What s left of non-gaussianity (i) after Planck? (ii) after BICEP2?

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1 PONT 04, Avignon 4th April 04 What s left of non-gaussianity (i) after Planc? (ii) after BICEP? David Wands Institute of Cosmology and Gravitation University of Portsmouth

2 Conclusions from Planc+BICEP Planc0 not easy to detect non- Gaussianity large non- Gaussianity (f NL >>0) ruled out need f NL < to discriminate inflaton vs alternahve models intrinsic+secondary non- Gaussianity (last- scaiering and line- of- sight) will be important BICEP04 (if confirmed) GUT- scale inflahon implies Gaussian (inflaton) perturbahons not negligible in slow- roll inflahon David Wands

3 WMAP0 standard model of primordial cosmology NASA

4 Planc0 - new standard model of primordial cosmology P() ESA

5 more informa=on in higher- order correlators fnl B( + + ) f NL Bζ (,, ) = P( )P( ) + P( )P( ) + P( )P( )

6 Primordial Gaussianity from infla=on Quantum field fluctua=ons during infla=on ground state of simple harmonic oscillator almost free field in almost de Si5er space almost scale- invariant and almost Gaussian Wiipedia: AllenMcC Power spectra probe bacground dynamics (H, ε,...) n ζ ζ = π P δ +, P ( ) ( ) ( ) ( ) 4 ζ contain all the informa:on in a Gaussian random field but many different models can produce similar power spectra Higher- order correla=ons probe interac:ons ζ physics+gravity! non- linearity! non- Gaussianity ( ) ( ) π B,, ( + ) ζ ζ = ζ δ + David Wands 6 ζ

7 Many possible sources of non- Gaussianity IniHal vacuum Excited state inflation Sub- Hubble evoluhon Hubble- exit Super- Hubble evoluhon Higher- derivahve interachons e.g. - inflahon, DBI, Galileons Features in potenhal ParHcle produchon during inflahon Self- interachons + gravity intrinsic End of inflahon Tachyonic instability (p)reheahng Modulated (p)reheahng A]er inflahon Curvaton decay Topological defects MagneHc fields primordial non-gaussianity Primary anisotropies Last- scaiering Secondary anisotropies ISW/lensing + foregrounds David Wands 7

8 Many possible shapes for bispectra local type (Komatsu&Spergel 00) local in real space max for squeezed triangles: <<, equilateral type (Creminelli et al 005) peas for ~~ orthogonal type (Senatore et al 009) independent of local + equilateral shapes separable basis (Ferguson et al 008) 8 ( ) + +,, B ζ ( ) ( )( )( ) + + +,, B ζ ( ) ( ) + + 8,, B ζ need templates to extract small ng signals

9 non- Gaussianity expected from infla=on? single- field slow- roll inflaton during convenhonal slow- roll inflahon adiaba:c perturba:ons => ζ constant on large scales => more generally: super- Hubble evolu=on non- adiaba:c perturba:ons during mulh- field inflahon => ζ constant at/a]er end of inflahon (curvaton, modulated reheahng, etc) e.g., curvaton local f NL f Ω χ, decay local NL ( ε ) N ʹ ʹ = O << Nʹ f local NL n ζ Maldacena 00 Creminelli & Zaldarriaga 004 Lyth & Wands 00 sub- Hubble interac=ons e.g. DBI inflahon, Galileon fields... or coupling to massive fields Achucarro et al (00+); Gao et al (0) L 4 ( ϕ) + ( ) +... = ϕ f equil NL c s Cheung et al 008

10 V(χ) curvaton scenario: Linde & Muhanov 997; Enqvist & Sloth, Lyth & Wands, Moroi & Taahashi 00 χ curvaton χ = a wealy-coupled, late-decaying scalar field - light during inflation (m<<h) hence acquires an almost scaleinvariant, Gaussian distribution of field fluctuations - quadratic energy density for massive field, ρ χ =m χ / - spectrum of initially non-adiabatic density perturbations ζ δρ χδχ + δχ χ χ χ ρχ - transferred to radiation when curvaton decays with some efficiency, 0<R χ <, where R χ Ω χ,decay ζ = R χ ζ χ ζ G + ζ G 4R χ f NL 5 4Rχ

11 CMB constraints on non-gaussianity WMAP constraints Ø Local: - < f NL < 77 (95% CL) Bennett et al < g NL / 0 5 < 8.6 Ferguson et al; Smidt et al 00 Ø Equilateral: - < f NL < Ø Orthogonal: -445 < f NL < -45 Planc constraints (Planc XXIV, arxiv:0.5084) Ø Local: -9.8 < f NL < 4. (95% CL) τ NL < 800 no bound yet on g NL Ø Equilateral: -9 < f NL < 08 Ø Orthogonal: -0 < f NL < 5 Ø Many other bispectrum shapes tested Ø some evidence for oscillatory features

12 QuadraHc curvaton non- linearity parameter Sasai, Valiviita & Wands (006) see also Mali & Lyth (006) Planc σ bound R χ > 0.08 inflaton f NL =0.0 R χ

13 Lesson #: Planc0 Primordial non- Gaussianity is not going to be so easy to find! f NL > would be a good way to falsify inflaton mechanism need f NL < to disprove curvaton- type mechanisms David Wands

14 Lesson #: Planc0 Instrinsic (last- scaiering) and secondary ng (line- of- sight) are important for f NL =O() see tal this aernoon by Filippo David Wands 4

15 Intrinsic bispectrum of CMB Existing 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 (0) (Paris) Pettinari, Fidler et al (Portsmouth) Su, Lim & Shellard (Cambridge & London) 4 Analytical approximation Numerical bispectrum 0 Ø need templates to identify intrinsic + secondary non-gaussianity Ø testing interactions at recombination Ø e.g., gravitational wave production δρ δρ h

16 Intrinsic bias on local non- Gaussianity Effects at recombina9on small compared to Planc sensi9vity.5.0 bias to f NL angular scale L max Pepnari, Fidler, RC, Koyama, Wands arxiv:0.08

17 Detec=ng the intrinsic bispectrum even using the correct template, hard to see the intrinsic TTT signal with Planc.4. Signal- to- noise ra9o signal of intrinsic bispectrum signal of local model with f NL =.0 S / N angular scale L max Pepnari, Fidler, CriIenden, Koyama, Wands arxiv:0.08

18 intrinsic bispectrum with polarisa:on correlahng TTT, TTE, TEE, TBB, etc, improves signal all 8 bispectra all 8 bispectra (-lensing) TTT only (-lensing) Fidler, Pe[nari, CriIenden, Koyama, Lewis, Wands, in prepara9on

19 Lensing- ISW signal Goldberg & Spergel 999 Selja and Zaldarriaga 999 Lewis, Challinor & Hanson 0 Lewis 0 Secondary bispectrum already seen from two late Hme gravitahonal effects: gravitahonal lensing and the integrated Sachs- Wolfe effect. In the ISW effect, large scale over- densihes and under- densihes appear hoier or colder as photons can gain or lose energy passing through their Hme dependent potenhals. These potenhals correlate to where gravitahonal lensing (seen on smaller scales) is largest or smallest, creahng mode coupling. Significant bias, local f NL of order 7, seen in the Planc analysis.

20 Large-scale structure constraints on f NL constraints on local f NL from scale-dependent bias in galaxy power spectrum (Dalal et al 007; Verde & Matarrese 008): -7 < f NL < 0 (95% CL) Giannantonio et al < g NL / 0 5 <.6 [cross-correlating SDSS+NVSS] constraints on local g NL may be possible from scale-dependent bias in galaxy bispectrum (Tasinato, Tellarini, Ross & Wands 04)

21 Intrinsic ng in large- scale structure (Bruni, Hidalgo & Wands, submiied) amplitude of maier density growing mode on large scales: δ(t,x)=c(x)d+(t)+ C(x) determines abundance of collapsed halos (and hence galaxies) set by gravitahonal potenhal, φ, in Newton gravity linear Poisson constraint - > Gaussian potenhal implies Gaussian density field set by intrinsic curvature, R, in Einstein gravity non- linear relahon between R and primordial metric ζ - > intrinsic non- Gaussianity characterishc of GR f GR NL = 5, g GR NL = 50, h GR NL = David Wands

22 Planc power spectrum constraints slow roll parameters ε = H H, η i = m i Inflaton P ζ " $ 8π ε # H * M Pl % ' & Curvaton H P ζ R " χ H * 9π $ # χ * % ' & tilt: n = 6ε + η ϕ P T " H $ * π # M Pl % ' & tensor-scalar ratio: r T =6ε tilt: n = ε + η χ P T " H $ * π # M Pl % ' & tensor-scalar: r T =8 χ * / R χ M Pl <6ε Planc0: n = ± r T < 0. David Wands

23 Different Planc0 perspechves Inflaton viewpoint Tensor- scalar raho bounds ε < 0.0 Scalar Hlt n=0.96 then favours η ϕ < 0 E.g., axion e.g., axion V(ϕ)=Λ 4 (- cos(ϕ/f)) Curvaton viewpoint Tensor- scalar raho bounds H inf (model- independent), not ε Scalar- Hlt implies either Large- field inflahon: ε 0.0 and η χ 0 e.g., λϕ 4 inflahon (with N 60) Small- field with η χ < 0 and ε << 0.0 e.g., axion V(χ)=Λ 4 (- cos(χ/f)) David Wands

24 f NL bounds on quadrahc curvaton V ( χ) = m χ R χ Fonseca & Wands (0) see also Naayama et al (00) R χ m Γ χ * M Pl << David Wands 4

25 f NL bounds on quadrahc curvaton + r T =P T /P ζ Fonseca & Wands (0) see also Naayama et al (00) V ( χ) = m χ R χ BICEP04 R χ m Γ χ * M Pl << David Wands 5

26 Lesson #: BICEP04 BICEP (if confirmed) P T 0.6 P ζ adiabahc inflaton perturbahons P ζ* = P T / 6ε cannot be arbitrarily small in slow- roll* inflahon (ε<) for curvaton+inflaton where w χ = curvaton/total r T = 6ε(-w χ ) 0.6 => ε 0.0 e.g., if ε = 0.0 then w χ 0.5 primordial perturbahons from inflaton, ζ *, are always Gaussian (Maldacena, 00) *curvaton- type mechanisms do not require slow- roll inflaton David Wands 6

27 Local non- Gaussianity from non- adiabahc fluctuahons curvaton, also mulh- field inflahon, modulated reheahng, inhomogeneous end of inflahon Inflaton curvaton δσ δχ adiabahc field perturbahons along bacground trajectory - > ζ remains constant ζ H δσ σ! + R # χ % $ δχ χ + δχ χ & ( ' David Wands 7

28 f NL + r T quadrahc curvaton + inflaton: for ε=0.0 Fonseca & Wands (0) V ( χ) = m χ BICEP04 inflaton f NL 5 w χ 4R χ curvaton Planc bounds f NL and r T David Wands 8

29 trispectrum quadrahc curvaton + inflaton: for ε=0.0 Fonseca & Wands (0) V ( χ) = m χ BICEP04 inflaton curvaton τ NL f NL w χ g NL f NL w χ Planc bounds f NL and r T David Wands 9

30 How to measure w χ? trispectrum (τ NL, Suyama- Yamaguchi inequality) w χ = 6 5 f NL τ NL tensor Hlt (n T = -ε) w χ = r T 6ε = r T 8n T David Wands 0

31 Non-Gaussian outloo: Complementary to power spectrum constraints requires multiple fields and/or unconventional physics detection of primordial non-gaussianity would ill textboo single-field slow-roll inflation models Planc0 not a game-changer large local fnl is dead long-live fnl = O() instrinsic non-gaussianity is important but BICEP04 could be pivotal tensor modes -> non-negligible inflaton (Gaussian) perturbations need more data Planc04, SPT, etc + large-scale structure surveys non-gaussianity has been detected need to disentangle primordial and generated non-gaussianity