NL ) 2 Perturbation theory that obeys usual (effective) field theory notions: patterns Non-zero NG, but no patterns in shape or size

15 For example, Scaling Patterns

16 For example, Scaling Patterns M n,r = δn R c δ 2 R n/2 c

17 For example, Scaling Patterns M n,r = δn R c δ 2 R n/2 c Self-interactions; eg, local ansatz

18 For example, Scaling Patterns M n,r = δn R c δ 2 R n/2 c Self-interactions; eg, local ansatz Hierarchical M (h) n = n!2 n 3 M (h) 3 6 n 2

19 For example, Scaling Patterns M n,r = δn R c δ 2 R n/2 c Self-interactions; eg, local ansatz Hierarchical M (h) n = n!2 n 3 M (h) 3 6 n 2 f NL P 1/2 ζ

20 For example, Scaling Patterns M n,r = δn R c δ 2 R n/2 c Self-interactions; eg, local ansatz Hierarchical M (h) n = n!2 n 3 M (h) 3 6 n 2 δa Extra source, eg, gauge field f NL P 1/2 ζ (Barnaby, Shandera; )

21 For example, Scaling Patterns M n,r = δn R c δ 2 R n/2 c Self-interactions; eg, local ansatz Hierarchical M (h) n = n!2 n 3 M (h) 3 6 n 2 δa Extra source, eg, gauge field f NL P 1/2 ζ Feeder M (f) n =(n 1)! 2 n 1 M (f) 3 8 n/3 (Barnaby, Shandera; )

22 Scaling Patterns, cont d (Quasi-single field) (Chen, Wang) Hybrid M (h) n (A) n (B) n 2 (Baumann, Smith)

23 Scaling Patterns, cont d (Quasi-single field) (Chen, Wang) Hybrid M (h) n (A) n (B) n 2 (Baumann, Smith) Hard to measure, but not totally irrelevant for observations...

24 Scaling Patterns, cont d (Quasi-single field) (Chen, Wang) Hybrid M (h) n (A) n (B) n 2 (Baumann, Smith) Hard to measure, but not totally irrelevant for (For the sake of discussion, please grant me LSS light+matter+systematics+data of 25 yrs +) observations...

25 X-ray cluster constraints redshift M 500 (10 14 M ) This work Williamson 2011 Benson X-ray clusters (ROSAT) Shandera, Mantz, Rapetti, Allen, (JCAP) Rare objects care about the total probability of large fluctuations: (Matarrese)

26 X-ray cluster constraints redshift M 500 (10 14 M ) This work Williamson 2011 Benson X-ray clusters (ROSAT) Shandera, Mantz, Rapetti, Allen, (JCAP) Rare objects care about the total probability of large fluctuations: Not B local (k 1,k 2,k 3 ) (Matarrese)

27 X-ray cluster constraints redshift M 500 (10 14 M ) This work Williamson 2011 Benson X-ray clusters (ROSAT) Shandera, Mantz, Rapetti, Allen, (JCAP) Rare objects care about the total probability of large fluctuations: Not B local (k 1,k 2,k 3 ) Not skewness alone ( ) M 3 (Matarrese)

28 Results f NL Φ 2 ΦF F

29 Results f NL Φ 2 ΦF F Not so far off from bias constraints...

30 A segue via the galaxy bias... A competitive constraint (pre-planck): 29 <f local NL < 70 8 <f local NL < 88 (Slosar et al,2008) (Xia et al, 2011) 37 <f local NL < 25 (Giannantonio et al, 2013) f NL 1 (Cunha, Dore, Huterer forecast for DES) But actually goes beyond the exact local ansatz...

31 NG bias, generalized b NG (k, M, f NL ) f NL k 2 A NL (b G (M)) k α (Desjacques; Shandera, Dalal, Huterer;) (Kendrick s talk, Nishant s talk, Simone s talk)

32 NG bias, generalized b NG (k, M, f NL ) f NL k 2 A NL (b G (M)) k α (Desjacques; Shandera, Dalal, Huterer;) (Kendrick s talk, Nishant s talk, Simone s talk) So far models give: 0 α 3 Standard Single field Multiple Light fields α =0 α =2±O(, η) Byrnes et al; Seery et al; Quasi Single field 1/2 α 2 Chen, Wang; Generalized Initial State α 3 Agullo, Parker; Agullo, Shandera; Ganc, Komatsu; Agarwal et al Non-attractor single field α =2 Chen, Firouzjahi, Sasaki et al; }finite k range

33 A generalized local bispectrum (Local type requires scenarios with multiple clocks/fields) (Shandera, Dalal, Huterer )

34 A generalized local bispectrum (Local type requires scenarios with multiple clocks/fields) B Φ (k 1, k 2, k 3 )=ξ s (k 3 )ξ m (k 1 )ξ m (k 2 )P Φ (k 1 )P Φ (k 2 ) + 5 perm. (Shandera, Dalal, Huterer )

35 A generalized local bispectrum (Local type requires scenarios with multiple clocks/fields) B Φ (k 1, k 2, k 3 )=ξ s (k 3 )ξ m (k 1 )ξ m (k 2 )P Φ (k 1 )P Φ (k 2 ) + 5 perm. Ratio of contributions of each field (Shandera, Dalal, Huterer )

36 A generalized local bispectrum (Local type requires scenarios with multiple clocks/fields) B Φ (k 1, k 2, k 3 )=ξ s (k 3 )ξ m (k 1 )ξ m (k 2 )P Φ (k 1 )P Φ (k 2 ) + 5 perm. Self-interactions of one field Ratio of contributions of each field (Shandera, Dalal, Huterer )

37 A generalized local bispectrum (Local type requires scenarios with multiple clocks/fields) B Φ (k 1, k 2, k 3 )=ξ s (k 3 )ξ m (k 1 )ξ m (k 2 )P Φ (k 1 )P Φ (k 2 ) + 5 perm. Self-interactions of one field Ratio of contributions of each field Mild Scale-Dependence: ξ s,m (k) =ξ s,m (k p ) k k p n (s),(m) f (Shandera, Dalal, Huterer )

38 A generalized local bispectrum (Local type requires scenarios with multiple clocks/fields) B Φ (k 1, k 2, k 3 )=ξ s (k 3 )ξ m (k 1 )ξ m (k 2 )P Φ (k 1 )P Φ (k 2 ) + 5 perm. Self-interactions of one field Ratio of contributions of each field Mild Scale-Dependence: ξ s,m (k) =ξ s,m (k p ) k k p n (s),(m) f f eff A (M,n(s) NL f (s) f k 2 n(m) f,n(m),n(m) ) f (also Desjacques et al) (Shandera, Dalal, Huterer )

39 A generalized local bispectrum (Local type requires scenarios with multiple clocks/fields) B Φ (k 1, k 2, k 3 )=ξ s (k 3 )ξ m (k 1 )ξ m (k 2 )P Φ (k 1 )P Φ (k 2 ) + 5 perm. Self-interactions of one field Ratio of contributions of each field Mild Scale-Dependence: ξ s,m (k) =ξ s,m (k p ) k k p n (s),(m) f f eff A (M,n(s) NL f (s) f k 2 n(m) f,n(m),n(m) ) f (also Desjacques et al) (Shandera, Dalal, Huterer )

40 Upshot (As I understood it ~12 months ago) Measuring several n-point correlations would neatly distinguish particle interactions, including multi-field aspects

41 Upshot (As I understood it ~12 months ago) Measuring several n-point correlations would neatly distinguish particle interactions, including multi-field aspects Is the clock of 1. Squeezed-ness of Shape perturbations the same as (standard) BG clock?

42 Upshot (As I understood it ~12 months ago) Measuring several n-point correlations would neatly distinguish particle interactions, including multi-field aspects Is the clock of 1. Squeezed-ness of Shape perturbations the same as (standard) BG clock? 1a. Shape details: Bispectral indices Non-minimal curvaton? Two sources for curvature?

43 Upshot (As I understood it ~12 months ago) Measuring several n-point correlations would neatly distinguish particle interactions, including multi-field aspects Is the clock of 1. Squeezed-ness of Shape perturbations the same as (standard) BG clock? 1a. Shape details: Bispectral indices 1I. Common scale in the amplitudes Non-minimal curvaton? Two sources for curvature? New energy/mass scale

44 Upshot (As I understood it ~12 months ago) Measuring several n-point correlations would neatly distinguish particle interactions, including multi-field aspects Is the clock of 1. Squeezed-ness of Shape perturbations the same as (standard) BG clock? 1a. Shape details: Bispectral indices 1I. Common scale in the amplitudes IIa. Scaling patterns Non-minimal curvaton? Two sources for curvature? New energy/mass scale Self-interactions only? Feeder fields?

45 Current reality: Local NG pretty well constrained... Currently, bias is not competitive with Planck

46 Current reality: Local NG pretty well constrained... Currently, bias is not competitive with Planck Is there a threshold we can aim for where physics changes f equil NL O(1) qualitatively? ( )

47 Current reality: Local NG pretty well constrained... Currently, bias is not competitive with Planck Is there a threshold we can aim for where physics changes f equil NL qualitatively? ( ) fnl local O(1)? O(1)

48 Current reality: Local NG pretty well constrained... Currently, bias is not competitive with Planck Is there a threshold we can aim for where physics changes f equil NL qualitatively? ( ) fnl local O(1)? O(1) 1. Tues/Wed answers: (vague?) threshold for curvaton type scenarios; non-linear GR effects sure to be detected

49 Current reality: Local NG pretty well constrained... Currently, bias is not competitive with Planck Is there a threshold we can aim for where physics changes f equil NL qualitatively? ( ) fnl local O(1)? O(1) 1. Tues/Wed answers: (vague?) threshold for curvaton type scenarios; non-linear GR effects sure to be detected 2. A cosmic variance threshold (or, a reason we should all be very glad Planck did not detect local non- Gaussianity)

50 A reason to keep pushing on local models: Mode coupling and subsampling Nelson, Shandera, (PRL); LoVerde, Nelson, Shandera, (JCAP); Bramante, Kumar, Nelson, Shandera, ;

51 A reason to keep pushing on local models: Mode coupling and subsampling Nelson, Shandera, (PRL); LoVerde, Nelson, Shandera, (JCAP); Bramante, Kumar, Nelson, Shandera, ; (Marilena Loverde s KITP talk last May)

52 A reason to keep pushing on local models: Mode coupling and subsampling Nelson, Shandera, (PRL); LoVerde, Nelson, Shandera, (JCAP); Bramante, Kumar, Nelson, Shandera, ; (Marilena Loverde s KITP talk last May) Linde, Muhkanov; Salopek, Bond; Mollerach et al; Lyth; Byrnes et al; papers related to anomaly...

53 Local non-gaussianity Consider a real space field of small fluctuations L defined in a volume with side L Let the field be a non-linear, local transformation of a Gaussian (homogeneous, isotropic)

54 Local non-gaussianity Consider a real space field of small fluctuations L defined in a volume with side L Let the field be a non-linear, local transformation of a Gaussian (homogeneous, isotropic) ζ NG (x) =f(ζ G (x)) f(ζ G ) ζ 2 G,L 1/2 1

55 Sub-volumes Consider a single sub-volume with side S L S Statistics of fluctuations in S vs those in L? Statistics in a typical sub-volume S?

56 Sub-volumes Consider a single sub-volume with side S L S Statistics of fluctuations in S vs those in L? Statistics in a typical sub-volume S? Kendrick s talk, Chris discussion

57 Local Ansatz ζ NG (x) = ζ G (x)+ 3 5 f NL ζ 2 G (x) ζg g NL ζ 3 G (x) 3ζGζ 2 G (x) h NL ζ 4 G 6ζGζ 2 G(x)+3ζ 2 G

58 Local Ansatz ζ NG (x) = ζ G (x)+ 3 5 f NL ζ 2 G (x) ζg g NL ζ 3 G (x) 3ζGζ 2 G (x) h NL ζ 4 G 6ζGζ 2 G(x)+3ζ 2 G Split the field up: ζ G (x) =ζ G,S (x)+ζ G,L (x)

59 Local Ansatz ζ NG (x) = ζ G (x)+ 3 5 f NL ζ 2 G (x) ζg g NL ζ 3 G (x) 3ζGζ 2 G (x) h NL ζ 4 G 6ζGζ 2 G(x)+3ζ 2 G ζ G,S (x) = ζ G,L (x) = Split the field up: ζ G (x) =ζ G,S (x)+ζ G,L (x) k k k <k d 3 k (2π) 3 ζ G(x)e ik x d 3 k (2π) 3 ζ G(k)e ik x

60 Sub-volume field: ζ NG S = χ G (x)+ 3 5 f NL S χ 2 G (x) χ 2 G g NL S χ 3 G 3χ 2 χ G (x) +... With: χ G (x) = f NLζ G,L + O(ζG,L) 2 ζ G,S f NL S = f NL g NLζ G,L 12 5 f 2 NLζ G,L + O(ζ 2 G,L)

61 The picture Assumption: In L, Same homogeneous background for inflation Same local physics/ L S thermodynamics Us after inflation We can define the perturbations on a single time slice

62 How big are the effects? χ G (x) = f NLζ G,L + O(ζG,L) 2 ζ G,S

63 How big are the effects? χ G (x) = f NLζ G,L + O(ζG,L) 2 ζ G,S ζ 2 G,L ns =1 = 2 GN ζg,l 2 1 e (n s 1)N ns =1 = 2 G(H 0 ) n s 1

64 How big are the effects? χ G (x) = f NLζ G,L + O(ζG,L) 2 ζ G,S ζ 2 G,L ns =1 = 2 GN ζg,l 2 1 e (n s 1)N ns =1 = 2 G(H 0 ) n s 1 Significant only if there is sufficient power in long wavelength modes (and local results are physically coupled the background)

65 How big are the effects? χ G (x) = f NLζ G,L + O(ζG,L) 2 ζ G,S ζ 2 G,L ns =1 = 2 GN ζg,l 2 1 e (n s 1)N ns =1 = 2 G(H 0 ) n s 1 Significant only if there is sufficient power in long wavelength modes (and local results are physically coupled the background) ζ 2 G,L,ζ G,L, f NL are unmeasurable

66 How big are the effects? χ G (x) = f NLζ G,L + O(ζG,L) 2 ζ G,S

67 How big are the effects? χ G (x) = f NLζ G,L + O(ζG,L) 2 ζ G,S

68 Weak non-gaussianity in L 1 f NL ζ 2 G g NLζ 2 Gh NL (ζ 2 G) 3/2

69 Weak non-gaussianity in L 1 f NL ζ 2 G g NLζ 2 Gh NL (ζ 2 G) 3/2 P NG (k) S P χ (k) = f NLζ G,L + O(ζ 2 G,L) P G (k)

70 Weak non-gaussianity in L 1 f NL ζ 2 G g NLζ 2 Gh NL (ζ 2 G) 3/2 P NG (k) S P χ (k) = f NLζ G,L + O(ζ 2 G,L) P G (k)

71 Weak non-gaussianity in L 1 f NL ζ 2 G g NLζ 2 Gh NL (ζ 2 G) 3/2 P NG (k) S P χ (k) = f NLζ G,L + O(ζ 2 G,L) P G (k) P NG (k) S P χ (k) = f NLζG 2 1/2 B + O(ζG,L) 2 P G (k)

72 Weak non-gaussianity in L 1 f NL ζ 2 G g NLζ 2 Gh NL (ζ 2 G) 3/2 P NG (k) S P χ (k) = f NLζ G,L + O(ζ 2 G,L) P G (k) P NG (k) S P χ (k) = f NLζG 2 1/2 B + O(ζG,L) 2 P G (k)

73 Weak non-gaussianity in L 1 f NL ζ 2 G g NLζ 2 Gh NL (ζ 2 G) 3/2 P NG (k) S P χ (k) = f NLζ G,L + O(ζ 2 G,L) P G (k) P NG (k) S P χ (k) = f NLζG 2 1/2 B + O(ζG,L) 2 P G (k) B ζ G,L ζ 2 G 1/2

74 Weak non-gaussianity in L B ζ G,L ζ 2 G 1/2 Bias Increases for: smaller sub-volumes rarer subvolumes

75 Weak non-gaussianity in L B ζ G,L ζ 2 G 1/2 Bias Increases for: smaller sub-volumes rarer subvolumes A single parameter that encodes all the uncertainty/unmeasurable stuff about the background that matters

76 Weakly non-gaussian in L, Power Spectrum

77 Weakly non-gaussian in L, Non-Gaussianity f NL S = f NL g NLζ G,L 12 5 f 2 NLζ G,L + O(ζ 2 G,L) See also: Nurmi, Byrnes, Tasinato

78 Weakly non-gaussian in L, Non-Gaussianity f NL S = f NL g NLζ G,L 12 5 f 2 NLζ G,L + O(ζ 2 G,L) g NL = 10 3 See also: Nurmi, Byrnes, Tasinato

79 Weakly non-gaussian in L, Non-Gaussianity f NL S = f NL g NLζ G,L 12 5 f 2 NLζ G,L + O(ζ 2 G,L) g NL = 10 3 g NL = 10 5 See also: Nurmi, Byrnes, Tasinato

80 Strongly non-gaussian in L ζ NG (x) =ζ p G (x) ζp G (can get Feeder Scaling)

81 Strongly non-gaussian in L ζ NG (x) =ζ p G (x) ζp G (can get Feeder Scaling) ζ NG (x) S = pζ p 1 G,L ζ G,S(x)+ p! 2!(p 2)! ζp 2 G,L ζ 2 G,S (x) ζ 2 G,S + p! 3!(p 3)! ζp 3 G,L ζ3 G,S +...

82 Strongly non-gaussian in L ζ NG (x) =ζ p G (x) ζp G (can get Feeder Scaling) ζ NG (x) S = pζ p 1 G,L ζ G,S(x)+ p! 2!(p 2)! ζp 2 G,L ζ 2 G,S (x) ζ 2 G,S + p! 3!(p 3)! ζp 3 G,L ζ3 G,S +... Dashed: ζ G,L =3 ζg,l 2 Solid: ζ G,L =5 ζg,l 2

83 Summary so far Weakly non-gaussian local ansatz is statistically natural

84 Summary so far Weakly non-gaussian local ansatz is statistically natural ζ NG (x) =f(ζ G (x)) f(ζ G ) biased sub-samples ζ NG S = χ G (x)+ 3 5 f NL S χ 2 G (x) χ 2 G g NL S χ 3 G 3χ 2 χ G (x) +...

85 Summary so far Weakly non-gaussian local ansatz is statistically natural - Hierarchical moments - One non-fundamental parameter (B) can control size of all terms ζ NG (x) =f(ζ G (x)) f(ζ G ) biased sub-samples ζ NG S = χ G (x)+ 3 5 f NL S χ 2 G (x) χ 2 G g NL S χ 3 G 3χ 2 χ G (x) +...

86 Summary so far Weakly non-gaussian local ansatz is statistically natural - Hierarchical moments - One non-fundamental parameter (B) can control size of all terms ζ NG (x) =f(ζ G (x)) f(ζ G ) biased sub-samples ζ NG S = χ G (x)+ 3 5 f NL S χ 2 G (x) χ 2 G g NL S χ 3 G 3χ 2 χ G (x) +... Nelson, Shandera, (PRL); Byrnes, Nurmi, Tasinato, Wands ;

87 Summary so far Weakly non-gaussian local ansatz is statistically natural - Hierarchical moments - One non-fundamental parameter (B) can control size of all terms ζ NG (x) =f(ζ G (x)) f(ζ G ) biased sub-samples ζ NG S = χ G (x)+ 3 5 f NL S χ 2 G (x) χ 2 G g NL S χ 3 G 3χ 2 χ G (x) +... Nelson, Shandera, (PRL); Byrnes, Nurmi, Tasinato, Wands ; Cosmic Variance: Locally observed power, NG drawn from a distribution of possible values Nurmi, Byrnes, Tasinato ; LoVerde, Nelson, Shandera

88 Can subsampling change/obscure features of the statistics we d like to map to qualitatively different primordial physics?

89 Can subsampling change/obscure features of the statistics we d like to map to qualitatively different primordial physics? (In this simple case) Yes: - strong vs weak NG - hierarchical scaling - origin of parameter controlling the amplitude

90 Can subsampling change/obscure features of the statistics we d like to map to qualitatively different primordial physics? (In this simple case) Yes: - strong vs weak NG - hierarchical scaling - origin of parameter controlling the amplitude Linde, Mukhanov; LoVerde, Hu: this applies to curvaton scenarios

91 A possible threshold for cosmic variance from mode coupling:

92 A possible threshold for cosmic variance from mode coupling: Consider the strongly non-gaussian case: ζ(x) = σ G (x)+ 3 5 f NL[σ G (x) 2 σ G (x) 2 ]

93 A possible threshold for cosmic variance from mode coupling: Consider the strongly non-gaussian case: ζ(x) = σ G (x)+ 3 5 f NL[σ G (x) 2 σ G (x) 2 ] The observed NG is: f obs NL 1 f NL ζ 2 Gl 1 ζ l

94 A possible threshold for cosmic variance from mode coupling: Consider the strongly non-gaussian case: ζ(x) = σ G (x)+ 3 5 f NL[σ G (x) 2 σ G (x) 2 ] The observed NG is: f obs NL 1 f NL ζ 2 Gl 1 ζ l f obs NL < 1 ζ l > 1 Non-perturbative regime in the original scenario

95 Generalizing...

96 I. Conclusions from the power spectra? Red Tilt: Inflationary era was not exactly de Sitter (scales now map to times during inflationary evolution Tensor to scalar ratio: Still no word on the scale H Still no word on n T < 0

97 Does scale-dependence mean what we think it means? Red tilt scalars? Red tilt tensors? Bispectral indices, bias?

98 Does scale-dependence mean what we think it means? Red tilt scalars? Red tilt tensors? Bispectral indices, bias? ξ s,m (k) =ξ s,m (k p ) k k p n (s),(m) f

99 Does scale-dependence mean what we think it means? Red tilt scalars? Red tilt tensors? Bispectral indices, bias? ξ s,m (k) =ξ s,m (k p ) k k p n (s),(m) f b NG (k, M, f NL ) f NL k 2 (N. Dalal et al) f eff NL (M,n(s) f k 2 n(m) f (S. Shandera et al; Desjacques et al),n(m) f )

100 Beyond the local ansatz? Multi-field models typically have weakly scaledependent NG: B ζ (k 1,k 2,k 3 )= 6 5 ξ m(k 1 )ξ m (k 2 )f NL (k 3 )P ζ (k 1 )P ζ (k 2 ) + 2 perms.

101 Beyond the local ansatz? Multi-field models typically have weakly scaledependent NG: B ζ (k 1,k 2,k 3 )= 6 5 ξ m(k 1 )ξ m (k 2 )f NL (k 3 )P ζ (k 1 )P ζ (k 2 ) + 2 perms. ξ m (k) P σ (k)/p ζ (k)

102 Beyond the local ansatz? Multi-field models typically have weakly scaledependent NG: B ζ (k 1,k 2,k 3 )= 6 5 ξ m(k 1 )ξ m (k 2 )f NL (k 3 )P ζ (k 1 )P ζ (k 2 ) + 2 perms. ξ m (k) P σ (k)/p ζ (k) ζ(x) =φ G (x)+σ G (x)+ 3 5 f NL [σ G (x) 2 σ G (x) 2 ] g NL σ G (x)

103 More simply If different short wavelength modes couple with different strengths to the (locally constant) background Locally observed spectral index is biased in subvolumes

104 Subsampling the generalized local ansatz Pζ obs (k) =P ζ (k) f NL (k)σ Gl f 2 NL (k)(σ2 Gl σ2 Gl ) f 2 NL (k)σ2 G (k), Shift to observed spectral index

105 The spectral index

106 The spectral index, cont d

107 Model Building Consequences

108 How to rule cosmic variance of spectral index out of observational relevance: Observationally rule out any significant blue tilt in f local NL Importance of smaller scale probes.

109 Summary 1: Bottle of wine for James: No detection of local NG means cosmic variance may not be too large!

110 Summary 1: Bottle of wine for James: No detection of local NG means cosmic variance may not be too large! Dutch Wine Bottle via google:

111 Summary 1: Bottle of wine for James: No detection of local NG means cosmic variance may not be too large! Dutch Wine Bottle via google: Bottle of wine for James: Planck says NG is small? Or, universe is very big?!

112 Summary 1: Bottle of wine for James: No detection of local NG means cosmic variance may not be too large! Dutch Wine Bottle via google: Bottle of wine for James: Planck says NG is small? Or, universe is very big?!

113 Summary 11: Non-Gaussianity is for inflation what collider physics is for the Higgs...

114 Summary 11: Non-Gaussianity is for inflation what collider physics is for the Higgs... (generically I d expect more than one energy scales, DOF)

115 Summary 11: Non-Gaussianity is for inflation what collider physics is for the Higgs... (generically I d expect more than one energy scales, DOF)...except

116 Summary 11: Non-Gaussianity is for inflation what collider physics is for the Higgs......except (generically I d expect more than one energy scales, DOF) Not all particle interactions leave an independent signature (thermodynamics, Myers, Byrnes) Experiment was performed at a fixed (unknown) energy One experiment

117 Summary 11: Non-Gaussianity is for inflation what collider physics is for the Higgs......except (generically I d expect more than one energy scales, DOF) Not all particle interactions leave an independent signature (thermodynamics, Myers, Byrnes) Experiment was performed at a fixed (unknown) energy One experiment Cosmic Variance: if mode coupling between significantly different scales, we circle back to IC/measure problems

118 Summary 1II:

119 Summary 1II: A familiar aspect of inflation, dressed up in different clothes: IC problem for our observable 60 e-folds region

120 Summary 1II: A familiar aspect of inflation, dressed up in different clothes: IC problem for our observable 60 e-folds region Nothing here depended on where you get the fluctuations:

121 Summary 1II: A familiar aspect of inflation, dressed up in different clothes: IC problem for our observable 60 e-folds region Nothing here depended on where you get the fluctuations: Good: can we find a natural pattern inflation does not predict? (If not, is that bad for inflation?)

122 Summary 1II: A familiar aspect of inflation, dressed up in different clothes: IC problem for our observable 60 e-folds region Nothing here depended on where you get the fluctuations: Good: can we find a natural pattern inflation does not predict? (If not, is that bad for inflation?) Bad: a random pattern in a big universe may not look random to local observers

123 Summary IV:?????

124 Summary IV: Easy to apply this to other models to check what level of confusion can occur (QSF, w/ Scott)?????

125 Summary IV: Easy to apply this to other models to check what level of confusion can occur (QSF, w/ Scott) Is there a useful notion of landscape and measure here? (not quite theory space?)?????

126 Summary IV: Easy to apply this to other models to check what level of confusion can occur (QSF, w/ Scott) Is there a useful notion of landscape and measure here? (not quite theory space?) Other signatures of long wavelength modes are correlated: anomaly explanations, small curvature. Statistical weight for minimal e-folds, Gaussian vs large universe, NG??????