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 B-mode polarization: PLANCK QUIET, EBEX, (Nov?) 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 String Pheno, 2008
I. NON-GAUSSIANITY
PHENO PICTURE 67,*-73&8"70-7,-)#*/ V( φ ) V( ) ! !"#$ ! %#""&%'()#* 2,34'5 ./0)"",-)#*/1 %'+',-)*( φ ! String Pheno, 2008
PHENO PICTURE 67,*-73&8"70-7,-)#*/ V( φ ) V( ) ! !"#$ ! %#""&%'()#* 2,34'5 ./0)"",-)#*/1 %'+',-)*( φ ! D ( k 1 + k 2 )(2 π 2 k − 3 ) P ζ ( k ) � ζ ( k 1 ) ζ ( k 2 ) � = (2 π ) 3 δ 3 Curvature String Pheno, 2008
PHENO PICTURE Amplitude 67,*-73&8"70-7,-)#*/ P ζ ≈ 10 − 9 V( φ ) V( ) ! !"#$ ! %#""&%'()#* Scale-dependence 2,34'5 ./0)"",-)#*/1 %'+',-)*( P ζ ( k ) ∝ k n s − 1 φ ! D ( k 1 + k 2 )(2 π 2 k − 3 ) P ζ ( k ) � ζ ( k 1 ) ζ ( k 2 ) � = (2 π ) 3 δ 3 Curvature 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 ( k 1 ) ζ ( k 2 ) ζ ( k 3 ) � = (2 π ) 3 δ 3 D ( k 1 + k 2 + k 3 ) B ( k 1 , k 2 , k 3 ) 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 k 1 � k 2 � k 3 Sensitive to detailed model Probability density function Count very large objects (galaxy clusters) Sensitive to over-all amount (and sign, scaling,...) of NG String Pheno, 2008
INFLATON TO DENSITY Inflaton Curvature δ φ ζ Curvature Density σ ζ δ Density Structure Gaussian δ Non-Gaussian Non-Gaussian 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 out large classes of models String Pheno, 2008
QUALITATIVE FEATURES Amplitude (how non-Gaussian?) Slow roll Shape (largest for which triangles?) Sign (positively skewed?) Scale-dependence (growing or shrinking on small scales?) Each of these features can rule out large classes of models String Pheno, 2008
QUALITATIVE FEATURES X Amplitude (how non-Gaussian?) Slow roll (Maldacena) Shape (largest for which triangles?) Sign (positively skewed?) Scale-dependence (growing or shrinking on small scales?) Each of these features can rule out large classes of models String Pheno, 2008
QUALITATIVE FEATURES X Amplitude (how non-Gaussian?) Slow roll (Maldacena) Shape (largest for which triangles?) Derivative terms Sign (positively skewed?) Scale-dependence (growing or shrinking on small scales?) Each of these features can rule out large classes of models String Pheno, 2008
QUALITATIVE FEATURES X Amplitude (how non-Gaussian?) Slow roll (Maldacena) X Shape (largest for which triangles?) Derivative terms Sign (positively skewed?) Scale-dependence (growing or shrinking on small scales?) Each of these features can rule out large classes of models String Pheno, 2008
QUALITATIVE FEATURES X Amplitude (how non-Gaussian?) Slow roll (Maldacena) X Shape (largest for which triangles?) Derivative terms DBI Sign (positively skewed?) Scale-dependence (growing or shrinking on small scales?) Each of these features can rule out large classes of models String Pheno, 2008
QUALITATIVE FEATURES X Amplitude (how non-Gaussian?) Slow roll (Maldacena) X Shape (largest for which triangles?) Derivative terms X DBI Sign (positively skewed?) Scale-dependence (growing or shrinking on small scales?) Each of these features can rule out large classes of models String Pheno, 2008
QUALITATIVE FEATURES X Amplitude (how non-Gaussian?) Slow roll (Maldacena) X Shape (largest for which triangles?) Derivative terms X DBI Sign (positively skewed?) Scale-dependence (growing or shrinking on small scales?) Local model Each of these features can rule out large classes of models String Pheno, 2008
QUALITATIVE FEATURES X Amplitude (how non-Gaussian?) Slow roll (Maldacena) X Shape (largest for which triangles?) Derivative terms X DBI Sign (positively skewed?) Scale-dependence (growing or shrinking on small X scales?) Local model Each of these features can rule out large classes of models String Pheno, 2008
II. PHYSICS PROBED: DERIVATIVE INTERACTIONS AND DBI
GENERAL SET-UP Action is a function of a single field and its first derivatives S = 1 � d 4 x √− g [ M 2 p R − 2 P ( X, φ )] 2 X = − 1 2 g µ ν ∂ µ φ∂ ν φ Sound speed P ,X c 2 s = P ,X + 2 XP ,XX Armendariz-Picon, Damour, Mukhanov; Garriga, Mukhanov String Pheno, 2008
EXAMPLE CASE: DBI P ,X = c − 1 = γ s D3 R 1 γ ( φ ) = � 1 − f ( φ ) ˙ φ 2 ρ 0 -4A r 0 , e 0 φ 2 < f ( φ ) − 1 = Sh ( φ ) − 1 ˙ h ≈ R 4 r 4 = R 4 T 2 3 φ 4 String Pheno, 2008
THE PARAMETERS Non-Gaussianity NL ∝ 1 f eff c 2 s Scale-dependence of the sound speed � k � κ c s ( k ) = c s ( k 0 ) k 0 (Seery, Lidsey; Chen, Huang, Kachru, Shiu) String Pheno, 2008
REASON TO KNOW UV PHYSICS I Suppose we have an action (Creminelli) X 2 X 3 P ( X, φ ) = − V ( φ ) + X + a 1 M 4 + a 2 M 8 + . . . Then X/M 4 ≪ 1 ⇒ c 2 s ∼ O (a few × 10 − 1 ) f eff NL ∝ 1 /c 2 s ∼ O (1) But for DBI, we know the sum � P ( X, φ ) = − f ( φ ) 1 − 2 Xf − 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 c 4 s ∼ P ζ ∼ 10 − 9 (Cheung, Creminelli, Fitzpatrick, Kaplan, Senatore; Leblond, S.S.) Warped deformed conifold: warp factor goes to a constant and we can use string theory to understand c 4 s < P ζ (talks by Klebanov;) String Pheno, 2008
III. OBSERVATIONAL PROSPECTS
NG ON A RANGE OF SCALES Larger κ = − 0 . 3 range of scales = κ = − 0 . 1 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 String Pheno, 2008
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