TESTING STRINGY NON-GAUSSIANITY Sarah Shandera Columbia University - - PowerPoint PPT Presentation

String Pheno, 2008

TESTING STRINGY NON-GAUSSIANITY

Sarah Shandera Columbia University

arXiv:0711.4126 (M. LoVerde, A. Miller, S.S., L. Verde) arXiv:0802.2290 (L. Leblond, S.S.)

String Pheno, 2008

NOT ONLY THE LHC...

Galaxy Surveys: SZA, ACT, SPT PLANCK (Nov?) B-mode polarization: QUIET, EBEX,

String Pheno, 2008

STRING COSMOLOGY

String theory is a likely place to look for models of very early universe physics: inflation or any alternatives String theory has already provided new ideas for cosmologists (e.g. slow-roll is hard) Depending on scales, Hubble vs. (warped) string, there may be signatures of stringy physics Much more observational information is on its way - potential to uncover interesting (and discriminating) features: non-Gaussianity

String Pheno, 2008

PLAN

Non-Gaussianity: Why? Qualitative features. What physics is probed by those qualitative features? Potential of near-future observations

String Pheno, 2008

PLAN

Non-Gaussianity: Why? Qualitative features. What physics is probed by those qualitative features? Potential of near-future observations

Focus on scale-dependence, a consequence and probe of warped extra dimensions

• I. NON-GAUSSIANITY

String Pheno, 2008

PHENO PICTURE

V( ) ! ! !"#$!%#""&%'()#* %'+',-)*( ./0)"",-)#*/1 2,34'5 67,*-73&8"70-7,-)#*/

φ V(φ)

String Pheno, 2008

PHENO PICTURE

V( ) ! ! !"#$!%#""&%'()#* %'+',-)*( ./0)"",-)#*/1 2,34'5 67,*-73&8"70-7,-)#*/

φ V(φ) Curvature ζ(k1)ζ(k2) = (2π)3δ3

D(k1 + k2)(2π2k−3)Pζ(k)

String Pheno, 2008

PHENO PICTURE

V( ) ! ! !"#$!%#""&%'()#* %'+',-)*( ./0)"",-)#*/1 2,34'5 67,*-73&8"70-7,-)#*/

φ V(φ) Pζ(k) ∝ kns−1 Pζ ≈ 10−9 Amplitude Scale-dependence Curvature ζ(k1)ζ(k2) = (2π)3δ3

D(k1 + k2)(2π2k−3)Pζ(k)

String Pheno, 2008

NON-GAUSSIANITY

Gaussian: all higher order, connected, n-point functions are zero Fluctuations are exactly Gaussian only for free fields; we know this can’t be true of the inflaton (nearly flat potential usually means nearly free) Non-zero 3-point is a first check (expect it to be easiest to measure)

String Pheno, 2008

NON-GAUSSIANITY

Gaussian: all higher order, connected, n-point functions are zero Fluctuations are exactly Gaussian only for free fields; we know this can’t be true of the inflaton (nearly flat potential usually means nearly free) Non-zero 3-point is a first check (expect it to be easiest to measure)

ζ(k1)ζ(k2)ζ(k3) = (2π)3δ3

D(k1 + k2 + k3)B(k1, k2, k3)

String Pheno, 2008

STRING EXAMPLES

Multiple fields...Many! Single field with additional structure D3/D7 + cosmic strings (Haack, Kallosh, Krause, Linde, Lust, Zagermann); Any field + sharp features in the potential/geometry (Chen, Easther, Lim; Bean, Chen, Hailu, Tye, Xu); deviations from Bunch-Davies (short inflation) (Holman,Tolley); Landscape inflation (Tye) Single field with derivative interactions DBI brane inflation; p-adic (Silverstein, Tong; Barnaby, Cline)

String Pheno, 2008

OBSERVABLES

Real space or k-space correlation functions CMB or galaxy bispectrum Sensitive to detailed model Probability density function Count very large objects (galaxy clusters) Sensitive to over-all amount (and sign, scaling,...)

• f NG
• k2
• k1
• k3

String Pheno, 2008

INFLATON TO DENSITY

Inflaton Curvature

φ

ζ

Density Structure

δ

δ

ζ

Curvature Density

δ

Gaussian Non-Gaussian Non-Gaussian σ

String Pheno, 2008

QUALITATIVE FEATURES

Amplitude (how non-Gaussian?) Shape (largest for which triangles?) Sign (positively skewed?) Scale-dependence (growing or shrinking on small scales?)

Each of these features can rule

• ut large classes of models

String Pheno, 2008

QUALITATIVE FEATURES

Amplitude (how non-Gaussian?) Shape (largest for which triangles?) Sign (positively skewed?) Scale-dependence (growing or shrinking on small scales?)

Each of these features can rule

• ut large classes of models

Slow roll

String Pheno, 2008

QUALITATIVE FEATURES

Amplitude (how non-Gaussian?) Shape (largest for which triangles?) Sign (positively skewed?) Scale-dependence (growing or shrinking on small scales?)

Each of these features can rule

• ut large classes of models

Slow roll

X

(Maldacena)

String Pheno, 2008

QUALITATIVE FEATURES

Amplitude (how non-Gaussian?) Shape (largest for which triangles?) Sign (positively skewed?) Scale-dependence (growing or shrinking on small scales?)

Each of these features can rule

• ut large classes of models

Slow roll Derivative terms

X

(Maldacena)

String Pheno, 2008

QUALITATIVE FEATURES

Amplitude (how non-Gaussian?) Shape (largest for which triangles?) Sign (positively skewed?) Scale-dependence (growing or shrinking on small scales?)

Each of these features can rule

• ut large classes of models

Slow roll Derivative terms

X X

(Maldacena)

String Pheno, 2008

QUALITATIVE FEATURES

Amplitude (how non-Gaussian?) Shape (largest for which triangles?) Sign (positively skewed?) Scale-dependence (growing or shrinking on small scales?)

Each of these features can rule

• ut large classes of models

Slow roll Derivative terms DBI

X X

(Maldacena)

String Pheno, 2008

QUALITATIVE FEATURES

Amplitude (how non-Gaussian?) Shape (largest for which triangles?) Sign (positively skewed?) Scale-dependence (growing or shrinking on small scales?)

Each of these features can rule

• ut large classes of models

Slow roll Derivative terms DBI

X X X

(Maldacena)

String Pheno, 2008

QUALITATIVE FEATURES

Amplitude (how non-Gaussian?) Shape (largest for which triangles?) Sign (positively skewed?) Scale-dependence (growing or shrinking on small scales?)

Each of these features can rule

• ut large classes of models

Slow roll Local model Derivative terms DBI

X X X

(Maldacena)

String Pheno, 2008

QUALITATIVE FEATURES

Amplitude (how non-Gaussian?) Shape (largest for which triangles?) Sign (positively skewed?) Scale-dependence (growing or shrinking on small scales?)

Each of these features can rule

• ut large classes of models

Slow roll Local model Derivative terms DBI

X X X X

(Maldacena)

• II. PHYSICS PROBED:

DERIVATIVE INTERACTIONS AND DBI

String Pheno, 2008

GENERAL SET-UP

Action is a function of a single field and its first derivatives Sound speed

c2

s =

P,X P,X + 2XP,XX

Armendariz-Picon, Damour, Mukhanov; Garriga, Mukhanov

S = 1 2

• d4x√−g[M 2

pR − 2P(X, φ)]

X = −1 2gµν∂µφ∂νφ

String Pheno, 2008

EXAMPLE CASE: DBI

R r0, e0

• 4A

D3

ρ0

h ≈ R4 r4 = R4T 2

3

φ4

˙ φ2 < f(φ)−1 = Sh(φ)−1

γ(φ) = 1

• 1− f(φ)˙

φ2

P,X = c−1

s

= γ

String Pheno, 2008

THE PARAMETERS

Non-Gaussianity Scale-dependence of the sound speed

cs(k) = cs(k0) k k0 κ f eff

NL ∝ 1

c2

s

(Seery, Lidsey; Chen, Huang, Kachru, Shiu)

String Pheno, 2008

REASON TO KNOW UV PHYSICS I

Suppose we have an action Then But for DBI, we know the sum

P(X, φ) = −V (φ) + X + a1 X2 M 4 + a2 X3 M 8 + . . .

X/M4 ≪ 1 ⇒ c2

s ∼ O(a few×10−1)

f eff

NL ∝ 1/c2 s ∼ O(1)

(Creminelli)

P(X, φ) = −f(φ)

• 1 − 2Xf −1(φ) + f(φ) − V (φ)

String Pheno, 2008

REASON TO KNOW UV PHYSICS II

‘EFT’ for the inflaton, perturbative calculations from the general sound speed action breaks down when Warped deformed conifold: warp factor goes to a constant and we can use string theory to understand

c4

s ∼ Pζ ∼ 10−9

c4

s < Pζ

(talks by Klebanov;)

(Cheung, Creminelli, Fitzpatrick, Kaplan, Senatore; Leblond, S.S.)

• III. OBSERVATIONAL

PROSPECTS

String Pheno, 2008

NG ON A RANGE OF SCALES

κ = −0.1

κ = −0.3

Larger range of scales = Larger range of geometry

String Pheno, 2008

OBSERVATIONS: CLUSTERS

Count the number of very large objects (several sigma fluctuations) Sensitive to magnitude of non-Gaussianity on the smallest ‘linear’ scales If NG is large at CMB scales and or has a large running, upcoming surveys can constrain it.

LoVerde, Miller, S.S., Verde

String Pheno, 2008

SUMMARY

Observations will soon be powerful enough to probe interactions of the inflaton Models of inflation from string theory have a range of interactions with surprising features Scale dependent non-Gaussianity, observable by combining CMB and large scale structure data, is a useful qualitative feature: most optimistic case, probes geometry of extra dimensions Large non-Gaussianity would require interesting physics