Primordial non-Gaussianity from inflation Cosmo-12, Beijing 13th September 2012 Primordial non-Gaussianity from inflation David Wands Institute of Cosmology and Gravitation University of Portsmouth work with Chris Byrnes, Jon Emery, Christian Fidler, Gianmassimo Tasinato, Kazuya Koyama, David Langlois, David Lyth, Misao Sasaki, Jussi Valiviita, Filippo Vernizzi… review: Classical & Quantum Gravity 27, 124002 (2010) arXiv:1004.0818

WMAP7 standard model of primordial cosmology Komatsu et al 2011

Gaussian random field, (x) normal distribution of values in real space, Prob[(x)] defined entirely by power spectrum in Fourier space bispectrum and (connected) higher-order correlations vanish David Wands

non-Gaussian random field, (x) anything else David Wands

Rocky Kolb non-Rocky Kolb

Primordial Gaussianity from inflation Quantum fluctuations from inflation ground state of simple harmonic oscillator almost free field in almost de Sitter space almost scale-invariant and almost Gaussian Power spectra probe background dynamics (H, , ...) but, many different models, can produce similar power spectra Higher-order correlations can distinguish different models non-Gaussianity  non-linearity  interactions = physics+gravity David Wands Wikipedia: AllenMcC

Many sources of non-Gaussianity Initial vacuum Excited state Sub-Hubble evolution Higher-derivative interactions e.g. k-inflation, DBI, Galileons Hubble-exit Features in potential Super-Hubble evolution Self-interactions + gravity End of inflation Tachyonic instability (p)Reheating Modulated (p)reheating After inflation Curvaton decay Magnetic fields Primary anisotropies Last-scattering Secondary anisotropies ISW/lensing + foregrounds inflation primordial non-Gaussianity David Wands

Many shapes for primordial bispectra local type (Komatsu&Spergel 2001) local in real space max for squeezed triangles: k<<k’,k’’ equilateral type (Creminelli et al 2005) peaks for k1~k2~k3 orthogonal type (Senatore et al 2009) independent of local + equilateral shapes separable basis (Ferguson et al 2008) David Wands

Primordial density perturbations from quantum field fluctuations  = curvature perturbation on uniform-density hypersurface in radiation-dominated era (x,ti ) during inflation field perturbations on initial spatially-flat hypersurface x on large scales, neglect spatial gradients, solve as “separate universes” Starobinsky 85; Salopek & Bond 90; Sasaki & Stewart 96; Lyth & Rodriguez 05; Langlois & Vernizzi...

order by order at Hubble exit e.g., <3> N’’ N’ N’ sub-Hubble field interactions super-Hubble classical evolution Byrnes, Koyama, Sasaki & DW (arXiv:0705.4096)

non-Gaussianity from inflation? single-field slow-roll inflaton during conventional slow-roll inflation adiabatic perturbations =>  constant on large scales => more generally: sub-Hubble interactions e.g. DBI inflation, Galileon fields... super-Hubble evolution non-adiabatic perturbations during multi-field inflation =>   constant see talks this afternoon by Emery & Kidani at/after end of inflation (curvaton, modulated reheating, etc) e.g., curvaton Maldacena 2002 Creminelli & Zaldarriaga 2004 Cheung et al 2008

multi-field inflation revisited light inflaton field + massive isocurvature fields Chen & Wang (2010+12) Tolley & Wyman (2010) Cremonini, Lalak & Turzynski (2011) Baumann & Green (2011) Pi & Shi (2012) Achucarro et al (2010-12); Gao, Langlois & Mizuno (2012) integrate out heavy modes coupled to inflaton, M>>H effective single-field model with reduced sound speed effectively single-field so long as c.f. effective field theory of inflation: Cheung et al (2008) see talk by Gao this afternoon multiple light fields, M<<H  fNLlocal

simplest local form of non-Gaussianity applies to many inflation models including curvaton, modulated reheating, etc   ( ) is local function of single Gaussian random field, (x) where odd factors of 3/5 because (Komatsu & Spergel, 2001, used) 1 (3/5)1 N’’ N’

Local trispectrum has 2 terms at tree-level NL gNL N’ N’ N’ N’ N’’ N’’ N’’’ N’ can distinguish by different momentum dependence Suyama-Yamaguchi consistency relation: NL = (6fNL/5)2 generalised to include loops: < T P > = < B2 > Tasinato, Byrnes, Nurmi & DW (2012) see talk by Tasinato this afternoon David Wands

Newtonian potential a Gaussian random field (x) = G(x) Liguori, Matarrese and Moscardini (2003)

T/T  -/3, so positive fNL  more cold spots in CMB Newtonian potential a local function of Gaussian random field (x) = G(x) + fNL ( G2(x) - <G2> ) fNL=+3000 T/T  -/3, so positive fNL  more cold spots in CMB Liguori, Matarrese and Moscardini (2003)

T/T  -/3, so negative fNL  more hot spots in CMB Newtonian potential a local function of Gaussian random field (x) = G(x) + fNL ( G2(x) - <G2> ) fNL=-3000 T/T  -/3, so negative fNL  more hot spots in CMB Liguori, Matarrese and Moscardini (2003)

Constraints on local non-Gaussianity WMAP CMB constraints using estimators based on matched templates: -10 < fNL < 74 (95% CL) Komatsu et al WMAP7 -5.6 < gNL / 105 < 8.6 Ferguson et al; Smidt et al 2010

(x) = G(x) + fNL ( G2(x) - <G2> ) Newtonian potential a local function of Gaussian random field (x) = G(x) + fNL ( G2(x) - <G2> ) Large-scale modulation of small-scale power split Gaussian field into long (L) and short (s) wavelengths G (X+x) = L(X) + s(x) two-point function on small scales for given L < (x1) (x2) >L = (1+4 fNL L ) < s (x1) s (x2) > +... X1 X2 i.e., inhomogeneous modulation of small-scale power P ( k , X ) -> [ 1 + 4 fNL L(X) ] Ps(k) but fNL <100 so any effect must be small

Inhomogeneous non-Gaussianity? Byrnes, Nurmi, Tasinato & DW (x) = G(x) + fNL ( G2(x) - <G2> ) + gNL G3(x) + ... split Gaussian field into long (L) and short (s) wavelengths G (X+x) = L(X) + s(x) three-point function on small scales for given L < (x1) (x2) (x3) >X = [ fNL +3gNL L (X)] < s (x1) s (x2) s2 (x3) > + ... X1 X2 local modulation of bispectrum could be significant < fNL2 (X) >  fNL2 +10-8 gNL2 e.g., fNL  10 but gNL 106

peak – background split for galaxy bias BBKS’87 Local density of galaxies determined by number of peaks in density field above threshold => leads to galaxy bias: b = g/ m Poisson equation relates primordial density to Newtonian potential  2 = 4 G => L = (3/2) ( aH / k L ) 2 L so local (x)  non-local form for primordial density field (x) from + inhomogeneous modulation of small-scale power  ( X ) = [ 1 + 6 fNL ( aH / k ) 2 L ( X ) ]  s  strongly scale-dependent bias on large scales Dalal et al, arXiv:0710.4560

Constraints on local non-Gaussianity WMAP CMB constraints using estimators based on optimal templates: -10 < fNL < 74 (95% CL) Komatsu et al WMAP7 -5.6 < gNL / 105 < 8.6 Ferguson et al; Smidt et al 2010 LSS constraints from galaxy power spectrum on large scales: -29 < fNL < 70 (95% CL) Slosar et al 2008 [SDSS] 27 < fNL < 117 (95% CL) Xia et al 2010 [NVSS survey of AGNs]

Tantalising evidence of local fNLlocal? Latest SDSS/BOSS data release (Ross et al 2012): Prob(fNL>0)=99.5% without any correction for systematics 65 < fNL < 405 (at 95% CL) no weighting for stellar density Prob(fNL>0)=91% -92 < fNL < 398 allowing for known systematics Prob(fNL>0)=68% -168 < fNL < 364 marginalising over unknown systematics

Beyond fNL? Higher-order statistics trispectrum  gNL (Seery & Lidsey; Byrnes, Sasaki & Wands 2006...) -7.4 < gNL / 105 < 8.2 (Smidt et al 2010) N() gives full probability distribution function (Sasaki, Valiviita & Wands 2007) abundance of most massive clusters (e.g., Hoyle et al 2010; LoVerde & Smith 2011) Scale-dependent fNL(Byrnes, Nurmi, Tasinato & Wands 2009) local function of more than one independent Gaussian field non-linear evolution of field during inflation -2.5 < nfNL < 2.3 (Smidt et al 2010) Planck: |nfNL | < 0.1 for ffNL =50 (Sefusatti et al 2009) Non-Gaussian primordial isocurvature perturbations extend N to isocurvature modes (Kawasaki et al; Langlois, Vernizzi & Wands 2008) limits on isocurvature density perturbations (Hikage et al 2008)

new era of second-order cosmology Existing non-Gaussianity templates based on non-linear primordial perturbations + linear Boltzmann codes (CMBfast, CAMB, etc) Second-order general relativistic Boltzmann codes in preparation Pitrou (2010): CMBquick in Mathematica: fNL ~ 5? Huang & Vernizzi (Paris) Fidler, Pettinari et al (Portsmouth) Lim et al (Cambridge & London) templates for secondary non-Gaussianity (inc. lensing) induced tensor and vector modes from density perturbations testing interactions at recombination e.g., gravitational wave production  h 

outlook ESA Planck satellite next all-sky survey data early 2013… fNL < 5 + future LSS constraints... Euclid satellite: fNL < 3? SKA ??

Non-Gaussian outlook: Great potential for discovery detection of primordial non-Gaussianity would kill textbook single-field slow-roll inflation models requires multiple fields and/or unconventional physics Scope for more theoretical ideas infinite variety of non-Gaussianity new theoretical models require new optimal (and sub-optimal) estimators More data coming Planck (early 2013) + large-scale structure surveys Non-Gaussianity will be detected non-linear physics inevitably generates non-Gaussianity need to disentangle primordial and generated non-Gaussianity