Primordial non-gaussianity from inflation

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1 Quantum Universe, Groningen 7 th March 0 Primordial non-gaussianity from inflation David Wands Institute of Cosmology and Gravitation University of Portsmouth wor with Chris Byrnes, Jon Emery, Christian Fidler, Gianmassimo Tasinato, Kazuya Koyama, David Langlois, David Lyth, Misao Sasai, Jussi Valiviita, Filippo Vernizzi review: Classical & Quantum Gravity 7, arxiv:

3 COBE launched 990, data 994 WMAP NASA launched 00, latest data 0

4 NASA

5 ESA

6 ε = n 4 π P δ +, P π B,, + = δ + Wiipedia: AllenMcC

7 +,-.#/%#%0!##4505!fNL!45#/5&!6! 78#9:!%!9,%050!;%0<!=5,>! fnl f NL B,, = P P + P P + P P

8 inflation primordial non-gaussianity

9 + +,, B + + +,, B + + 8,, B

10 t = curvature perturbation on uniform-density hypersurface in radiation-dominated era φ,t i N = final initial Hdt on large scales, neglect spatial gradients, solve as separate universes N = N i I φ φ, t N δφ +... Starobinsy 85; Salope & Bond 90; Sasai & Stewart 96; Lyth & Rodriguez 05; Langlois & Vernizzi... I I

11 δφi = δφ I + δφi = = e.g., < > I N φ I +... δφ + I I N δφi + φ I I, J N φ φ I I δφ Iδφ J +... N N N N N N sub-hubble field interactions super-hubble classical evolution Byrnes, Koyama, Sasai & DW arxiv:

12 = δφ δφ Φ =/ = + = + = + + = f N N N N N NL δφ δφ δφ δφ δφ δφ δφ N N N

13 = N δφ + N 6 τ NL δφ + N δφ +... N N N g NL N N N N τ NL 6f NL /5 < T P > = < B > N

14 local f NL f Ω χ, decay local NL ε N = O << N f local NL n Maldacena 00 Creminelli & Zaldarriaga 004

15 Vχ χ - light field, m<<h, during inflation acquires almost scale-invariant, Gaussian distribution of field fluctuations δχ on large scales - quadratic energy density for free field, ρ χ =m χ / - spectrum of initially isocurvature density perturbations χ δρ χ δχ ρ χ χ - transferred to radiation when curvaton decays with some efficiency, 0<r<, where r Ω χ,decay =r χ r δχ χ

16 simplest quadratic curvaton: V=m χ / first-order perturbations =r χ where r= Ω χ 4 Ω χ decay second-order perturbations = r r f NL = 5 4r 5 5r third-order perturbations = 9 r + +0r+r g NL = 5 6r r 8 0r 9 r 9 Predictions of the simplest quadratic curvaton model: for r f NL = 5 4, g NL = 9 for r << f NL >>, τ NL = 6 5 f NL >> g NL = 0 f NL

17 local f NL f Ω χ, decay local NL ε N = O << N f local NL n Maldacena 00 Creminelli & Zaldarriaga 004 Lyth & Wands 00 L 4 ϕ = ϕ f equil NL c s Cheung et al 008

18 c M eff equil s = f NL Meff + 4θ cs << M eff θ θ f local NL

19 Constraints on f NL non-gaussianity WMAP9 constraints using estimators based on optimal templates: Local: - < f NL < 77 95% CL Bennett et al < g NL / 05 < 8.6 Ferguson et al; Smidt et al 00 Equilateral: - < f NL < Orthogonal: -445 < f NL < -45 LSS constraints on local ng from galay power spectrum: Local: -9 < f NL < 70 95% CL Slosar et al 008 [SDSS] 7 < f NL < 7 95% CL Xia et al 00 [NVSS survey of AGNs] -7 < f NL < 0 95% CL Giannantonio et al < g NL / 0 5 <.6 [cross-correlating SDSS+NVSS] Planc constraints Ade et al March 0 Local: f NL =.7 ± % CL Equilateral: f NL = -4 ± 75 Orthogonal: f NL = -5 ± 9

20 Constraints on f NL non-gaussianity WMAP9 constraints using estimators based on optimal templates: Local: - < f NL < 77 95% CL Bennett et al < g NL / 05 < 8.6 Ferguson et al; Smidt et al 00 Equilateral: - < f NL < Orthogonal: -445 < f NL < -45 LSS constraints on local ng from galay power spectrum: Local: -9 < f NL < 70 95% CL Slosar et al 008 [SDSS] 7 < f NL < 7 95% CL Xia et al 00 [NVSS survey of AGNs] -7 < f NL < 0 95% CL Giannantonio et al < g NL / 0 5 <.6 [cross-correlating SDSS+NVSS] Planc constraints Ade et al March 0 Local: -9.8 < f NL < 4. 95% CL Equilateral: -9 < f NL < 08 Orthogonal: -0 < f NL < 5

signals in the data: Large-scale anomalies

21 signals in the data: Large-scale anomalies Lac of power at low multipoles Hemispherical power asymmetry Dipole modulation? Octopole L= feature in trispectrum? Oscillatory features in the bispectrum? step inflation? resonant features in the potential e.g., aion-mondromy? features in the power spectrum? Folded bispectrum = = non-bunch-davies vacuum? -sigma result

22 +,-.#/%#%0!##4505!fNL!45#/5&!6! 78#9:!%!9,%050!;%0<!=5,>! fnl f NL B,, = P P + P P + P P

23 non-linearity parameter Sasai, Valiviita & Wands 006 see also Mali & Lyth 006 c.f. eact numerical calculation Planc σ bound r > 0.09

24 Intrinsic bispectrum of CMB Eisting non-gaussianity templates based on non-linear primordial perturbations + linear Boltzmann codes CMBfast, CAMB, etc Second-order general relativistic Boltzmann codes now available Pitrou 00: CMBquic in Mathematica: f NL ~ 5? Huang & Vernizzi Paris Pettinari, Fidler et al Portsmouth Su, Lim & Shellard Cambridge & London 4 Analytical approimation Numerical bispectrum 0 need templates for secondary non-gaussianity e.g. lensing-isw induced tensor and vector modes from density perturbations testing interactions at recombination δρ e.g., gravitational wave production δρ h

26 δ = δ +δ +...

27 .5.0 bias to f NL angular scale L ma

28 .4. signal of intrinsic bispectrum signal of local model with f NL =.0 S / N angular scale L ma

29 Non-Gaussian outloo: Complementary to power spectrum detection of primordial non-gaussianity would ill tetboo single-field slow-roll inflation models requires multiple fields and/or unconventional physics No evidence yet for fnl-type non-gaussianity Large fnl is dead long-live fnl = O Need more data Planc 04 + large-scale structure surveys Euclid+SKA? Non-Gaussianity has been detected non-linear physics inevitably generates non-gaussianity infinite variety of non-gaussianity possible need to disentangle primordial and generated non-gaussianity

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