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 Cosmo-12, Beijing 13 th September 2012
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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…
– generalised to include loops: < T P > = < B2 > Tasinato, Byrnes, Nurmi & DW (2012) see talk by Tasinato this afternoon
David Wands 14
N’’ N’’ N’’’
N’ N’ N’ N’
N’
...)(6
1)(
2
1)()(
22 xNxNxNx
Liguori, Matarrese and Moscardini (2003)
Newtonian potential a Gaussian random field (x) = G(x)
Liguori, Matarrese and Moscardini (2003)
fNL=+3000
Newtonian potential a local function of Gaussian random field (x) = G(x) + fNL ( G
2(x) - <G2> )
T/T -/3, so positive fNL more cold spots in CMB
Liguori, Matarrese and Moscardini (2003)
fNL=-3000
Newtonian potential a local function of Gaussian random field (x) = G(x) + fNL ( G
2(x) - <G2> )
T/T -/3, so negative fNL more hot spots in CMB
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
Newtonian potential a local function of Gaussian random field (x) = G(x) + fNL ( G
2(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
3(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) s
2 (x3) > + ...
X1 X2 local modulation of bispectrum could be significant < fNL
2 (X) > fNL2 +10-8 gNL
2 e.g., fNL 10 but gNL 106
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
peak – background split for galaxy bias BBKS’87
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